mathematics n p t e l national programme on technology … · n p t e l national programme on...

National Programme on Technology Enhanced LearningNational Programme on Technology Enhanced LearningN P T E L

Mathematics

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 | MP3 Audio Lectures - Available / Unavailable

Lecture 1 - Rational Numbers and Rational CutsLecture 2 - Irrational numbers, Dedekind's TheoremLecture 3 - Continuum and ExercisesLecture 4 - Continuum and Exercises (Continued.)Lecture 5 - Cantor's Theory of Irrational NumbersLecture 6 - Cantor's Theory of Irrational Numbers (Continued.)Lecture 7 - Equivalence of Dedekind and Cantor's TheoryLecture 8 - Finite, Infinite, Countable and Uncountable Sets of Real NumbersLecture 9 - Types of Sets with Examples, Metric SpaceLecture 10 - Various properties of open set, closure of a setLecture 11 - Ordered set, Least upper bound, greatest lower bound of a setLecture 12 - Compact Sets and its propertiesLecture 13 - Weiersstrass Theorem, Heine Borel Theorem, Connected setLecture 14 - Tutorial - IILecture 15 - Concept of limit of a sequenceLecture 16 - Some Important limits, Ratio tests for sequences of Real NumbersLecture 17 - Cauchy theorems on limit of sequences with examplesLecture 18 - Fundamental theorems on limits, Bolzano-Weiersstrass TheoremLecture 19 - Theorems on Convergent and divergent sequencesLecture 20 - Cauchy sequence and its propertiesLecture 21 - Infinite series of real numbersLecture 22 - Comparison tests for series, Absolutely convergent and Conditional convergent seriesLecture 23 - Tests for absolutely convergent seriesLecture 24 - Raabe's test, limit of functions, Cluster pointLecture 25 - Some results on limit of functionsLecture 26 - Limit Theorems for functionsLecture 27 - Extension of limit concept (one sided limits)Lecture 28 - Continuity of FunctionsLecture 29 - Properties of Continuous Functions

NPTEL Video Lecture Topic List - Created by LinuXpert Systems, Chennai---------------------------------------------------------------------------------------------------

---------------------------------------------------------------------------------------------------------------------------------------------Get Digi-MAT (Digital Media Access Terminal) For High-Speed Video Streaming of NPTEL and Educational Video Courses in LAN

www.digimat.in

Lecture 30 - Boundedness Theorem, Max-Min Theorem and Bolzano's theoremLecture 31 - Uniform Continuity and Absolute ContinuityLecture 32 - Types of Discontinuities, Continuity and CompactnessLecture 33 - Continuity and Compactness (Continued.), ConnectednessLecture 34 - Differentiability of real valued function, Mean Value TheoremLecture 35 - Mean Value Theorem (Continued.)Lecture 36 - Application of MVT , Darboux Theorem, L Hospital RuleLecture 37 - L'Hospital Rule and Taylor's TheoremLecture 38 - Tutorial - IIILecture 39 - Riemann/Riemann Stieltjes IntegralLecture 40 - Existence of Reimann Stieltjes IntegralLecture 41 - Properties of Reimann Stieltjes IntegralLecture 42 - Properties of Reimann Stieltjes Integral (Continued.)Lecture 43 - Definite and Indefinite IntegralLecture 44 - Fundamental Theorems of Integral CalculusLecture 45 - Improper IntegralsLecture 46 - Convergence Test for Improper Integrals



www.digimat.in

NPTEL Video Course - Mathematics - Advanced Engineering Mathematics

Subject Co-ordinator - Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar



Lecture 1 - Review Groups, Fields and MatricesLecture 2 - Vector Spaces, Subspaces, Linearly Dependent/Independent of VectorsLecture 3 - Basis, Dimension, Rank and Matrix InverseLecture 4 - Linear Transformation, Isomorphism and Matrix RepresentationLecture 5 - System of Linear Equations, Eigenvalues and EigenvectorsLecture 6 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of MatricesLecture 7 - Jordan Canonical Form, Cayley Hamilton TheoremLecture 8 - Inner Product Spaces, Cauchy-Schwarz InequalityLecture 9 - Orthogonality, Gram-Schmidt Orthogonalization ProcessLecture 10 - Spectrum of special matrices,positive/negative definite matricesLecture 11 - Concept of Domain, Limit, Continuity and DifferentiabilityLecture 12 - Analytic Functions, C-R EquationsLecture 13 - Harmonic FunctionsLecture 14 - Line Integral in the ComplexLecture 15 - Cauchy Integral TheoremLecture 16 - Cauchy Integral Theorem (Continued.)Lecture 17 - Cauchy Integral FormulaLecture 18 - Power and Taylor's Series of Complex NumbersLecture 19 - Power and Taylor's Series of Complex Numbers (Continued.)Lecture 20 - Taylor's, Laurent Series of f(z) and SingularitiesLecture 21 - Classification of Singularities, Residue and Residue TheoremLecture 22 - Laplace Transform and its ExistenceLecture 23 - Properties of Laplace TransformLecture 24 - Evaluation of Laplace and Inverse Laplace TransformLecture 25 - Applications of Laplace Transform to Integral Equations and ODEsLecture 26 - Applications of Laplace Transform to PDEsLecture 27 - Fourier SeriesLecture 28 - Fourier Series (Continued.)Lecture 29 - Fourier Integral Representation of a Function



www.digimat.in

Lecture 30 - Introduction to Fourier TransformLecture 31 - Applications of Fourier Transform to PDEsLecture 32 - Laws of Probability - ILecture 33 - Laws of Probability - IILecture 34 - Problems in ProbabilityLecture 35 - Random VariablesLecture 36 - Special Discrete DistributionsLecture 37 - Special Continuous DistributionsLecture 38 - Joint Distributions and Sampling DistributionsLecture 39 - Point EstimationLecture 40 - Interval EstimationLecture 41 - Basic Concepts of Testing of HypothesisLecture 42 - Tests for Normal Populations



www.digimat.in

NPTEL Video Course - Mathematics - Advanced Matrix Theory and Linear Algebra for Engineers

Subject Co-ordinator - Prof. Vittal Rao

Co-ordinating Institute - IISc - Bangalore


Lecture 1 - Prologue - Part 1Lecture 2 - Prologue - Part 2Lecture 3 - Prologue - Part 3Lecture 4 - Linear Systems - Part 1Lecture 5 - Linear Systems - Part 2Lecture 6 - Linear Systems - Part 3Lecture 7 - Linear Systems - Part 4Lecture 8 - Vector Spaces - Part 1Lecture 9 - Vector Spaces - Part 2Lecture 10 - Linear Independence and Subspaces - Part 1Lecture 11 - Linear Independence and Subspaces - Part 2Lecture 12 - Linear Independence and Subspaces - Part 3Lecture 13 - Linear Independence and Subspaces - Part 4Lecture 14 - Basis - Part 1Lecture 15 - Basis - Part 2Lecture 16 - Basis - Part 3Lecture 17 - Linear Transformations - Part 1Lecture 18 - Linear Transformations - Part 2Lecture 19 - Linear Transformations - Part 3Lecture 20 - Linear Transformations - Part 4Lecture 21 - Linear Transformations - Part 5Lecture 22 - Inner Product and Orthogonality - Part 1Lecture 23 - Inner Product and Orthogonality - Part 2Lecture 24 - Inner Product and Orthogonality - Part 3Lecture 25 - Inner Product and Orthogonality - Part 4Lecture 26 - Inner Product and Orthogonality - Part 5Lecture 27 - Inner Product and Orthogonality - Part 6Lecture 28 - Diagonalization - Part 1Lecture 29 - Diagonalization - Part 2



www.digimat.in

Lecture 30 - Diagonalization - Part 3Lecture 31 - Diagonalization - Part 4Lecture 32 - Hermitian and Symmetric matrices - Part 1Lecture 33 - Hermitian and Symmetric matrices - Part 2Lecture 34 - Hermitian and Symmetric matrices - Part 3Lecture 35 - Hermitian and Symmetric matrices - Part 4Lecture 36 - Singular Value Decomposition (SVD) - Part 1Lecture 37 - Singular Value Decomposition (SVD) - Part 2Lecture 38 - Back To Linear Systems - Part 1Lecture 39 - Back To Linear Systems - Part 2Lecture 40 - Epilogue



www.digimat.in

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


Lecture 1 - The Idea of a Riemann SurfaceLecture 2 - Simple Examples of Riemann SurfacesLecture 3 - Maximal Atlases and Holomorphic Maps of Riemann SurfacesLecture 4 - A Riemann Surface Structure on a CylinderLecture 5 - A Riemann Surface Structure on a TorusLecture 6 - Riemann Surface Structures on Cylinders and Tori via Covering SpacesLecture 7 - Moebius Transformations Make up Fundamental Groups of Riemann SurfacesLecture 8 - Homotopy and the First Fundamental GroupLecture 9 - A First Classification of Riemann SurfacesLecture 10 - The Importance of the Path-lifting PropertyLecture 11 - Fundamental groups as Fibres of the Universal covering SpaceLecture 12 - The Monodromy ActionLecture 13 - The Universal covering as a Hausdorff Topological SpaceLecture 14 - The Construction of the Universal Covering MapLecture 15 - Completion of the Construction of the Universal CoveringLecture 16 - Completion of the Construction of the Universal CoveringLecture 17 - The Riemann Surface Structure on the Topological Covering of a Riemann SurfaceLecture 18 - Riemann Surfaces with Universal Covering the Plane or the SphereLecture 19 - Classifying Complex CylindersLecture 20 - Characterizing Moebius Transformations with a Single Fixed PointLecture 21 - Characterizing Moebius Transformations with Two Fixed PointsLecture 22 - Torsion-freeness of the Fundamental Group of a Riemann SurfaceLecture 23 - Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian Fundamental GroupsLecture 24 - Classifying Annuli up to Holomorphic IsomorphismLecture 25 - Orbits of the Integral Unimodular Group in the Upper Half-PlaneLecture 26 - Galois Coverings are precisely Quotients by Properly Discontinuous Free ActionsLecture 27 - Local Actions at the Region of Discontinuity of a Kleinian Subgroup of Moebius Transformations



www.digimat.in

Lecture 28 - Quotients by Kleinian Subgroups give rise to Riemann SurfacesLecture 29 - The Unimodular Group is KleinianLecture 30 - The Necessity of Elliptic Functions for the Classification of Complex ToriLecture 31 - The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the PlaneLecture 32 - The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstrass Phe-functionLecture 33 - The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing Analytic Functions on the Upper Half-PlaneLecture 34 - The Construction of a Modular Form of Weight Two on the Upper Half-PlaneLecture 35 - The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half-PlaneLecture 36 - The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-planeLecture 37 - The Weight Two Modular Form Vanishes at InfinityLecture 38 - The Weight Two Modular Form Decays Exponentially in a Neighbourhood of InfinityLecture 39 - A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism onto the Upper Half-PlaneLecture 40 - The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic CurveLecture 41 - A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-InvariantLecture 42 - The Fundamental Region in the Upper Half-Plane for the Unimodular GroupLecture 43 - A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly OnceLecture 44 - Moduli of Elliptic CurvesLecture 45 - Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-SpaceLecture 46 - The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane CurveLecture 47 - Complex Projective 2-Space as a Compact Complex Manifold of Dimension TwoLecture 48 - Complex Tori are the same as Elliptic Algebraic Projective Curves



www.digimat.in

NPTEL Video Course - Mathematics - Applied Multivariate Analysis

Subject Co-ordinator - Dr. Sharmishtha Mitra

Co-ordinating Institute - IIT - Kanpur


Lecture 1 - PrologueLecture 2 - Basic concepts on multivariate distributionLecture 3 - Basic concepts on multivariate distributionLecture 4 - Multivariate normal distribution â�� ILecture 5 - Multivariate normal distribution â�� IILecture 6 - Multivariate normal distribution â�� IIILecture 7 - Some problems on multivariate distributions â�� ILecture 8 - Some problems on multivariate distributions â�� IILecture 9 - Random sampling from multivariate normal distribution and Wishart distribution - ILecture 10 - Random sampling from multivariate normal distribution and Wishart distribution - IILecture 11 - Random sampling from multivariate normal distribution and Wishart distribution - IIILecture 12 - Wishart distribution and itâ��s properties - ILecture 13 - Wishart distribution and itâ��s properties - IILecture 14 - Hotellingâ��s T2 distribution and itâ��s applicationsLecture 15 - Hotellingâ��s T2 distribution and various confidence intervals and regionsLecture 16 - Hotellingâ��s T2 distribution and Profile analysisLecture 17 - Profile analysis - ILecture 18 - Profile analysis - IILecture 19 - MANOVA - ILecture 20 - MANOVA - IILecture 21 - MANOVA - IIILecture 22 - MANOVA & Multiple Correlation CoefficientLecture 23 - Multiple Correlation CoefficientLecture 24 - Principal Component AnalysisLecture 25 - Principal Component AnalysisLecture 26 - Principal Component AnalysisLecture 27 - Cluster AnalysisLecture 28 - Cluster AnalysisLecture 29 - Cluster Analysis



www.digimat.in

Lecture 30 - Cluster AnalysisLecture 31 - Discriminant Analysis and ClassificationLecture 32 - Discriminant Analysis and ClassificationLecture 33 - Discriminant Analysis and ClassificationLecture 34 - Discriminant Analysis and ClassificationLecture 35 - Discriminant Analysis and ClassificationLecture 36 - Discriminant Analysis and ClassificationLecture 37 - Discriminant Analysis and ClassificationLecture 38 - Factor_AnalysisLecture 39 - Factor_AnalysisLecture 40 - Factor_AnalysisLecture 41 - Cannonical Correlation AnalysisLecture 42 - Cannonical Correlation AnalysisLecture 43 - Cannonical Correlation AnalysisLecture 44 - Cannonical Correlation Analysis



www.digimat.in

NPTEL Video Course - Mathematics - Calculus of Variations and Integral Equations

Subject Co-ordinator - Dr. Malay Banerjee, Prof. D. Bahuguna



Lecture 1 - Calculus of Variations and Integral EquationsLecture 2 - Calculus of Variations and Integral EquationsLecture 3 - Calculus of Variations and Integral EquationsLecture 4 - Calculus of Variations and Integral EquationsLecture 5 - Calculus of Variations and Integral EquationsLecture 6 - Calculus of Variations and Integral EquationsLecture 7 - Calculus of Variations and Integral EquationsLecture 8 - Calculus of Variations and Integral EquationsLecture 9 - Calculus of Variations and Integral EquationsLecture 10 - Calculus of Variations and Integral EquationsLecture 11 - Calculus of Variations and Integral EquationsLecture 12 - Calculus of Variations and Integral EquationsLecture 13 - Calculus of Variations and Integral EquationsLecture 14 - Calculus of Variations and Integral EquationsLecture 15 - Calculus of Variations and Integral EquationsLecture 16 - Calculus of Variations and Integral EquationsLecture 17 - Calculus of Variations and Integral EquationsLecture 18 - Calculus of Variations and Integral EquationsLecture 19 - Calculus of Variations and Integral EquationsLecture 20 - Calculus of Variations and Integral EquationsLecture 21 - Calculus of Variations and Integral EquationsLecture 22 - Calculus of Variations and Integral EquationsLecture 23 - Calculus of Variations and Integral EquationsLecture 24 - Calculus of Variations and Integral EquationsLecture 25 - Calculus of Variations and Integral EquationsLecture 26 - Calculus of Variations and Integral EquationsLecture 27 - Calculus of Variations and Integral EquationsLecture 28 - Calculus of Variations and Integral EquationsLecture 29 - Calculus of Variations and Integral Equations



www.digimat.in

Lecture 30 - Calculus of Variations and Integral EquationsLecture 31 - Calculus of Variations and Integral EquationsLecture 32 - Calculus of Variations and Integral EquationsLecture 33 - Calculus of Variations and Integral EquationsLecture 34 - Calculus of Variations and Integral EquationsLecture 35 - Calculus of Variations and Integral EquationsLecture 36 - Calculus of Variations and Integral EquationsLecture 37 - Calculus of Variations and Integral EquationsLecture 38 - Calculus of Variations and Integral EquationsLecture 39 - Calculus of Variations and Integral EquationsLecture 40 - Calculus of Variations and Integral Equations



www.digimat.in

NPTEL Video Course - Mathematics - Complex Analysis

Subject Co-ordinator - Prof. P.A.S. Sree Krishna

Co-ordinating Institute - IIT - Guwahati


Lecture 1 - IntroductionLecture 2 - Introduction to Complex NumbersLecture 3 - de Moivreâ��s Formula and Stereographic ProjectionLecture 4 - Topology of the Complex Plane - Part-ILecture 5 - Topology of the Complex Plane - Part-IILecture 6 - Topology of the Complex Plane - Part-IIILecture 7 - Introduction to Complex FunctionsLecture 8 - Limits and ContinuityLecture 9 - DifferentiationLecture 10 - Cauchy-Riemann Equations and DifferentiabilityLecture 11 - Analytic functions; the exponential functionLecture 12 - Sine, Cosine and Harmonic functionsLecture 13 - Branches of Multifunctions; Hyperbolic FunctionsLecture 14 - Problem Solving Session ILecture 15 - Integration and ContoursLecture 16 - Contour IntegrationLecture 17 - Introduction to Cauchyâ��s TheoremLecture 18 - Cauchyâ��s Theorem for a RectangleLecture 19 - Cauchyâ��s theorem - Part-IILecture 20 - Cauchyâ��s Theorem - Part-IIILecture 21 - Cauchyâ��s Integral Formula and its ConsequencesLecture 22 - The First and Second Derivatives of Analytic FunctionsLecture 23 - Moreraâ��s Theorem and Higher Order Derivatives of Analytic FunctionsLecture 24 - Problem Solving Session IILecture 25 - Introduction to Complex Power SeriesLecture 26 - Analyticity of Power SeriesLecture 27 - Taylorâ��s TheoremLecture 28 - Zeroes of Analytic FunctionsLecture 29 - Counting the Zeroes of Analytic Functions



www.digimat.in

Lecture 30 - Open mapping theorem - Part-ILecture 31 - Open mapping theorem - Part-IILecture 32 - Properties of Mobius Transformations - Part-ILecture 33 - Properties of Mobius Transformations - Part-IILecture 34 - Problem Solving Session IIILecture 35 - Removable SingularitiesLecture 36 - Poles Classification of Isolated SingularitiesLecture 37 - Essential Singularity & Introduction to Laurent SeriesLecture 38 - Laurentâ��s TheoremLecture 39 - Residue Theorem and ApplicationsLecture 40 - Problem Solving Session IV



www.digimat.in

NPTEL Video Course - Mathematics - Convex Optimization

Subject Co-ordinator - Dr. Joydeep Dutta



Lecture 1 - Convex OptimizationLecture 2 - Convex OptimizationLecture 3 - Convex OptimizationLecture 4 - Convex OptimizationLecture 5 - Convex OptimizationLecture 6 - Convex OptimizationLecture 7 - Convex OptimizationLecture 8 - Convex OptimizationLecture 9 - Convex OptimizationLecture 10 - Convex OptimizationLecture 11 - Convex OptimizationLecture 12 - Convex OptimizationLecture 13 - Convex OptimizationLecture 14 - Convex OptimizationLecture 15 - Convex OptimizationLecture 16 - Convex OptimizationLecture 17 - Convex OptimizationLecture 18 - Convex OptimizationLecture 19 - Convex OptimizationLecture 20 - Convex OptimizationLecture 21 - Convex OptimizationLecture 22 - Convex OptimizationLecture 23 - Convex OptimizationLecture 24 - Convex OptimizationLecture 25 - Convex OptimizationLecture 26 - Convex OptimizationLecture 27 - Convex OptimizationLecture 28 - Convex OptimizationLecture 29 - Convex Optimization



www.digimat.in

Lecture 30 - Convex OptimizationLecture 31 - Convex OptimizationLecture 32 - Convex OptimizationLecture 33 - Convex OptimizationLecture 34 - Convex OptimizationLecture 35 - Convex OptimizationLecture 36 - Convex OptimizationLecture 37 - Convex OptimizationLecture 38 - Convex OptimizationLecture 39 - Convex OptimizationLecture 40 - Convex OptimizationLecture 41 - Convex OptimizationLecture 42 - Convex Optimization



www.digimat.in

NPTEL Video Course - Mathematics - Elementary Numerical Analysis

Subject Co-ordinator - Prof. Rekha P. Kulkarni

Co-ordinating Institute - IIT - Bombay


Lecture 1 - IntroductionLecture 2 - Polynomial ApproximationLecture 3 - Interpolating PolynomialsLecture 4 - Properties of Divided DifferenceLecture 5 - Error in the Interpolating polynomialLecture 6 - Cubic Hermite InterpolationLecture 7 - Piecewise Polynomial ApproximationLecture 8 - Cubic Spline InterpolationLecture 9 - Tutorial 1Lecture 10 - Numerical IntegrationLecture 11 - Composite Numerical IntegrationLecture 12 - Gauss 2-point RuleLecture 13 - Gauss 2-point RuleLecture 14 - Convergence of Gaussian IntegrationLecture 15 - Tutorial 2Lecture 16 - Numerical DifferentiationLecture 17 - Gauss EliminationLecture 18 - L U decompositionLecture 19 - Cholesky decompositionLecture 20 - Gauss Elimination with partial pivotingLecture 21 - Vector and Matrix NormsLecture 22 - Perturbed Linear SystemsLecture 23 - Ill-conditioned Linear SystemLecture 24 - Tutorial 3Lecture 25 - Effect of Small PivotsLecture 26 - Solution of Non-linear EquationsLecture 27 - Quadratic Convergence of Newton's MethodLecture 28 - Jacobi MethodLecture 29 - Gauss-Seidel Method



www.digimat.in

Lecture 30 - Tutorial 4Lecture 31 - Initial Value ProblemLecture 32 - Multi-step MethodsLecture 33 - Predictor-Corrector FormulaeLecture 34 - Boundary Value ProblemsLecture 35 - Eigenvalues and EigenvectorsLecture 36 - Spectral TheoremLecture 37 - Power MethodLecture 38 - Inverse Power MethodLecture 39 - Q R DecompositionLecture 40 - Q R Method



www.digimat.in

NPTEL Video Course - Mathematics - Formal Languages and Automata Theory

Subject Co-ordinator - Dr. K.V. Krishna, Dr. Diganta Goswami

Co-ordinating Institute - IIT - Guwahati


Lecture 1 - IntroductionLecture 2 - Alphabet, Strings, LanguagesLecture 3 - Finite RepresentationLecture 4 - Grammars (CFG)Lecture 5 - Derivation TreesLecture 6 - Regular GrammarsLecture 7 - Finite AutomataLecture 8 - Nondeterministic Finite AutomataLecture 9 - NFA <=> DFALecture 10 - Myhill-Nerode TheoremLecture 11 - MinimizationLecture 12 - RE => FALecture 13 - FA => RELecture 14 - FA <=> RGLecture 15 - Variants of FALecture 16 - Closure Properties of RLLecture 17 - HomomorphismLecture 18 - Pumping LemmaLecture 19 - Simplification of CFGLecture 20 - Normal Forms of CFGLecture 21 - Properties of CFLsLecture 22 - Pushdown AutomataLecture 23 - PDA <=> CFGLecture 24 - Turing MachinesLecture 25 - Turing Computable FunctionsLecture 26 - Combining Turing MachinesLecture 27 - Multi InputLecture 28 - Turing Decidable LanguagesLecture 29 - Varients of Turing Machines



www.digimat.in

Lecture 30 - Structured GrammarsLecture 31 - DecidabilityLecture 32 - Undecidability 1Lecture 33 - Undecidability 2Lecture 34 - Undecidability 3Lecture 35 - Time Bounded Turing MachinesLecture 36 - P and NPLecture 37 - NP-CompletenessLecture 38 - NP-Complete Problems 1Lecture 39 - NP-Complete Problems 2Lecture 40 - NP-Complete Problems 3Lecture 41 - Chomsky Hierarchy



www.digimat.in

NPTEL Video Course - Mathematics - Foundations of Optimization

Subject Co-ordinator - Dr. Joydeep Dutta



Lecture 1 - OptimizationLecture 2 - OptimizationLecture 3 - OptimizationLecture 4 - OptimizationLecture 5 - OptimizationLecture 6 - OptimizationLecture 7 - OptimizationLecture 8 - OptimizationLecture 9 - OptimizationLecture 10 - OptimizationLecture 11 - OptimizationLecture 12 - OptimizationLecture 13 - OptimizationLecture 14 - OptimizationLecture 15 - OptimizationLecture 16 - OptimizationLecture 17 - OptimizationLecture 18 - OptimizationLecture 19 - OptimizationLecture 20 - OptimizationLecture 21 - OptimizationLecture 22 - OptimizationLecture 23 - OptimizationLecture 24 - OptimizationLecture 25 - OptimizationLecture 26 - OptimizationLecture 27 - OptimizationLecture 28 - OptimizationLecture 29 - Optimization



www.digimat.in

Lecture 30 - OptimizationLecture 31 - OptimizationLecture 32 - OptimizationLecture 33 - OptimizationLecture 34 - OptimizationLecture 35 - OptimizationLecture 36 - OptimizationLecture 37 - OptimizationLecture 38 - Optimization



www.digimat.in

NPTEL Video Course - Mathematics - Functional Analysis

Subject Co-ordinator - Prof. P.D. Srivastava



Lecture 1 - Metric Spaces with ExamplesLecture 2 - Holder Inequality and Minkowski InequalityLecture 3 - Various Concepts in a Metric SpaceLecture 4 - Separable Metrics Spaces with ExamplesLecture 5 - Convergence, Cauchy Sequence, CompletenessLecture 6 - Examples of Complete and Incomplete Metric SpacesLecture 7 - Completion of Metric Spaces + TutorialLecture 8 - Vector Spaces with ExamplesLecture 9 - Normed Spaces with ExamplesLecture 10 - Banach Spaces and Schauder BasicLecture 11 - Finite Dimensional Normed Spaces and SubspacesLecture 12 - Compactness of Metric/Normed SpacesLecture 13 - Linear Operators-definition and ExamplesLecture 14 - Bounded Linear Operators in a Normed SpaceLecture 15 - Bounded Linear Functionals in a Normed SpaceLecture 16 - Concept of Algebraic Dual and Reflexive SpaceLecture 17 - Dual Basis & Algebraic Reflexive SpaceLecture 18 - Dual Spaces with ExamplesLecture 19 - Tutorial - ILecture 20 - Tutorial - IILecture 21 - Inner Product & Hilbert SpaceLecture 22 - Further Properties of Inner Product SpacesLecture 23 - Projection Theorem, Orthonormal Sets and SequencesLecture 24 - Representation of Functionals on a Hilbert SpacesLecture 25 - Hilbert Adjoint OperatorLecture 26 - Self Adjoint, Unitary & Normal OperatorsLecture 27 - Tutorial - IIILecture 28 - Annihilator in an IPSLecture 29 - Total Orthonormal Sets And Sequences



www.digimat.in

Lecture 30 - Partially Ordered Set and Zorns LemmaLecture 31 - Hahn Banach Theorem for Real Vector SpacesLecture 32 - Hahn Banach Theorem for Complex V.S. & Normed SpacesLecture 33 - Baires Category & Uniform Boundedness TheoremsLecture 34 - Open Mapping TheoremLecture 35 - Closed Graph TheoremLecture 36 - Adjoint OperatorLecture 37 - Strong and Weak ConvergenceLecture 38 - Convergence of Sequence of Operators and FunctionalsLecture 39 - LP - SpaceLecture 40 - LP - Space (Continued.)



www.digimat.in

NPTEL Video Course - Mathematics - Linear Algebra

Subject Co-ordinator - Dr. K.C. Sivakumar



Lecture 1 - Introduction to the Course ContentsLecture 2 - Linear EquationsLecture 3a - Equivalent Systems of Linear Equations ILecture 3b - Equivalent Systems of Linear Equations IILecture 4 - Row-reduced Echelon MatricesLecture 5 - Row-reduced Echelon Matrices and Non-homogeneous EquationsLecture 6 - Elementary Matrices, Homogeneous Equations and Non-homogeneous EquationsLecture 7 - Invertible matrices, Homogeneous Equations Non-homogeneous EquationsLecture 8 - Vector spacesLecture 9 - Elementary Properties in Vector Spaces. SubspacesLecture 10 - Subspaces (Continued...), Spanning Sets, Linear Independence, DependenceLecture 11 - Basis for a vector spaceLecture 12 - Dimension of a vector spaceLecture 13 - Dimensions of Sums of SubspacesLecture 14 - Linear TransformationsLecture 15 - The Null Space and the Range Space of a Linear TransformationLecture 16 - The Rank-Nullity-Dimension Theorem. Isomorphisms Between Vector SpacesLecture 17 - Isomorphic Vector Spaces, Equality of the Row-rank and the Column-rank - ILecture 18 - Equality of the Row-rank and the Column-rank - IILecture 19 - The Matrix of a Linear TransformationLecture 20 - Matrix for the Composition and the Inverse. Similarity TransformationLecture 21 - Linear Functionals. The Dual Space. Dual Basis - ILecture 22 - Dual Basis II. Subspace Annihilators - ILecture 23 - Subspace Annihilators - IILecture 24 - The Double Dual. The Double AnnihilatorLecture 25 - The Transpose of a Linear Transformation. Matrices of a Linear Transformation and its TransposeLecture 26 - Eigenvalues and Eigenvectors of Linear OperatorsLecture 27 - Diagonalization of Linear Operators. A CharacterizationLecture 28 - The Minimal Polynomial



www.digimat.in

Lecture 29 - The Cayley-Hamilton TheoremLecture 30 - Invariant SubspacesLecture 31 - Triangulability, Diagonalization in Terms of the Minimal PolynomialLecture 32 - Independent Subspaces and Projection OperatorsLecture 33 - Direct Sum Decompositions and Projection Operators - ILecture 34 - Direct Sum Decompositions and Projection Operators - IILecture 35 - The Primary Decomposition Theorem and Jordan DecompositionLecture 36 - Cyclic Subspaces and AnnihilatorsLecture 37 - The Cyclic Decomposition Theorem - ILecture 38 - The Cyclic Decomposition Theorem - II. The Rational FormLecture 39 - Inner Product SpacesLecture 40 - Norms on Vector spaces. The Gram-Schmidt Procedure ILecture 41 - The Gram-Schmidt Procedure II. The QR DecompositionLecture 42 - Bessel's Inequality, Parseval's Indentity, Best ApproximationLecture 43 - Best ApproximationLecture 44 - Orthogonal Complementary Subspaces, Orthogonal ProjectionsLecture 45 - Projection Theorem. Linear FunctionalsLecture 46 - The Adjoint OperatorLecture 47 - Properties of the Adjoint Operation. Inner Product Space IsomorphismLecture 48 - Unitary OperatorsLecture 49 - Unitary operators - II. Self-Adjoint Operators - I.Lecture 50 - Self-Adjoint Operators - II - Spectral TheoremLecture 51 - Normal Operators - Spectral Theorem



www.digimat.in

NPTEL Video Course - Mathematics - Linear programming and Extensions

Subject Co-ordinator - Prof. Prabha Sharma



Lecture 1 - Introduction to Linear Programming ProblemsLecture 2 - Vector space, Linear independence and dependence, basisLecture 3 - Moving from one basic feasible solution to another, optimality criteriaLecture 4 - Basic feasible solutions, existence & derivationLecture 5 - Convex sets, dimension of a polyhedron, Faces, Example of a polytopeLecture 6 - Direction of a polyhedron, correspondence between bfs and extreme pointsLecture 7 - Representation theorem, LPP solution is a bfs, Assignment 1Lecture 8 - Development of the Simplex Algorithm, Unboundedness, Simplex TableauLecture 9 - Simplex Tableau & algorithm ,Cycling, Blandâ��s anti-cycling rules, Phase I & Phase IILecture 10 - Big-M method,Graphical solutions, adjacent extreme pts and adjacent bfsLecture 11 - Assignment 2, progress of Simplex algorithm on a polytope, bounded variable LPPLecture 12 - LPP Bounded variable, Revised Simplex algorithm, Duality theory, weak duality theoremLecture 13 - Weak duality theorem, economic interpretation of dual variables, Fundamental theorem of dualityLecture 14 - Examples of writing the dual, complementary slackness theoremLecture 15 - Complementary slackness conditions, Dual Simplex algorithm, Assignment 3Lecture 16 - Primal-dual algorithmLecture 17 - Problem in lecture 16, starting dual feasible solution, Shortest Path ProblemLecture 18 - Shortest Path Problem, Primal-dual method, exampleLecture 19 - Shortest Path Problem-complexity, interpretation of dual variables, post-optimality analysis-changes in the cost vectorLecture 20 - Assignment 4, postoptimality analysis, changes in b, adding a new constraint, changes in {aij} , Parametric analysisLecture 21 - Parametric LPP-Right hand side vectorLecture 22 - Parametric cost vector LPPLecture 23 - Parametric cost vector LPP, Introduction to Min-cost flow problemLecture 24 - Mini-cost flow problem-Transportation problemLecture 25 - Transportation problem degeneracy, cyclingLecture 26 - Sensitivity analysisLecture 27 - Sensitivity analysisLecture 28 - Bounded variable transportation problem, min-cost flow problemLecture 29 - Min-cost flow problem



www.digimat.in

Lecture 30 - Starting feasible solution, Lexicographic method for preventing cycling ,strongly feasible solutionLecture 31 - Assignment 6, Shortest path problem, Shortest Path between any two nodes,Detection of negative cyclesLecture 32 - Min-cost-flow Sensitivity analysis Shortest path problem sensitivity analysisLecture 33 - Min-cost flow changes in arc capacities , Max-flow problem, assignment 7Lecture 34 - Problem 3 (assignment 7), Min-cut Max-flow theorem, Labelling algorithmLecture 35 - Max-flow - Critical capacity of an arc, starting solution for min-cost flow problemLecture 36 - Improved Max-flow algorithmLecture 37 - Critical Path Method (CPM)Lecture 38 - Programme Evaluation and Review Technique (PERT)Lecture 39 - Simplex Algorithm is not polynomial time- An exampleLecture 40 - Interior Point Methods



www.digimat.in

NPTEL Video Course - Mathematics - Mathematical Logic

Subject Co-ordinator - Prof. Arindama Singh



Lecture 1 - Sets and StringsLecture 2 - Syntax of Propositional LogicLecture 3 - Unique ParsingLecture 4 - Semantics of PLLecture 5 - Consequences and EquivalencesLecture 6 - Five results about PLLecture 7 - Calculations and Informal ProofsLecture 8 - More Informal ProofsLecture 9 - Normal formsLecture 10 - SAT and 3SATLecture 11 - Horn-SAT and ResolutionLecture 12 - ResolutionLecture 13 - Adequacy of ResolutionLecture 14 - Adequacy and Resolution StrategiesLecture 15 - Propositional Calculus (PC)Lecture 16 - Some Results about PCLecture 17 - Arguing with ProofsLecture 18 - Adequacy of PCLecture 19 - Compactness & Analytic TableauLecture 20 - Examples of Tableau ProofsLecture 21 - Adequacy of TableauxLecture 22 - Syntax of First order Logic (FL)Lecture 23 - Symbolization & Scope of QuantifiersLecture 24 - Hurdles in giving MeaningLecture 25 - Semantics of FLLecture 26 - Relevance LemmaLecture 27 - Validity, Satisfiability & EquivalenceLecture 28 - Six Results about FLLecture 29 - Laws, Calculation & Informal Proof



www.digimat.in

Lecture 30 - Quantifier Laws and ConsequencesLecture 31 - More Proofs and Prenex FormLecture 32 - Prenex Form ConversionLecture 33 - Skolem FormLecture 34 - Syntatic InterpretationLecture 35 - Herbrand's TheoremLecture 36 - Most General UnifiersLecture 37 - Resolution RulesLecture 38 - Resolution ExamplesLecture 39 - Ariomatic System FCLecture 40 - FC and Semidecidability of FLLecture 41 - Analytic Tableau for FLLecture 42 - Godels Incompleteness Theorems



www.digimat.in

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


Lecture 1 - Indian MathematicsLecture 2 - Vedas and Sulbasutras - Part 1Lecture 3 - Vedas and Sulbasutras - Part 2Lecture 4 - Panini's AstadhyayiLecture 5 - Pingala's ChandahsastraLecture 6 - Decimal place value systemLecture 7 - Aryabhatiya of Aryabhata - Part 1Lecture 8 - Aryabhatiya of Aryabhata - Part 2Lecture 9 - Aryabhatiya of Aryabhata - Part 3Lecture 10 - Aryabhatiya of Aryabhata - Part 4 and Introduction to Jaina MathematicsLecture 11 - Brahmasphutasiddhanta of Brahmagupta - Part 1Lecture 12 - Brahmasphutasiddhanta of Brahmagupta - Part 2Lecture 13 - Brahmasphutasiddhanta of Brahmagupta - Part 3Lecture 14 - Brahmasphutasiddhanta of Brahmagupta - Part 4 and The Bakhshali ManuscriptLecture 15 - Mahaviras Ganitasarasangraha - Part 1Lecture 16 - Mahaviras Ganitasarasangraha - Part 2Lecture 17 - Mahaviras Ganitasarasangraha - Part 3Lecture 18 - Development of Combinatorics - Part 1Lecture 19 - Development of Combinatorics - Part 2Lecture 20 - Lilavati of Bhaskaracarya - Part 1Lecture 21 - Lilavati of Bhaskaracarya - Part 2Lecture 22 - Lilavati of Bhaskaracarya - Part 3Lecture 23 - Bijaganita of Bhaskaracarya - Part 1Lecture 24 - Bijaganita of Bhaskaracarya - Part 2Lecture 25 - Ganitakaumudi of Narayana Pandita - Part 1Lecture 26 - Ganitakaumudi of Narayana Pandita - Part 2Lecture 27 - Ganitakaumudi of Narayana Pandita - Part 3Lecture 28 - Magic Squares - Part 1Lecture 29 - Magic Squares - Part 2



www.digimat.in

Lecture 30 - Development of Calculus in India - Part 1Lecture 31 - Development of Calculus in India - Part 2Lecture 32 - JyanayanamLecture 33 - Trigonometry and Spherical Trigonometry - Part 1Lecture 34 - Trigonometry and Spherical Trigonometry - Part 2Lecture 35 - Trigonometry and Spherical Trigonometry - Part 3Lecture 36 - Proofs in Indian Mathematics - Part 1Lecture 37 - Proofs in Indian Mathematics - Part 2Lecture 38 - Proofs in Indian Mathematics - Part 3Lecture 39 - Mathematics in Modern India - Part 1Lecture 40 - Mathematics in Modern India - Part 2



www.digimat.in

NPTEL Video Course - Mathematics - Measure and Integration

Subject Co-ordinator - Prof. Inder K Rana

Co-ordinating Institute - IIT - Bombay


Lecture 1 - Introduction, Extended Real numbersLecture 2 - Algebra and Sigma Algebra of a subset of a setLecture 3 - Sigma Algebra generated by a classLecture 4 - Monotone ClassLecture 5 - Set functionLecture 6 - The Length function and its propertiesLecture 7 - Countably additive set functions on intervalsLecture 8 - Uniqueness Problem for MeasureLecture 9 - Extension of measureLecture 10 - Outer measure and its propertiesLecture 11 - Measurable setsLecture 12 - Lebesgue measure and its propertiesLecture 13 - Characterization of Lebesque measurable setsLecture 14 - Measurable functionsLecture 15 - Properties of measurable functionsLecture 16 - Measurable functions on measure spacesLecture 17 - Integral of non negative simple measurable functionsLecture 18 - Properties of non negative simple measurable functionsLecture 19 - Monotone convergence theorem & Fatou's LemmaLecture 20 - Properties of Integral functions & Dominated Convergence TheoremLecture 21 - Dominated Convergence Theorem and applicationsLecture 22 - Lebesgue Integral and its propertiesLecture 23 - Denseness of continuous functionLecture 24 - Product measures, an IntroductionLecture 25 - Construction of Product MeasureLecture 26 - Computation of Product Measure - ILecture 27 - Computation of Product Measure - IILecture 28 - Integration on Product spacesLecture 29 - Fubini's Theorems



www.digimat.in

Lecture 30 - Lebesgue Measure and integral on R2Lecture 31 - Properties of Lebesgue Measure and integral on RnLecture 32 - Lebesgue integral on R2Lecture 33 - Integrating complex-valued functionsLecture 34 - Lp - spacesLecture 35 - L2(X,S,mue)Lecture 36 - Fundamental Theorem of calculas for Lebesgue Integral - ILecture 37 - Fundamental Theorem of calculus for Lebesgue Integral - IILecture 38 - Absolutely continuous measuresLecture 39 - Modes of convergenceLecture 40 - Convergence in Measure



www.digimat.in

NPTEL Video Course - Mathematics - Numerical methods of Ordinary and Partial Differential Equations

Subject Co-ordinator - Dr. G.P. Raja Sekhar



Lecture 1 - Motivation with few ExamplesLecture 2 - Single - Step Methods for IVPsLecture 3 - Analysis of Single Step MethodsLecture 4 - Runge - Kutta Methods for IVPsLecture 5 - Higher Order Methods/EquationsLecture 6 - Error - Stability - Convergence of Single Step MethodsLecture 7 - Tutorial - ILecture 8 - Tutorial - IILecture 9 - Multi-Step Methods (Explicit)Lecture 10 - Multi-Step Methods (Implicit)Lecture 11 - Convergence and Stability of multi step methodsLecture 12 - General methods for absolute stabilityLecture 13 - Stability Analysis of Multi Step MethodsLecture 14 - Predictor - Corrector MethodsLecture 15 - Some Comments on Multi - Step MethodsLecture 16 - Finite Difference Methods - Linear BVPsLecture 17 - Linear/Non - Linear Second Order BVPsLecture 18 - BVPS - Derivative Boundary ConditionsLecture 19 - Higher Order BVPsLecture 20 - Shooting Method BVPsLecture 21 - Tutorial - IIILecture 22 - Introduction to First Order PDELecture 23 - Introduction to Second Order PDELecture 24 - Finite Difference Approximations to Parabolic PDEsLecture 25 - Implicit Methods for Parabolic PDEsLecture 26 - Consistency, Stability and ConvergenceLecture 27 - Other Numerical Methods for Parabolic PDEsLecture 28 - Tutorial - IVLecture 29 - Matrix Stability Analysis of Finite Difference Scheme



www.digimat.in

Lecture 30 - Fourier Series Stability Analysis of Finite Difference SchemeLecture 31 - Finite Difference Approximations to Elliptic PDEs - ILecture 32 - Finite Difference Approximations to Elliptic PDEs - IILecture 33 - Finite Difference Approximations to Elliptic PDEs - IIILecture 34 - Finite Difference Approximations to Elliptic PDEs - IVLecture 35 - Finite Difference Approximations to Hyperbolic PDEs - ILecture 36 - Finite Difference Approximations to Hyperbolic PDEs - IILecture 37 - Method of characteristics for Hyperbolic PDEs - ILecture 38 - Method of characterisitcs for Hyperbolic PDEs - IILecture 39 - Finite Difference Approximations to 1st order Hyperbolic PDEsLecture 40 - Summary, Appendices, Remarks



www.digimat.in

NPTEL Video Course - Mathematics - Optimization

Subject Co-ordinator - Prof. A. Goswami, Dr. Debjani Chakraborty



Lecture 1 - Optimization - IntroductionLecture 2 - Formulation of LPPLecture 3 - Geometry of LPP and Graphical Solution of LPPLecture 4 - Solution of LPPLecture 5 - Big - M MethodLecture 6 - Two - Phase MethodLecture 7 - Special Cases in Simple ApplicationsLecture 8 - Introduction to Duality TheoryLecture 9 - Dual Simplex MethodLecture 10 - Post Optimaility AnalysisLecture 11 - Integer Programming - ILecture 12 - Integer Programming - IILecture 13 - Introduction to Transportation ProblemsLecture 14 - Solving Various types of Transportation ProblemsLecture 15 - Assignment ProblemsLecture 16 - Project ManagementLecture 17 - Critical Path AnalysisLecture 18 - PERTLecture 19 - Shortest Path AlgorithmLecture 20 - Travelling Salesman ProblemLecture 21 - Classical optimization techniquesLecture 22 - Unconstarined multivariable optimizationLecture 23 - Nonlinear programming with equality constraintLecture 24 - Nonlinear programming KKT conditionsLecture 25 - Numerical optimizationLecture 26 - Numerical optimizationLecture 27 - Fibonacci MethodLecture 28 - Golden Section MethodsLecture 29 - Interpolation Methods



www.digimat.in

Lecture 30 - Unconstarined optimization techniquesLecture 31 - Unconstarined optimization techniquesLecture 32 - Nonlinear programmingLecture 33 - Interior and Exterior penulty Function MethodLecture 34 - Separable Programming ProblemLecture 35 - Introduction to Geometric ProgrammingLecture 36 - Constrained Geometric Programming ProblemLecture 37 - Dynamic Programming ProblemLecture 38 - Dynamic Programming Problem (Continued.)Lecture 39 - Multi Objective Decision MakingLecture 40 - Multi attribute decision making



www.digimat.in

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


Lecture 1 - General IntroductionLecture 2 - ExamplesLecture 3 - Examples (Continued - I)Lecture 4 - Examples (Continued - II)Lecture 5 - Linear AlgebraLecture 6 - Linear Algebra (Continued - I)Lecture 7 - Linear Algebra (Continued - II)Lecture 8 - AnalysisLecture 9 - Analysis (Continued...)Lecture 10 - First Order Linear EquationsLecture 11 - Exact EquationsLecture 12 - Second Order Linear EquationsLecture 13 - Second Order Linear Equations (Continued - I)Lecture 14 - Second Order Linear Equations (Continued - II)Lecture 15 - Well-posedness and Examples of IVPLecture 16 - Gronwall's LemmaLecture 17 - Basic Lemma and Uniqueness TheoremLecture 18 - Picard's Existence and Uniqueness TheoremLecture 19 - Picard's Existence and Uniqueness (Continued...)Lecture 20 - Cauchy Peano Existence TheoremLecture 21 - Existence using Fixed Point TheoremLecture 22 - Continuation of SolutionsLecture 23 - Series SolutionLecture 24 - General System and DiagonalizabilityLecture 25 - 2 by 2 systems and Phase Plane AnalysisLecture 26 - 2 by 2 systems and Phase Plane Analysis (Continued...)Lecture 27 - General SystemsLecture 28 - General Systems (Continued...) and Non-homogeneous SystemsLecture 29 - Basic Definitions and Examples



www.digimat.in

Lecture 30 - Stability Equilibrium PointsLecture 31 - Stability Equilibrium Points (Continued - I)Lecture 32 - Stability Equilibrium Points (Continued - II)Lecture 33 - Second Order Linear Equations (Continued - III)Lecture 34 - Lyapunov FunctionLecture 35 - Lyapunov Function (Continued...)Lecture 36 - Periodic Orbits and Poincare Bendixon TheoryLecture 37 - Periodic Orbits and Poincare Bendixon Theory (Continued...)Lecture 38 - Linear Second Order EquationsLecture 39 - General Second Order EquationsLecture 40 - General Second Order Equations (Continued...)



www.digimat.in

NPTEL Video Course - Mathematics - Probability and Statistics

Subject Co-ordinator - Prof. Somesh Kumar



Lecture 1 - Algebra of Sets - ILecture 2 - Algebra of Sets - IILecture 3 - Introduction to ProbabilityLecture 4 - Laws of Probability - ILecture 5 - Laws of Probability - IILecture 6 - Problems in ProbabilityLecture 7 - Random VariablesLecture 8 - Probability DistributionsLecture 9 - Characteristics of DistributionLecture 10 - Special Distributions - ILecture 11 - Special Distributions - IILecture 12 - Special Distributions - IIILecture 13 - Special Distributions - IVLecture 14 - Special Distributions - VLecture 15 - Special Distributions - VILecture 16 - Special Distributions - VIILecture 17 - Functions of a Random VariableLecture 18 - Joint Distributions - ILecture 19 - Joint Distributions - IILecture 20 - Joint Distributions - IIILecture 21 - Joint Distributions - IVLecture 22 - Transformations of Random VectorsLecture 23 - Sampling Distributions - ILecture 24 - Sampling Distributions - IILecture 25 - Descriptive Statistics - ILecture 26 - Descriptive Statistics - IILecture 27 - Estimation - ILecture 28 - Estimation - IILecture 29 - Estimation - III



www.digimat.in

Lecture 30 - Estimation - IVLecture 31 - Estimation - VLecture 32 - Estimation - VILecture 33 - Testing of Hypothesis - ILecture 34 - Testing of Hypothesis - IILecture 35 - Testing of Hypothesis - IIILecture 36 - Testing of Hypothesis - IVLecture 37 - Testing of Hypothesis - VLecture 38 - Testing of Hypothesis - VILecture 39 - Testing of Hypothesis - VIILecture 40 - Testing of Hypothesis - VIII



www.digimat.in

NPTEL Video Course - Mathematics - Probability Theory and Applications

Subject Co-ordinator - Prof. Prabha Sharma



Lecture 1 - Basic principles of countingLecture 2 - Sample space, events, axioms of probabilityLecture 3 - Conditional probability, Independence of eventsLecture 4 - Random variables, cumulative density function, expected valueLecture 5 - Discrete random variables and their distributionsLecture 6 - Discrete random variables and their distributionsLecture 7 - Discrete random variables and their distributionsLecture 8 - Continuous random variables and their distributionsLecture 9 - Continuous random variables and their distributionsLecture 10 - Continuous random variables and their distributionsLecture 11 - Function of random variables, Momement generating functionLecture 12 - Jointly distributed random variables, Independent r. v. and their sumsLecture 13 - Independent r. v. and their sumsLecture 14 - Chi â�� square r. v., sums of independent normal r. v., Conditional distrLecture 15 - Conditional disti, Joint distr. of functions of r. v., Order statisticsLecture 16 - Order statistics, Covariance and correlationLecture 17 - Covariance, Correlation, Cauchy- Schwarz inequalities, Conditional expectationLecture 18 - Conditional expectation, Best linear predictorLecture 19 - Inequalities and boundsLecture 20 - Convergence and limit theoremsLecture 21 - Central limit theoremLecture 22 - Applications of central limit theoremLecture 23 - Strong law of large numbers, Joint mgfLecture 24 - ConvolutionsLecture 25 - Stochastic processesLecture 26 - Transition and state probabilitiesLecture 27 - State prob., First passage and First return probLecture 28 - First passage and First return prob. Classification of statesLecture 29 - Random walk, periodic and null states



www.digimat.in

Lecture 30 - Reducible Markov chainsLecture 31 - Time reversible Markov chainsLecture 32 - Poisson ProcessesLecture 33 - Inter-arrival times, Properties of Poisson processesLecture 34 - Queuing ModelsLecture 35 - Analysis of L, Lq ,W and Wq , M/M/S modelLecture 36 - M/M/S , M/M/I/K modelsLecture 37 - M/M/I/K and M/M/S/K modelsLecture 38 - Application to reliability theory failure lawLecture 39 - Exponential failure law, Weibull lawLecture 40 - Reliability of systems



www.digimat.in

NPTEL Video Course - Mathematics - Real Analysis

Subject Co-ordinator - Prof. S.H. Kulkarni



Lecture 1 - IntroductionLecture 2 - Functions and RelationsLecture 3 - Finite and Infinite SetsLecture 4 - Countable SetsLecture 5 - Uncountable Sets, Cardinal NumberLecture 6 - Real Number SystemLecture 7 - LUB AxiomLecture 8 - Sequences of Real NumbersLecture 9 - Sequences of Real Numbers - (Continued.)Lecture 10 - Sequences of Real Numbers - (Continued.)Lecture 11 - Infinite Series of Real NumbersLecture 12 - Series of nonnegative Real NumbersLecture 13 - Conditional ConvergenceLecture 14 - Metric SpacesLecture 15 - Metric SpacesLecture 16 - Balls and SpheresLecture 17 - Open SetsLecture 18 - Closure Points, Limit Points and isolated PointsLecture 19 - Closed setsLecture 20 - Sequences in Metric SpacesLecture 21 - CompletenessLecture 22 - Baire Category TheoremLecture 23 - Limit and Continuity of a Function defined on a Metric spaceLecture 24 - Continuous Functions on a Metric SpaceLecture 25 - Uniform ContinuityLecture 26 - ConnectednessLecture 27 - Connected SetsLecture 28 - CompactnessLecture 29 - Compactness (Continued.)



www.digimat.in

Lecture 30 - Characterizations of Compact SetsLecture 31 - Continuous Functions on Compact SetsLecture 32 - Types of DiscontinuityLecture 33 - DifferentiationLecture 34 - Mean Value TheoremsLecture 35 - Mean Value Theorems (Continued.)Lecture 36 - Taylor's TheoremLecture 37 - Differentiation of Vector Valued FunctionsLecture 38 - IntegrationLecture 39 - IntegrabilityLecture 40 - Integrable FunctionsLecture 41 - Integrable Functions (Continued.)Lecture 42 - Integration as a Limit of SumLecture 43 - Integration and DifferentiationLecture 44 - Integration of Vector Valued FunctionsLecture 45 - More Theorems on IntegralsLecture 46 - Sequences and Series of FunctionsLecture 47 - Uniform ConvergenceLecture 48 - Uniform Convergence and IntegrationLecture 49 - Uniform Convergence and DifferentiationLecture 50 - Construction of Everywhere Continuous Nowhere Differentiable FunctionLecture 51 - Approximation of a Continuous Function by PolynomialsLecture 52 - Equicontinuous family of Functions



www.digimat.in

NPTEL Video Course - Mathematics - Regression Analysis

Subject Co-ordinator - Dr. Soumen Maity



Lecture 1 - Simple Linear RegressionLecture 2 - Simple Linear Regression (Continued...1)Lecture 3 - Simple Linear Regression (Continued...2)Lecture 4 - Simple Linear Regression (Continued...3)Lecture 5 - Simple Linear Regression (Continued...4)Lecture 6 - Multiple Linear RegressionLecture 7 - Multiple Linear Regression (Continued...1)Lecture 8 - Multiple Linear Regression (Continued...2)Lecture 9 - Multiple Linear Regression (Continued...3)Lecture 10 - Selecting the BEST Regression modelLecture 11 - Selecting the BEST Regression model (Continued...1)Lecture 12 - Selecting the BEST Regression model (Continued...2)Lecture 13 - Selecting the BEST Regression model (Continued...3)Lecture 14 - MulticollinearityLecture 15 - Multicollinearity (Continued...1)Lecture 16 - Multicollinearity (Continued...2)Lecture 17 - Model Adequacy CheckingLecture 18 - Model Adequacy Checking (Continued...1)Lecture 19 - Model Adequacy Checking (Continued...2)Lecture 20 - Test for Influential ObservationsLecture 21 - Transformations and Weighting to correct model inadequaciesLecture 22 - Transformations and Weighting to correct model inadequacies (Continued...1)Lecture 23 - Transformations and Weighting to correct model inadequacies (Continued...2)Lecture 24 - Dummy VariablesLecture 25 - Dummy Variables (Continued...1)Lecture 26 - Dummy Variables (Continued...2)Lecture 27 - Polynomial Regression ModelsLecture 28 - Polynomial Regression Models (Continued...1)Lecture 29 - Polynomial Regression Models (Continued...2)



www.digimat.in

Lecture 30 - Generalized Linear ModelsLecture 31 - Generalized Linear Models (Continued.)Lecture 32 - Non-Linear EstimationLecture 33 - Regression Models with Autocorrelated ErrorsLecture 34 - Regression Models with Autocorrelated Errors (Continued.)Lecture 35 - Measurement Errors & Calibration ProblemLecture 36 - Tutorial - ILecture 37 - Tutorial - IILecture 38 - Tutorial - IIILecture 39 - Tutorial - IVLecture 40 - Tutorial - V



www.digimat.in

NPTEL Video Course - Mathematics - Statistical Inference

Subject Co-ordinator - Prof. Somesh Kumar



Lecture 1 - Introduction and MotivationLecture 2 - Basic Concepts of Point Estimations - ILecture 3 - Basic Concepts of Point Estimations - IILecture 4 - Finding Estimators - ILecture 5 - Finding Estimators - IILecture 6 - Finding Estimators - IIILecture 7 - Properties of MLEsLecture 8 - Lower Bounds for Variance - ILecture 9 - Lower Bounds for Variance - IILecture 10 - Lower Bounds for Variance - IIILecture 11 - Lower Bounds for Variance - IVLecture 12 - SufficiencyLecture 13 - Sufficiency and InformationLecture 14 - Minimal Sufficiency, CompletenessLecture 15 - UMVU Estimation, AncillarityLecture 16 - Invariance - ILecture 17 - Invariance - IILecture 18 - Bayes and Minimax Estimation - ILecture 19 - Bayes and Minimax Estimation - IILecture 20 - Bayes and Minimax Estimation - IIILecture 21 - Testing of HypothesesLecture 22 - Neyman Pearson Fundamental LemmaLecture 23 - Applications of NP lemmaLecture 24 - UMP TestsLecture 25 - UMP Tests (Continued.)Lecture 26 - UMP Unbiased TestsLecture 27 - UMP Unbiased Tests (Continued.)Lecture 28 - UMP Unbiased TestsLecture 29 - Unbiased Tests for Normal Populations



www.digimat.in

Lecture 30 - Unbiased Tests for Normal Populations (Continued.)Lecture 31 - Likelihood Ratio Tests - ILecture 32 - Likelihood Ratio Tests - IILecture 33 - Likelihood Ratio Tests - IIILecture 34 - Likelihood Ratio Tests - IVLecture 35 - Invariant TestsLecture 36 - Test for Goodness of FitLecture 37 - Sequential ProcedureLecture 38 - Sequential Procedure (Continued.)Lecture 39 - Confidence IntervalsLecture 40 - Confidence Intervals (Continued.)



www.digimat.in

NPTEL Video Course - Mathematics - Stochastic Processes

Subject Co-ordinator - Dr. S. Dharmaraja

Co-ordinating Institute - IIT - Delhi


Lecture 1 - Introduction to Stochastic ProcessesLecture 2 - Introduction to Stochastic Processes (Continued.)Lecture 3 - Problems in Random Variables and DistributionsLecture 4 - Problems in Sequences of Random VariablesLecture 5 - Definition, Classification and ExamplesLecture 6 - Simple Stochastic ProcessesLecture 7 - Stationary ProcessesLecture 8 - Autoregressive ProcessesLecture 9 - Introduction, Definition and Transition Probability MatrixLecture 10 - Chapman-Kolmogrov EquationsLecture 11 - Classification of States and Limiting DistributionsLecture 12 - Limiting and Stationary DistributionsLecture 13 - Limiting Distributions, Ergodicity and Stationary DistributionsLecture 14 - Time Reversible Markov Chain, Application of Irreducible Markov Chain in Queueing ModelsLecture 15 - Reducible Markov ChainsLecture 16 - Definition, Kolmogrov Differential Equations and Infinitesimal Generator MatrixLecture 17 - Limiting and Stationary Distributions, Birth Death ProcessesLecture 18 - Poisson ProcessesLecture 19 - M/M/1 Queueing ModelLecture 20 - Simple Markovian Queueing ModelsLecture 21 - Queueing NetworksLecture 22 - Communication SystemsLecture 23 - Stochastic Petri NetsLecture 24 - Conditional Expectation and FiltrationLecture 25 - Definition and Simple ExamplesLecture 26 - Definition and PropertiesLecture 27 - Processes Derived from Brownian MotionLecture 28 - Stochastic Differential EquationsLecture 29 - Ito Integrals



www.digimat.in

Lecture 30 - Ito Formula and its VariantsLecture 31 - Some Important SDE`s and Their SolutionsLecture 32 - Renewal Function and Renewal EquationLecture 33 - Generalized Renewal Processes and Renewal Limit TheoremsLecture 34 - Markov Renewal and Markov Regenerative ProcessesLecture 35 - Non Markovian QueuesLecture 36 - Non Markovian Queues Cont,,Lecture 37 - Application of Markov Regenerative ProcessesLecture 38 - Galton-Watson ProcessLecture 39 - Markovian Branching Process



www.digimat.in

mathematics n p t e l national programme on technology … · n p t e l national programme on...

Documents