NPTEL VIDEO LECTURE TOPICS FOR
MATHEMATICS
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Elementary Numerical Analysis Subject Co-ordinator - Prof. Rekha P. Kulkarni Co-ordinating Institute - IIT - Bombay Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction 2 - Polynomial Approximation 3 - Interpolating Polynomials 4 - Properties of Divided Difference 5 - Error in the Interpolating polynomial 6 - Cubic Hermite Interpolation 7 - Piecewise Polynomial Approximation 8 - Cubic Spline Interpolation 9 - Tutorial 1 10 - Numerical Integration 11 - Composite Numerical Integration 12 - Gauss 2-point Rule 13 - Gauss 2-point Rule 14 - Convergence of Gaussian Integration 15 - Tutorial 2 16 - Numerical Differentiation 17 - Gauss Elimination 18 - L U decomposition 19 - Cholesky decomposition 20 - Gauss Elimination with partial pivoting 21 - Vector and Matrix Norms 22 - Perturbed Linear Systems 23 - Ill-conditioned Linear System 24 - Tutorial 3 25 - Effect of Small Pivots 26 - Solution of Non-linear Equations 27 - Quadratic Convergence of Newton's Method 28 - Jacobi Method 29 - Gauss-Seidel Method
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Tutorial 4 Initial Value Problem Multi-step Methods Predictor-Corrector Formulae Boundary Value Problems Eigenvalues and Eigenvectors Spectral Theorem Power Method Inverse Power Method Q R Decomposition Q R Method
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Measure and Integration Subject Co-ordinator - Prof. Inder K Rana Co-ordinating Institute - IIT - Bombay Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction, Extended Real numbers 2 - Algebra and Sigma Algebra of a subset of a set 3 - Sigma Algebra generated by a class 4 - Monotone Class 5 - Set function 6 - The Length function and its properties 7 - Countably additive set functions on intervals 8 - Uniqueness Problem for Measure 9 - Extension of measure 10 - Outer measure and its properties 11 - Measurable sets 12 - Lebesgue measure and its properties 13 - Characterization of Lebesque measurable sets 14 - Measurable functions 15 - Properties of measurable functions 16 - Measurable functions on measure spaces 17 - Integral of non negative simple measurable functions 18 - Properties of non negative simple measurable functions 19 - Monotone convergence theorem & Fatou's Lemma 20 - Properties of Integral functions & Dominated Convergence Theorem 21 - Dominated Convergence Theorem and applications 22 - Lebesgue Integral and its properties 23 - Denseness of continuous function 24 - Product measures, an Introduction 25 - Construction of Product Measure 26 - Computation of Product Measure - I 27 - Computation of Product Measure - II 28 - Integration on Product spaces 29 - Fubini's Theorems
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Lebesgue Measure and integral on R2 Properties of Lebesgue Measure and integral on Rn Lebesgue integral on R2 Integrating complex-valued functions Lp - spaces L2(X,S,mue) Fundamental Theorem of calculas for Lebesgue Integral - I Fundamental Theorem of calculus for Lebesgue Integral - II Absolutely continuous measures Modes of convergence Convergence in Measure
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Mathematics in India - From Vedic Period to Modern Times Subject Co-ordinator - Prof. M.D. Srinivas, Prof. K. Ramasubramanian, Prof. M.S. Sriram Co-ordinating Institute - Centre for Policy Studies, Chennai | IIT - Bombay | University of Madras, Chennai Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Indian Mathematics 2 - Vedas and Sulbasutras - Part 1 3 - Vedas and Sulbasutras - Part 2 4 - Panini's Astadhyayi 5 - Pingala's Chandahsastra 6 - Decimal place value system 7 - Aryabhatiya of Aryabhata - Part 1 8 - Aryabhatiya of Aryabhata - Part 2 9 - Aryabhatiya of Aryabhata - Part 3 10 - Aryabhatiya of Aryabhata - Part 4 and Introduction to Jaina Mathematics 11 - Brahmasphutasiddhanta of Brahmagupta - Part 1 12 - Brahmasphutasiddhanta of Brahmagupta - Part 2 13 - Brahmasphutasiddhanta of Brahmagupta - Part 3 14 - Brahmasphutasiddhanta of Brahmagupta - Part 4 and The Bakhshali Manuscript 15 - Mahaviras Ganitasarasangraha - Part 1 16 - Mahaviras Ganitasarasangraha - Part 2 17 - Mahaviras Ganitasarasangraha - Part 3 18 - Development of Combinatorics - Part 1 19 - Development of Combinatorics - Part 2 20 - Lilavati of Bhaskaracarya - Part 1 21 - Lilavati of Bhaskaracarya - Part 2 22 - Lilavati of Bhaskaracarya - Part 3 23 - Bijaganita of Bhaskaracarya - Part 1 24 - Bijaganita of Bhaskaracarya - Part 2 25 - Ganitakaumudi of Narayana Pandita - Part 1 26 - Ganitakaumudi of Narayana Pandita - Part 2 27 - Ganitakaumudi of Narayana Pandita - Part 3 28 - Magic Squares - Part 1 29 - Magic Squares - Part 2
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Development of Calculus in India - Part Development of Calculus in India - Part Jyanayanam Trigonometry and Spherical Trigonometry Trigonometry and Spherical Trigonometry Trigonometry and Spherical Trigonometry Proofs in Indian Mathematics - Part 1 Proofs in Indian Mathematics - Part 2 Proofs in Indian Mathematics - Part 3 Mathematics in Modern India - Part 1 Mathematics in Modern India - Part 2
1 2 - Part 1 - Part 2 - Part 3
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Stochastic Processes Subject Co-ordinator - Dr. S. Dharmaraja Co-ordinating Institute - IIT - Delhi Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction to Stochastic Processes 2 - Introduction to Stochastic Processes (Continued.) 3 - Problems in Random Variables and Distributions 4 - Problems in Sequences of Random Variables 5 - Definition, Classification and Examples 6 - Simple Stochastic Processes 7 - Stationary Processes 8 - Autoregressive Processes 9 - Introduction, Definition and Transition Probability Matrix 10 - Chapman-Kolmogrov Equations 11 - Classification of States and Limiting Distributions 12 - Limiting and Stationary Distributions 13 - Limiting Distributions, Ergodicity and Stationary Distributions 14 - Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing Models 15 - Reducible Markov Chains 16 - Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix 17 - Limiting and Stationary Distributions, Birth Death Processes 18 - Poisson Processes 19 - M/M/1 Queueing Model 20 - Simple Markovian Queueing Models 21 - Queueing Networks 22 - Communication Systems 23 - Stochastic Petri Nets 24 - Conditional Expectation and Filtration 25 - Definition and Simple Examples 26 - Definition and Properties 27 - Processes Derived from Brownian Motion 28 - Stochastic Differential Equations 29 - Ito Integrals
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Ito Formula and its Variants Some Important SDE`s and Their Solutions Renewal Function and Renewal Equation Generalized Renewal Processes and Renewal Limit Theorems Markov Renewal and Markov Regenerative Processes Non Markovian Queues Non Markovian Queues Cont,, Application of Markov Regenerative Processes Galton-Watson Process Markovian Branching Process
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Formal Languages and Automata Theory Subject Co-ordinator - Dr. K.V. Krishna, Dr. Diganta Goswami Co-ordinating Institute - IIT - Guwahati Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction 2 - Alphabet, Strings, Languages 3 - Finite Representation 4 - Grammars (CFG) 5 - Derivation Trees 6 - Regular Grammars 7 - Finite Automata 8 - Nondeterministic Finite Automata 9 - NFA <=> DFA 10 - Myhill-Nerode Theorem 11 - Minimization 12 - RE => FA 13 - FA => RE 14 - FA <=> RG 15 - Variants of FA 16 - Closure Properties of RL 17 - Homomorphism 18 - Pumping Lemma 19 - Simplification of CFG 20 - Normal Forms of CFG 21 - Properties of CFLs 22 - Pushdown Automata 23 - PDA <=> CFG 24 - Turing Machines 25 - Turing Computable Functions 26 - Combining Turing Machines 27 - Multi Input 28 - Turing Decidable Languages 29 - Varients of Turing Machines
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Structured Grammars Decidability Undecidability 1 Undecidability 2 Undecidability 3 Time Bounded Turing Machines P and NP NP-Completeness NP-Complete Problems 1 NP-Complete Problems 2 NP-Complete Problems 3 Chomsky Hierarchy
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Complex Analysis Subject Co-ordinator - Prof. P.A.S. Sree Krishna Co-ordinating Institute - IIT - Guwahati Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction 2 - Introduction to Complex Numbers 3 - de Moivreâ s Formula and Stereographic Projection 4 - Topology of the Complex Plane - Part-I 5 - Topology of the Complex Plane - Part-II 6 - Topology of the Complex Plane - Part-III 7 - Introduction to Complex Functions 8 - Limits and Continuity 9 - Differentiation 10 - Cauchy-Riemann Equations and Differentiability 11 - Analytic functions; the exponential function 12 - Sine, Cosine and Harmonic functions 13 - Branches of Multifunctions; Hyperbolic Functions 14 - Problem Solving Session I 15 - Integration and Contours 16 - Contour Integration 17 - Introduction to Cauchyâ s Theorem 18 - Cauchyâ s Theorem for a Rectangle 19 - Cauchyâ s theorem - Part-II 20 - Cauchyâ s Theorem - Part-III 21 - Cauchyâ s Integral Formula and its Consequences 22 - The First and Second Derivatives of Analytic Functions 23 - Moreraâ s Theorem and Higher Order Derivatives of Analytic Functions 24 - Problem Solving Session II 25 - Introduction to Complex Power Series 26 - Analyticity of Power Series 27 - Taylorâ s Theorem 28 - Zeroes of Analytic Functions 29 - Counting the Zeroes of Analytic Functions
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Open mapping theorem - Part-I Open mapping theorem - Part-II Properties of Mobius Transformations - Part-I Properties of Mobius Transformations - Part-II Problem Solving Session III Removable Singularities Poles Classification of Isolated Singularities Essential Singularity & Introduction to Laurent Series Laurentâ s Theorem Residue Theorem and Applications Problem Solving Session IV
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Applied Multivariate Analysis Subject Co-ordinator - Dr. Sharmishtha Mitra Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Prologue 2 - Basic concepts on multivariate distribution 3 - Basic concepts on multivariate distribution 4 - Multivariate normal distribution â I 5 - Multivariate normal distribution â II 6 - Multivariate normal distribution â III 7 - Some problems on multivariate distributions â I 8 - Some problems on multivariate distributions â II 9 - Random sampling from multivariate normal distribution and Wishart distribution - I 10 - Random sampling from multivariate normal distribution and Wishart distribution - II 11 - Random sampling from multivariate normal distribution and Wishart distribution - III 12 - Wishart distribution and itâ s properties - I 13 - Wishart distribution and itâ s properties - II 14 - Hotellingâ s T2 distribution and itâ s applications 15 - Hotellingâ s T2 distribution and various confidence intervals and regions 16 - Hotellingâ s T2 distribution and Profile analysis 17 - Profile analysis - I 18 - Profile analysis - II 19 - MANOVA - I 20 - MANOVA - II 21 - MANOVA - III 22 - MANOVA & Multiple Correlation Coefficient 23 - Multiple Correlation Coefficient 24 - Principal Component Analysis 25 - Principal Component Analysis 26 - Principal Component Analysis 27 - Cluster Analysis 28 - Cluster Analysis 29 - Cluster Analysis
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Cluster Analysis Discriminant Analysis and Classification Discriminant Analysis and Classification Discriminant Analysis and Classification Discriminant Analysis and Classification Discriminant Analysis and Classification Discriminant Analysis and Classification Discriminant Analysis and Classification Factor_Analysis Factor_Analysis Factor_Analysis Cannonical Correlation Analysis Cannonical Correlation Analysis Cannonical Correlation Analysis Cannonical Correlation Analysis
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Calculus of Variations and Integral Equations Subject Co-ordinator - Dr. Malay Banerjee, Prof. D. Bahuguna Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Calculus of Variations and Integral Equations 2 - Calculus of Variations and Integral Equations 3 - Calculus of Variations and Integral Equations 4 - Calculus of Variations and Integral Equations 5 - Calculus of Variations and Integral Equations 6 - Calculus of Variations and Integral Equations 7 - Calculus of Variations and Integral Equations 8 - Calculus of Variations and Integral Equations 9 - Calculus of Variations and Integral Equations 10 - Calculus of Variations and Integral Equations 11 - Calculus of Variations and Integral Equations 12 - Calculus of Variations and Integral Equations 13 - Calculus of Variations and Integral Equations 14 - Calculus of Variations and Integral Equations 15 - Calculus of Variations and Integral Equations 16 - Calculus of Variations and Integral Equations 17 - Calculus of Variations and Integral Equations 18 - Calculus of Variations and Integral Equations 19 - Calculus of Variations and Integral Equations 20 - Calculus of Variations and Integral Equations 21 - Calculus of Variations and Integral Equations 22 - Calculus of Variations and Integral Equations 23 - Calculus of Variations and Integral Equations 24 - Calculus of Variations and Integral Equations 25 - Calculus of Variations and Integral Equations 26 - Calculus of Variations and Integral Equations 27 - Calculus of Variations and Integral Equations 28 - Calculus of Variations and Integral Equations 29 - Calculus of Variations and Integral Equations
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Calculus Calculus Calculus Calculus Calculus Calculus Calculus Calculus Calculus Calculus Calculus
of of of of of of of of of of of
Variations Variations Variations Variations Variations Variations Variations Variations Variations Variations Variations
and and and and and and and and and and and
Integral Integral Integral Integral Integral Integral Integral Integral Integral Integral Integral
Equations Equations Equations Equations Equations Equations Equations Equations Equations Equations Equations
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Linear programming and Extensions Subject Co-ordinator - Prof. Prabha Sharma Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction to Linear Programming Problems 2 - Vector space, Linear independence and dependence, basis 3 - Moving from one basic feasible solution to another, optimality criteria 4 - Basic feasible solutions, existence & derivation 5 - Convex sets, dimension of a polyhedron, Faces, Example of a polytope 6 - Direction of a polyhedron, correspondence between bfs and extreme points 7 - Representation theorem, LPP solution is a bfs, Assignment 1 8 - Development of the Simplex Algorithm, Unboundedness, Simplex Tableau 9 - Simplex Tableau & algorithm ,Cycling, Blandâ s anti-cycling rules, Phase I & Phase II 10 - Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfs 11 - Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPP 12 - LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theorem 13 - Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of duality 14 - Examples of writing the dual, complementary slackness theorem 15 - Complementary slackness conditions, Dual Simplex algorithm, Assignment 3 16 - Primal-dual algorithm 17 - Problem in lecture 16, starting dual feasible solution, Shortest Path Problem 18 - Shortest Path Problem, Primal-dual method, example 19 - Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-cha 20 - Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , 21 - Parametric LPP-Right hand side vector 22 - Parametric cost vector LPP 23 - Parametric cost vector LPP, Introduction to Min-cost flow problem 24 - Mini-cost flow problem-Transportation problem 25 - Transportation problem degeneracy, cycling 26 - Sensitivity analysis 27 - Sensitivity analysis 28 - Bounded variable transportation problem, min-cost flow problem 29 - Min-cost flow problem
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solut Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative c Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysis Min-cost flow changes in arc capacities , Max-flow problem, assignment 7 Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithm Max-flow - Critical capacity of an arc, starting solution for min-cost flow problem Improved Max-flow algorithm Critical Path Method (CPM) Programme Evaluation and Review Technique (PERT) Simplex Algorithm is not polynomial time- An example Interior Point Methods
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Convex Optimization Subject Co-ordinator - Dr. Joydeep Dutta Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Convex Optimization 2 - Convex Optimization 3 - Convex Optimization 4 - Convex Optimization 5 - Convex Optimization 6 - Convex Optimization 7 - Convex Optimization 8 - Convex Optimization 9 - Convex Optimization 10 - Convex Optimization 11 - Convex Optimization 12 - Convex Optimization 13 - Convex Optimization 14 - Convex Optimization 15 - Convex Optimization 16 - Convex Optimization 17 - Convex Optimization 18 - Convex Optimization 19 - Convex Optimization 20 - Convex Optimization 21 - Convex Optimization 22 - Convex Optimization 23 - Convex Optimization 24 - Convex Optimization 25 - Convex Optimization 26 - Convex Optimization 27 - Convex Optimization 28 - Convex Optimization 29 - Convex Optimization
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Convex Convex Convex Convex Convex Convex Convex Convex Convex Convex Convex Convex Convex
Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Foundations of Optimization Subject Co-ordinator - Dr. Joydeep Dutta Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Optimization 2 - Optimization 3 - Optimization 4 - Optimization 5 - Optimization 6 - Optimization 7 - Optimization 8 - Optimization 9 - Optimization 10 - Optimization 11 - Optimization 12 - Optimization 13 - Optimization 14 - Optimization 15 - Optimization 16 - Optimization 17 - Optimization 18 - Optimization 19 - Optimization 20 - Optimization 21 - Optimization 22 - Optimization 23 - Optimization 24 - Optimization 25 - Optimization 26 - Optimization 27 - Optimization 28 - Optimization 29 - Optimization
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization Optimization
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Probability Theory and Applications Subject Co-ordinator - Prof. Prabha Sharma Co-ordinating Institute - IIT - Kanpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Basic principles of counting 2 - Sample space, events, axioms of probability 3 - Conditional probability, Independence of events 4 - Random variables, cumulative density function, expected value 5 - Discrete random variables and their distributions 6 - Discrete random variables and their distributions 7 - Discrete random variables and their distributions 8 - Continuous random variables and their distributions 9 - Continuous random variables and their distributions 10 - Continuous random variables and their distributions 11 - Function of random variables, Momement generating function 12 - Jointly distributed random variables, Independent r. v. and their sums 13 - Independent r. v. and their sums 14 - Chi â square r. v., sums of independent normal r. v., Conditional distr 15 - Conditional disti, Joint distr. of functions of r. v., Order statistics 16 - Order statistics, Covariance and correlation 17 - Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectation 18 - Conditional expectation, Best linear predictor 19 - Inequalities and bounds 20 - Convergence and limit theorems 21 - Central limit theorem 22 - Applications of central limit theorem 23 - Strong law of large numbers, Joint mgf 24 - Convolutions 25 - Stochastic processes 26 - Transition and state probabilities 27 - State prob., First passage and First return prob 28 - First passage and First return prob. Classification of states 29 - Random walk, periodic and null states
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Reducible Markov chains Time reversible Markov chains Poisson Processes Inter-arrival times, Properties of Poisson processes Queuing Models Analysis of L, Lq ,W and Wq , M/M/S model M/M/S , M/M/I/K models M/M/I/K and M/M/S/K models Application to reliability theory failure law Exponential failure law, Weibull law Reliability of systems
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Advanced Engineering Mathematics Subject Co-ordinator - Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Review Groups, Fields and Matrices 2 - Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors 3 - Basis, Dimension, Rank and Matrix Inverse 4 - Linear Transformation, Isomorphism and Matrix Representation 5 - System of Linear Equations, Eigenvalues and Eigenvectors 6 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices 7 - Jordan Canonical Form, Cayley Hamilton Theorem 8 - Inner Product Spaces, Cauchy-Schwarz Inequality 9 - Orthogonality, Gram-Schmidt Orthogonalization Process 10 - Spectrum of special matrices,positive/negative definite matrices 11 - Concept of Domain, Limit, Continuity and Differentiability 12 - Analytic Functions, C-R Equations 13 - Harmonic Functions 14 - Line Integral in the Complex 15 - Cauchy Integral Theorem 16 - Cauchy Integral Theorem (Continued.) 17 - Cauchy Integral Formula 18 - Power and Taylor's Series of Complex Numbers 19 - Power and Taylor's Series of Complex Numbers (Continued.) 20 - Taylor's, Laurent Series of f(z) and Singularities 21 - Classification of Singularities, Residue and Residue Theorem 22 - Laplace Transform and its Existence 23 - Properties of Laplace Transform 24 - Evaluation of Laplace and Inverse Laplace Transform 25 - Applications of Laplace Transform to Integral Equations and ODEs 26 - Applications of Laplace Transform to PDEs 27 - Fourier Series 28 - Fourier Series (Continued.) 29 - Fourier Integral Representation of a Function
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Introduction to Fourier Transform Applications of Fourier Transform to PDEs Laws of Probability - I Laws of Probability - II Problems in Probability Random Variables Special Discrete Distributions Special Continuous Distributions Joint Distributions and Sampling Distributions Point Estimation Interval Estimation Basic Concepts of Testing of Hypothesis Tests for Normal Populations
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Functional Analysis Subject Co-ordinator - Prof. P.D. Srivastava Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Metric Spaces with Examples 2 - Holder Inequality and Minkowski Inequality 3 - Various Concepts in a Metric Space 4 - Separable Metrics Spaces with Examples 5 - Convergence, Cauchy Sequence, Completeness 6 - Examples of Complete and Incomplete Metric Spaces 7 - Completion of Metric Spaces + Tutorial 8 - Vector Spaces with Examples 9 - Normed Spaces with Examples 10 - Banach Spaces and Schauder Basic 11 - Finite Dimensional Normed Spaces and Subspaces 12 - Compactness of Metric/Normed Spaces 13 - Linear Operators-definition and Examples 14 - Bounded Linear Operators in a Normed Space 15 - Bounded Linear Functionals in a Normed Space 16 - Concept of Algebraic Dual and Reflexive Space 17 - Dual Basis & Algebraic Reflexive Space 18 - Dual Spaces with Examples 19 - Tutorial - I 20 - Tutorial - II 21 - Inner Product & Hilbert Space 22 - Further Properties of Inner Product Spaces 23 - Projection Theorem, Orthonormal Sets and Sequences 24 - Representation of Functionals on a Hilbert Spaces 25 - Hilbert Adjoint Operator 26 - Self Adjoint, Unitary & Normal Operators 27 - Tutorial - III 28 - Annihilator in an IPS 29 - Total Orthonormal Sets And Sequences
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Partially Ordered Set and Zorns Lemma Hahn Banach Theorem for Real Vector Spaces Hahn Banach Theorem for Complex V.S. & Normed Spaces Baires Category & Uniform Boundedness Theorems Open Mapping Theorem Closed Graph Theorem Adjoint Operator Strong and Weak Convergence Convergence of Sequence of Operators and Functionals LP - Space LP - Space (Continued.)
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Numerical methods of Ordinary and Partial Differential Equations Subject Co-ordinator - Dr. G.P. Raja Sekhar Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Motivation with few Examples 2 - Single - Step Methods for IVPs 3 - Analysis of Single Step Methods 4 - Runge - Kutta Methods for IVPs 5 - Higher Order Methods/Equations 6 - Error - Stability - Convergence of Single Step Methods 7 - Tutorial - I 8 - Tutorial - II 9 - Multi-Step Methods (Explicit) 10 - Multi-Step Methods (Implicit) 11 - Convergence and Stability of multi step methods 12 - General methods for absolute stability 13 - Stability Analysis of Multi Step Methods 14 - Predictor - Corrector Methods 15 - Some Comments on Multi - Step Methods 16 - Finite Difference Methods - Linear BVPs 17 - Linear/Non - Linear Second Order BVPs 18 - BVPS - Derivative Boundary Conditions 19 - Higher Order BVPs 20 - Shooting Method BVPs 21 - Tutorial - III 22 - Introduction to First Order PDE 23 - Introduction to Second Order PDE 24 - Finite Difference Approximations to Parabolic PDEs 25 - Implicit Methods for Parabolic PDEs 26 - Consistency, Stability and Convergence 27 - Other Numerical Methods for Parabolic PDEs 28 - Tutorial - IV 29 - Matrix Stability Analysis of Finite Difference Scheme
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Fourier Series Stability Analysis of Finite Difference Scheme Finite Difference Approximations to Elliptic PDEs - I Finite Difference Approximations to Elliptic PDEs - II Finite Difference Approximations to Elliptic PDEs - III Finite Difference Approximations to Elliptic PDEs - IV Finite Difference Approximations to Hyperbolic PDEs - I Finite Difference Approximations to Hyperbolic PDEs - II Method of characteristics for Hyperbolic PDEs - I Method of characterisitcs for Hyperbolic PDEs - II Finite Difference Approximations to 1st order Hyperbolic PDEs Summary, Appendices, Remarks
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Optimization Subject Co-ordinator - Prof. A. Goswami, Dr. Debjani Chakraborty Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Optimization - Introduction 2 - Formulation of LPP 3 - Geometry of LPP and Graphical Solution of LPP 4 - Solution of LPP 5 - Big - M Method 6 - Two - Phase Method 7 - Special Cases in Simple Applications 8 - Introduction to Duality Theory 9 - Dual Simplex Method 10 - Post Optimaility Analysis 11 - Integer Programming - I 12 - Integer Programming - II 13 - Introduction to Transportation Problems 14 - Solving Various types of Transportation Problems 15 - Assignment Problems 16 - Project Management 17 - Critical Path Analysis 18 - PERT 19 - Shortest Path Algorithm 20 - Travelling Salesman Problem 21 - Classical optimization techniques 22 - Unconstarined multivariable optimization 23 - Nonlinear programming with equality constraint 24 - Nonlinear programming KKT conditions 25 - Numerical optimization 26 - Numerical optimization 27 - Fibonacci Method 28 - Golden Section Methods 29 - Interpolation Methods
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36 37 38 39 40
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Unconstarined optimization techniques Unconstarined optimization techniques Nonlinear programming Interior and Exterior penulty Function Method Separable Programming Problem Introduction to Geometric Programming Constrained Geometric Programming Problem Dynamic Programming Problem Dynamic Programming Problem (Continued.) Multi Objective Decision Making Multi attribute decision making
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Probability and Statistics Subject Co-ordinator - Prof. Somesh Kumar Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Algebra of Sets - I 2 - Algebra of Sets - II 3 - Introduction to Probability 4 - Laws of Probability - I 5 - Laws of Probability - II 6 - Problems in Probability 7 - Random Variables 8 - Probability Distributions 9 - Characteristics of Distribution 10 - Special Distributions - I 11 - Special Distributions - II 12 - Special Distributions - III 13 - Special Distributions - IV 14 - Special Distributions - V 15 - Special Distributions - VI 16 - Special Distributions - VII 17 - Functions of a Random Variable 18 - Joint Distributions - I 19 - Joint Distributions - II 20 - Joint Distributions - III 21 - Joint Distributions - IV 22 - Transformations of Random Vectors 23 - Sampling Distributions - I 24 - Sampling Distributions - II 25 - Descriptive Statistics - I 26 - Descriptive Statistics - II 27 - Estimation - I 28 - Estimation - II 29 - Estimation - III
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Estimation Estimation Estimation Testing of Testing of Testing of Testing of Testing of Testing of Testing of Testing of
- IV - V - VI Hypothesis Hypothesis Hypothesis Hypothesis Hypothesis Hypothesis Hypothesis Hypothesis
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I II III IV V VI VII VIII
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Regression Analysis Subject Co-ordinator - Dr. Soumen Maity Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Simple Linear Regression 2 - Simple Linear Regression (Continued...1) 3 - Simple Linear Regression (Continued...2) 4 - Simple Linear Regression (Continued...3) 5 - Simple Linear Regression (Continued...4) 6 - Multiple Linear Regression 7 - Multiple Linear Regression (Continued...1) 8 - Multiple Linear Regression (Continued...2) 9 - Multiple Linear Regression (Continued...3) 10 - Selecting the BEST Regression model 11 - Selecting the BEST Regression model (Continued...1) 12 - Selecting the BEST Regression model (Continued...2) 13 - Selecting the BEST Regression model (Continued...3) 14 - Multicollinearity 15 - Multicollinearity (Continued...1) 16 - Multicollinearity (Continued...2) 17 - Model Adequacy Checking 18 - Model Adequacy Checking (Continued...1) 19 - Model Adequacy Checking (Continued...2) 20 - Test for Influential Observations 21 - Transformations and Weighting to correct model inadequacies 22 - Transformations and Weighting to correct model inadequacies (Continued...1) 23 - Transformations and Weighting to correct model inadequacies (Continued...2) 24 - Dummy Variables 25 - Dummy Variables (Continued...1) 26 - Dummy Variables (Continued...2) 27 - Polynomial Regression Models 28 - Polynomial Regression Models (Continued...1) 29 - Polynomial Regression Models (Continued...2)
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36 37 38 39 40
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Generalized Linear Models Generalized Linear Models (Continued.) Non-Linear Estimation Regression Models with Autocorrelated Errors Regression Models with Autocorrelated Errors (Continued.) Measurement Errors & Calibration Problem Tutorial - I Tutorial - II Tutorial - III Tutorial - IV Tutorial - V
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Statistical Inference Subject Co-ordinator - Prof. Somesh Kumar Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction and Motivation 2 - Basic Concepts of Point Estimations - I 3 - Basic Concepts of Point Estimations - II 4 - Finding Estimators - I 5 - Finding Estimators - II 6 - Finding Estimators - III 7 - Properties of MLEs 8 - Lower Bounds for Variance - I 9 - Lower Bounds for Variance - II 10 - Lower Bounds for Variance - III 11 - Lower Bounds for Variance - IV 12 - Sufficiency 13 - Sufficiency and Information 14 - Minimal Sufficiency, Completeness 15 - UMVU Estimation, Ancillarity 16 - Invariance - I 17 - Invariance - II 18 - Bayes and Minimax Estimation - I 19 - Bayes and Minimax Estimation - II 20 - Bayes and Minimax Estimation - III 21 - Testing of Hypotheses 22 - Neyman Pearson Fundamental Lemma 23 - Applications of NP lemma 24 - UMP Tests 25 - UMP Tests (Continued.) 26 - UMP Unbiased Tests 27 - UMP Unbiased Tests (Continued.) 28 - UMP Unbiased Tests 29 - Unbiased Tests for Normal Populations
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Unbiased Tests for Normal Populations (Continued.) Likelihood Ratio Tests - I Likelihood Ratio Tests - II Likelihood Ratio Tests - III Likelihood Ratio Tests - IV Invariant Tests Test for Goodness of Fit Sequential Procedure Sequential Procedure (Continued.) Confidence Intervals Confidence Intervals (Continued.)
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - A Basic Course in Real Analysis Subject Co-ordinator - Prof. P.D. Srivastava Co-ordinating Institute - IIT - Kharagpur Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Rational Numbers and Rational Cuts 2 - Irrational numbers, Dedekind's Theorem 3 - Continuum and Exercises 4 - Continuum and Exercises (Continued.) 5 - Cantor's Theory of Irrational Numbers 6 - Cantor's Theory of Irrational Numbers (Continued.) 7 - Equivalence of Dedekind and Cantor's Theory 8 - Finite, Infinite, Countable and Uncountable Sets of Real Numbers 9 - Types of Sets with Examples, Metric Space 10 - Various properties of open set, closure of a set 11 - Ordered set, Least upper bound, greatest lower bound of a set 12 - Compact Sets and its properties 13 - Weiersstrass Theorem, Heine Borel Theorem, Connected set 14 - Tutorial - II 15 - Concept of limit of a sequence 16 - Some Important limits, Ratio tests for sequences of Real Numbers 17 - Cauchy theorems on limit of sequences with examples 18 - Fundamental theorems on limits, Bolzano-Weiersstrass Theorem 19 - Theorems on Convergent and divergent sequences 20 - Cauchy sequence and its properties 21 - Infinite series of real numbers 22 - Comparison tests for series, Absolutely convergent and Conditional convergent series 23 - Tests for absolutely convergent series 24 - Raabe's test, limit of functions, Cluster point 25 - Some results on limit of functions 26 - Limit Theorems for functions 27 - Extension of limit concept (one sided limits) 28 - Continuity of Functions 29 - Properties of Continuous Functions
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Boundedness Theorem, Max-Min Theorem and Bolzano's theorem Uniform Continuity and Absolute Continuity Types of Discontinuities, Continuity and Compactness Continuity and Compactness (Continued.), Connectedness Differentiability of real valued function, Mean Value Theorem Mean Value Theorem (Continued.) Application of MVT , Darboux Theorem, L Hospital Rule L'Hospital Rule and Taylor's Theorem Tutorial - III Riemann/Riemann Stieltjes Integral Existence of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral Properties of Reimann Stieltjes Integral (Continued.) Definite and Indefinite Integral Fundamental Theorems of Integral Calculus Improper Integrals Convergence Test for Improper Integrals
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves Subject Co-ordinator - Dr. T.E. Venkata Balaji Co-ordinating Institute - IIT - Madras Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - The Idea of a Riemann Surface 2 - Simple Examples of Riemann Surfaces 3 - Maximal Atlases and Holomorphic Maps of Riemann Surfaces 4 - A Riemann Surface Structure on a Cylinder 5 - A Riemann Surface Structure on a Torus 6 - Riemann Surface Structures on Cylinders and Tori via Covering Spaces 7 - Moebius Transformations Make up Fundamental Groups of Riemann Surfaces 8 - Homotopy and the First Fundamental Group 9 - A First Classification of Riemann Surfaces 10 - The Importance of the Path-lifting Property 11 - Fundamental groups as Fibres of the Universal covering Space 12 - The Monodromy Action 13 - The Universal covering as a Hausdorff Topological Space 14 - The Construction of the Universal Covering Map 15 - Completion of the Construction of the Universal Covering 16 - Completion of the Construction of the Universal Covering 17 - The Riemann Surface Structure on the Topological Covering of a Riemann Surface 18 - Riemann Surfaces with Universal Covering the Plane or the Sphere 19 - Classifying Complex Cylinders 20 - Characterizing Moebius Transformations with a Single Fixed Point 21 - Characterizing Moebius Transformations with Two Fixed Points 22 - Torsion-freeness of the Fundamental Group of a Riemann Surface 23 - Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental Groups 24 - Classifying Annuli up to Holomorphic Isomorphism 25 - Orbits of the Integral Unimodular Group in the Upper Half-Plane 26 - Galois Coverings are precisely Quotients by Properly Discontinuous Free Actions 27 - Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture
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Lecture 33 Lecture 34 Lecture 35 Lecture Lecture Lecture Lecture
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Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Quotients by Kleinian Subgroups give rise to Riemann Surfaces The Unimodular Group is Kleinian The Necessity of Elliptic Functions for the Classification of Complex Tori The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the Plane The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-function The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-Plane The Construction of a Modular Form of Weight Two on the Upper Half-Plane The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-Plane The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-plane The Weight Two Modular Form Vanishes at Infinity The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-Plane The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant The Fundamental Region in the Upper Half-Plane for the Unimodular Group A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once Moduli of Elliptic Curves Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two Complex Tori are the same as Elliptic Algebraic Projective Curves
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Linear Algebra Subject Co-ordinator - Dr. K.C. Sivakumar Co-ordinating Institute - IIT - Madras Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction to the Course Contents 2 - Linear Equations 3a - Equivalent Systems of Linear Equations I 3b - Equivalent Systems of Linear Equations II 4 - Row-reduced Echelon Matrices 5 - Row-reduced Echelon Matrices and Non-homogeneous Equations 6 - Elementary Matrices, Homogeneous Equations and Non-homogeneous Equations 7 - Invertible matrices, Homogeneous Equations Non-homogeneous Equations 8 - Vector spaces 9 - Elementary Properties in Vector Spaces. Subspaces 10 - Subspaces (Continued...), Spanning Sets, Linear Independence, Dependence 11 - Basis for a vector space 12 - Dimension of a vector space 13 - Dimensions of Sums of Subspaces 14 - Linear Transformations 15 - The Null Space and the Range Space of a Linear Transformation 16 - The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector Spaces 17 - Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank - I 18 - Equality of the Row-rank and the Column-rank - II 19 - The Matrix of a Linear Transformation 20 - Matrix for the Composition and the Inverse. Similarity Transformation 21 - Linear Functionals. The Dual Space. Dual Basis - I 22 - Dual Basis II. Subspace Annihilators - I 23 - Subspace Annihilators - II 24 - The Double Dual. The Double Annihilator 25 - The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its Transpose 26 - Eigenvalues and Eigenvectors of Linear Operators 27 - Diagonalization of Linear Operators. A Characterization 28 - The Minimal Polynomial
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51
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The Cayley-Hamilton Theorem Invariant Subspaces Triangulability, Diagonalization in Terms of the Minimal Polynomial Independent Subspaces and Projection Operators Direct Sum Decompositions and Projection Operators - I Direct Sum Decompositions and Projection Operators - II The Primary Decomposition Theorem and Jordan Decomposition Cyclic Subspaces and Annihilators The Cyclic Decomposition Theorem - I The Cyclic Decomposition Theorem - II. The Rational Form Inner Product Spaces Norms on Vector spaces. The Gram-Schmidt Procedure I The Gram-Schmidt Procedure II. The QR Decomposition Bessel's Inequality, Parseval's Indentity, Best Approximation Best Approximation Orthogonal Complementary Subspaces, Orthogonal Projections Projection Theorem. Linear Functionals The Adjoint Operator Properties of the Adjoint Operation. Inner Product Space Isomorphism Unitary Operators Unitary operators - II. Self-Adjoint Operators - I. Self-Adjoint Operators - II - Spectral Theorem Normal Operators - Spectral Theorem
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Mathematical Logic Subject Co-ordinator - Prof. Arindama Singh Co-ordinating Institute - IIT - Madras Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Sets and Strings 2 - Syntax of Propositional Logic 3 - Unique Parsing 4 - Semantics of PL 5 - Consequences and Equivalences 6 - Five results about PL 7 - Calculations and Informal Proofs 8 - More Informal Proofs 9 - Normal forms 10 - SAT and 3SAT 11 - Horn-SAT and Resolution 12 - Resolution 13 - Adequacy of Resolution 14 - Adequacy and Resolution Strategies 15 - Propositional Calculus (PC) 16 - Some Results about PC 17 - Arguing with Proofs 18 - Adequacy of PC 19 - Compactness & Analytic Tableau 20 - Examples of Tableau Proofs 21 - Adequacy of Tableaux 22 - Syntax of First order Logic (FL) 23 - Symbolization & Scope of Quantifiers 24 - Hurdles in giving Meaning 25 - Semantics of FL 26 - Relevance Lemma 27 - Validity, Satisfiability & Equivalence 28 - Six Results about FL 29 - Laws, Calculation & Informal Proof
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36 37 38 39 40 41 42
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Quantifier Laws and Consequences More Proofs and Prenex Form Prenex Form Conversion Skolem Form Syntatic Interpretation Herbrand's Theorem Most General Unifiers Resolution Rules Resolution Examples Ariomatic System FC FC and Semidecidability of FL Analytic Tableau for FL Godels Incompleteness Theorems
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Real Analysis Subject Co-ordinator - Prof. S.H. Kulkarni Co-ordinating Institute - IIT - Madras Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction 2 - Functions and Relations 3 - Finite and Infinite Sets 4 - Countable Sets 5 - Uncountable Sets, Cardinal Number 6 - Real Number System 7 - LUB Axiom 8 - Sequences of Real Numbers 9 - Sequences of Real Numbers - (Continued.) 10 - Sequences of Real Numbers - (Continued.) 11 - Infinite Series of Real Numbers 12 - Series of nonnegative Real Numbers 13 - Conditional Convergence 14 - Metric Spaces 15 - Metric Spaces 16 - Balls and Spheres 17 - Open Sets 18 - Closure Points, Limit Points and isolated Points 19 - Closed sets 20 - Sequences in Metric Spaces 21 - Completeness 22 - Baire Category Theorem 23 - Limit and Continuity of a Function defined on a Metric space 24 - Continuous Functions on a Metric Space 25 - Uniform Continuity 26 - Connectedness 27 - Connected Sets 28 - Compactness 29 - Compactness (Continued.)
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52
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Characterizations of Compact Sets Continuous Functions on Compact Sets Types of Discontinuity Differentiation Mean Value Theorems Mean Value Theorems (Continued.) Taylor's Theorem Differentiation of Vector Valued Functions Integration Integrability Integrable Functions Integrable Functions (Continued.) Integration as a Limit of Sum Integration and Differentiation Integration of Vector Valued Functions More Theorems on Integrals Sequences and Series of Functions Uniform Convergence Uniform Convergence and Integration Uniform Convergence and Differentiation Construction of Everywhere Continuous Nowhere Differentiable Function Approximation of a Continuous Function by Polynomials Equicontinuous family of Functions
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - NOC:An Invitation to Mathematics Subject Co-ordinator - Prof. Sankaran Vishwanath Co-ordinating Institute - Institute of Mathematical Sciences Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction 2 - Long division 3 - Applications of Long division 4 - Lagrange interpolation 5 - The 0-1 idea in other contexts - dot and cross product 6 - Taylors formula 7 - The Chebyshev polynomials 8 - Counting number of monomials - several variables 9 - Permutations, combinations and the binomial theorem 10 - Combinations with repetition, and counting monomials 11 - Combinations with restrictions, recurrence relations 12 - Fibonacci numbers; an identity and a bijective proof 13 - Permutations and cycle type 14 - The sign of a permutation, composition of permutations 15 - Rules for drawing tangle diagrams 16 - Signs and cycle decompositions 17 - Sorting lists of numbers, and crossings in tangle diagrams 18 - Real and integer valued polynomials 19 - Integer valued polynomials revisited 20 - Functions on the real line, continuity 21 - The intermediate value property 22 - Visualizing functions 23 - Functions on the plane, Rigid motions 24 - More examples of functions on the plane, dilations 25 - Composition of functions 26 - Affine and Linear transformations 27 - Length and Area dilation, the derivative 28 - Examples-I 29 - Examples-II
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36
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Linear equations, Lagrange interpolation revisited Completed Matrices in combinatorics Polynomials acting on matrices Divisibility, prime numbers Congruences, Modular arithmetic The Chinese remainder theorem The Euclidean algorithm, the 0-1 idea and the Chinese remainder theorem
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Advanced Complex Analysis Subject Co-ordinator - Dr. T.E. Venkata Balaji Co-ordinating Institute - IIT - Madras Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Fundamental Theorems Connected with Zeros of Analytic Functions 2 - The Argument (Counting) Principle, Rouche's Theorem and The Fundamental Theorem of Algebra 3 - Morera's Theorem and Normal Limits of Analytic Functions 4 - Hurwitz's Theorem and Normal Limits of Univalent Functions 5 - Local Constancy of Multiplicities of Assumed Values 6 - The Open Mapping Theorem 7 - Introduction to the Inverse Function Theorem 8 - Completion of the Proof of the Inverse Function Theorem 9 - Univalent Analytic Functions have never-zero Derivatives and are Analytic Isomorphisms 10 - Introduction to the Implicit Function Theorem 11 - Proof of the Implicit Function Theorem 12 - Proof of the Implicit Function Theorem 13 - Doing Complex Analysis on a Real Surface 14 - F(z,w)=0 is naturally a Riemann Surface 15 - Constructing the Riemann Surface for the Complex Logarithm 16 - Constructing the Riemann Surface for the m-th root function 17 - The Riemann Surface for the functional inverse of an analytic mapping at a critical point 18 - The Algebraic nature of the functional inverses of an analytic mapping at a critical point 19 - The Idea of a Direct Analytic Continuation or an Analytic Extension 20 - General or Indirect Analytic Continuation and the Lipschitz Nature of the Radius of Convergence
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Discrete Mathematics Subject Co-ordinator - Dr. Aditi Gangopadhyay, Dr. Sugata Gangopadhyay, Dr. Tanuja Srivastava Co-ordinating Institute - IIT - Roorkee Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Introduction to the theory of sets 2 - Set operation and laws of set operation 3 - The principle of inclusion and exclusion 4 - Application of the principle of inclusion and exclusion 5 - Fundamentals of logic 6 - Logical Inferences 7 - Methods of proof of an implication 8 - First order logic (1) 9 - First order logic (2) 10 - Rules of influence for quantified propositions 11 - Mathematical Induction (1) 12 - Mathematical Induction (2) 13 - Sample space, events 14 - Probability, conditional probability 15 - Independent events, Bayes theorem 16 - Information and mutual information 17 - Basic definition 18 - Isomorphism and sub graphs 19 - Walks, paths and circuits operations on graphs 20 - Euler graphs, Hamiltonian circuits 21 - Shortest path problem 22 - Planar graphs 23 - Basic definition 24 - Properties of relations 25 - Graph of relations 26 - Matrix of relation 27 - Closure of relaton (1) 28 - Closure of relaton (2) 29 - Warshall's algorithm
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Partially ordered relation Partially ordered sets Lattices Boolean algebra Boolean function (1) Boolean function (2) Discrete numeric function Generating function Introduction to recurrence relations Second order recurrence relation with constant coefficients (1) Second order recurrence relation with constant coefficients (2) Application of recurrence relation
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Advanced Matrix Theory and Linear Algebra for Engineers Subject Co-ordinator - Prof. Vittal Rao Co-ordinating Institute - IISc - Bangalore Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - Prologue - Part 1 2 - Prologue - Part 2 3 - Prologue - Part 3 4 - Linear Systems - Part 1 5 - Linear Systems - Part 2 6 - Linear Systems - Part 3 7 - Linear Systems - Part 4 8 - Vector Spaces - Part 1 9 - Vector Spaces - Part 2 10 - Linear Independence and Subspaces 11 - Linear Independence and Subspaces 12 - Linear Independence and Subspaces 13 - Linear Independence and Subspaces 14 - Basis - Part 1 15 - Basis - Part 2 16 - Basis - Part 3 17 - Linear Transformations - Part 1 18 - Linear Transformations - Part 2 19 - Linear Transformations - Part 3 20 - Linear Transformations - Part 4 21 - Linear Transformations - Part 5 22 - Inner Product and Orthogonality 23 - Inner Product and Orthogonality 24 - Inner Product and Orthogonality 25 - Inner Product and Orthogonality 26 - Inner Product and Orthogonality 27 - Inner Product and Orthogonality 28 - Diagonalization - Part 1 29 - Diagonalization - Part 2
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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Diagonalization - Part 3 Diagonalization - Part 4 Hermitian and Symmetric matrices Hermitian and Symmetric matrices Hermitian and Symmetric matrices Hermitian and Symmetric matrices Singular Value Decomposition (SVD) Singular Value Decomposition (SVD) Back To Linear Systems - Part 1 Back To Linear Systems - Part 2 Epilogue
Part 1 Part 2 Part 3 Part 4 - Part 1 - Part 2
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------NPTEL Video Course - Mathematics - Ordinary Differential Equations and Applications Subject Co-ordinator - Prof. A.K. Nandakumaran, Prof. Raju K. George, Prof. P.S. Datti Co-ordinating Institute - IISc - Bangalore | IIST - Trivandrum | TIFR-CAM - Bangalore Sub-Titles - Available / Unavailable Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
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MP3 Audio Lectures - Available / Unavailable
1 - General Introduction 2 - Examples 3 - Examples (Continued - I) 4 - Examples (Continued - II) 5 - Linear Algebra 6 - Linear Algebra (Continued - I) 7 - Linear Algebra (Continued - II) 8 - Analysis 9 - Analysis (Continued...) 10 - First Order Linear Equations 11 - Exact Equations 12 - Second Order Linear Equations 13 - Second Order Linear Equations (Continued - I) 14 - Second Order Linear Equations (Continued - II) 15 - Well-posedness and Examples of IVP 16 - Gronwall's Lemma 17 - Basic Lemma and Uniqueness Theorem 18 - Picard's Existence and Uniqueness Theorem 19 - Picard's Existence and Uniqueness (Continued...) 20 - Cauchy Peano Existence Theorem 21 - Existence using Fixed Point Theorem 22 - Continuation of Solutions 23 - Series Solution 24 - General System and Diagonalizability 25 - 2 by 2 systems and Phase Plane Analysis 26 - 2 by 2 systems and Phase Plane Analysis (Continued...) 27 - General Systems 28 - General Systems (Continued...) and Non-homogeneous Systems 29 - Basic Definitions and Examples
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NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai --------------------------------------------------------------------------------------------------Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture
30 31 32 33 34 35 36 37 38 39 40
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Stability Equilibrium Points Stability Equilibrium Points (Continued - I) Stability Equilibrium Points (Continued - II) Second Order Linear Equations (Continued - III) Lyapunov Function Lyapunov Function (Continued...) Periodic Orbits and Poincare Bendixon Theory Periodic Orbits and Poincare Bendixon Theory (Continued...) Linear Second Order Equations General Second Order Equations General Second Order Equations (Continued...)
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