Media Storage Type : DVD-ROM
NPTEL Course Name : Mathematics - III
NPTEL Subject Matter Expert : Dr. M. Guru Prem Prasad
NPTEL Co-ordinating Institute : IIT Guwahati
NPTEL Lecture Count : 107
Lecture Titles:
Lecture 1 - Motivation
Lecture 2 - Definition and Geometric Interpretation
Lecture 3 - Algebraic Operations
Lecture 4 - Bilinear form
Lecture 5 - Conjugate of a Complex Number
Lecture 6 - Modulus of a Complex Number
Lecture 7 - Polar form
Lecture 8 - Exponential form
Lecture 9 - Powers of Complex Numbers
Lecture 10 - Planar Sets
Lecture 11 - Complex Functions
Lecture 12 - Limits
Lecture 13 - Continuity
Lecture 14 - Differentiability
Lecture 15 - Analytic Functions
Lecture 16 - Exponential Function
Lecture 17 - Trigonometric Functions
Lecture 18 - Logarithmic Functions
Lecture 19 - Integration of f:[a,b] -- C
Lecture 20 - Curves
Lecture 21 - Line Integrals
Lecture 22 - Antiderivatives
Lecture 23 - Cauchy-Goursat Theorem
Lecture 24 - Cauchy's Integral Formula
Lecture 25 - Other Important Theorem
Lecture 26 - Introduction
Lecture 27 - Power Series
Lecture 28 - Taylors Series and Analytic Functions
Lecture 29 - Power Series of F(z)
Lecture 30 - Laurent Series
Lecture 31 - Zeros
Lecture 32 - Singularites
Lecture 33 - Residues
Lecture 34 - Residue Theorem
Lecture 35 - Argument Principle
Lecture 36 - Rouche's Theorem
Lecture 37 - Definite Integral of Trigonometric Function
Lecture 38 - Improper Integrals of Real Functions
Lecture 39 - Improper Integrals of Certain Functions
Lecture 40 - Improper Integrals of Rational Functions
Lecture 41 - Indented Contour Integration
Lecture 42 - Inverse Laplace Transform
Lecture 43 - Conformal Mappings
Lecture 44 - Riemann Mapping Theorem
Lecture 45 - Mobius Transform
Lecture 46 - Basics from Linear Algebra (Basic Definitions)
Lecture 47 - Fourier series
Lecture 48 - Pointwise convergence of Fourier series
Lecture 49 - Uniform convergence of Fourier series
Lecture 50 - Bessel's Inequality and Parseval's Identity
Lecture 51 - Complex Form of Fourier Series
Lecture 52 - Half Range Series
Lecture 53 - Partial Differential Equation - An Introduction
Lecture 54 - Formulation of second order PDE
Lecture 55 - Type Of PDEs
Lecture 56 - Classification of second order PDE
Lecture 57 - Canonical forms
Lecture 58 - Canonical Forms for Hyperbolic Type Equations
Lecture 59 - Canonical form for Parabolic Type Equations
Lecture 60 - Canonical Form for Elliptic Type Equations
Lecture 61 - Transverse vibration of a string
Lecture 62 - Solution of one-dimensional wave equation by the reduction to its canonical form
Lecture 63 - Initial Value Problem (IVP)
Lecture 64 - Solutions of the Non-Homogeneous Wave Equation
Lecture 65 - Solution of non-homogeneous wave equation
Lecture 66 - Separation of variables method
Lecture 67 - Derivation of heat equation
Lecture 68 - Boundary conditions
Lecture 69 - Initial Boundary Value Problem
Lecture 70 - Transforming nonhomogeneous boundary conditions to homogeneous ones
Lecture 71 - Derivation of Laplace Equation
Lecture 72 - Properties of Harmonic functions
Lecture 73 - Elliptic Equation in Different Coordinate Systems
Lecture 74 - Separation of Variables
Lecture 75 - Dirichlet problem for a circle
Lecture 76 - Interior Dirichlet problem
Lecture 77 - Exterior Dirichlet problem
Lecture 78 - Laplace equation in cylindrical coordinates
Lecture 79 - Laplace equation in spherical coordinates
Lecture 80 - Fourier Integral Representation
Lecture 81 - Fourier Transform and Inverse Fourier Transform
Lecture 82 - Properties of Fourier Transform
Lecture 83 - Application of Fourier Transform
Lecture 84 - Fourier Cosine and Sine Transform
Lecture 85 - Properties of Cosine and Sine Transform
Lecture 86 - Application of Cosine and Sine Transforms to solve PDEs
Lecture 87 - Laplace Transform and its Properties
Lecture 88 - Inverse Laplace Transform and its Properties
Lecture 89 - Convolution
Lecture 90 - Applications of Laplace transform
Lecture 91 - Assignment-Complex Numbers and Complex Algebra
Lecture 92 - Assignment-Complex Functions
Lecture 93 - Assignment-Elementary Analytic Function
Lecture 94 - Assignment-Complex Integration
Lecture 95 - Assignment-Power Series
Lecture 96 - Assignment-Zeros ,Singularities
Lecture 97 - Assignment-Application of Contour Integration
Lecture 98 - Assignment-Conformal Mappings and Applications
Lecture 99 - Assignment-Fourier Series
Lecture 100 - Assignment-Second Order PDE
Lecture 101 - Assignment-Wave Equation
Lecture 102 - Assignment-Heat Equation
Lecture 103 - Assignment-Laplace Equation
Lecture 104 - Exercise-fourier Transform
Lecture 105 - Exercise-Laplace Transform
Lecture 106 - Assignment-Fourier Transform
Lecture 107 - Assignment-Laplace Transform