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