Media Storage Type : 32 GB USB Stick
NPTEL Subject Matter Expert : Prof. Auditya Sharma
NPTEL Co-ordinating Institute : IISER Bhopal
NPTEL Lecture Count : 80
NPTEL Course Size : 4.6 GB
NPTEL PDF Text Transcription : Available and Included
NPTEL Subtitle Transcription : Available and Included (SRT)
Lecture Titles:
Lecture 1 - Introduction to complex numbers
Lecture 2 - The triangle inequality
Lecture 3 - The de Moivre formula
Lecture 4 - Roots of unity
Lecture 5 - Functions of a complex variable and the notion of continuity
Lecture 6 - Derivative of a complex function
Lecture 7 - Differentiation rules for a complex function
Lecture 8 - Cauchy-Riemann Equations
Lecture 9 - Sufficient conditions for differentiability
Lecture 10 - Cauchy-Riemann conditions in polar coordinates
Lecture 11 - More persepective on differentiability
Lecture 12 - The value of the derivative
Lecture 13 - Analytic functions
Lecture 14 - Harmonic functions
Lecture 15 - The exponential function
Lecture 16 - Complex logarithm
Lecture 17 - Complex exponents
Lecture 18 - Trigonometric functions of complex variables
Lecture 19 - Hyperbolic functions of complex variables
Lecture 20 - Inverse Trigonometric and Hyperbolic functions
Lecture 21 - Branch of a multivalued function
Lecture 22 - Contour Integrals
Lecture 23 - Green's Theorem
Lecture 24 - Path dependence of the contour intergal
Lecture 25 - Antiderivatives
Lecture 26 - The Cauchy theorem
Lecture 27 - Crossing contours and multiply connected domains
Lecture 28 - Cauchy Integral formula
Lecture 29 - Derivatives of an analytic function
Lecture 30 - Liouville's theorem and the Fundamental theorem of algebra
Lecture 31 - Taylor Series
Lecture 32 - Laurent Series
Lecture 33 - Convergence
Lecture 34 - Differentiation and integration of power series
Lecture 35 - Isolated Singularities
Lecture 36 - Residues
Lecture 37 - Residue Theorem
Lecture 38 - Evaluation of integrals - I
Lecture 39 - Evaluation of integrals - II
Lecture 40 - Analytic Continuation
Lecture 41 - Introduction of orthogonal polynomials
Lecture 42 - How to construct orthogonal polynomials
Lecture 43 - The weight function
Lecture 44 - Recursion relations
Lecture 45 - Differential equation satisfied by the orthogonal polynomials
Lecture 46 - Hermite polynomials
Lecture 47 - Properties of Hemite polynomials
Lecture 48 - Legendre polynomials
Lecture 49 - Legendre polynomials: recurrence relation
Lecture 50 - Differential equation corresponding to Legendre polynomials
Lecture 51 - The generating function corresponding to Legendre polynomials
Lecture 52 - Laguerre Polynomials
Lecture 53 - Laguerre Polynomials: recurrence relation
Lecture 54 - Laguerre polynomials: differential equation
Lecture 55 - Laguerre polynomials: generating function
Lecture 56 - Bessel functions: series defination
Lecture 57 - Bessel functions: recurrence relations
Lecture 58 - Bessel functions: differential equation
Lecture 59 - Bessel functions of integral order: generating function
Lecture 60 - Bessel functions: orthogonality
Lecture 61 - Classification of Second Order PDEs
Lecture 62 - Canonical Forms for Hyperbolic PDEs
Lecture 63 - Canonical Forms for Parabolic PDEs
Lecture 64 - Canonical Forms for Elliptic PDEs
Lecture 65 - Tha Laplace Equation
Lecture 66 - The Laplace Equation: Separation of Variables
Lecture 67 - The Laplace Equation: Dirichlet and Neumann boundary conditions
Lecture 68 - The Laplace Equation in Cartesian coordinates
Lecture 69 - The Laplace Equation for a 3-D rectangular box
Lecture 70 - The Laplace Equation in spherical coordinates
Lecture 71 - The Laplace Equation in Spherical Coordinates: Solution
Lecture 72 - The Laplace Equation in Spherical Coordinates: illustrative examples
Lecture 73 - The Poisson's Equation: Green's function solution
Lecture 74 - The heat equation: a heuristic discussion
Lecture 75 - From the random walk to the diffusion equation
Lecture 76 - Solution of the Diffusion equation
Lecture 77 - The Diffusion equation with Dirichlet and Neumann boundary conditions
Lecture 78 - The Heat equation: illustrative examples
Lecture 79 - The Wave equation: Method of characteristics
Lecture 80 - The Wave equation: Separation of variables