Mathematical Methods in Physics 2 9T7Y4MX156

URI	`m2://res/9T7Y4MX156`
Kind	course
Creators	Auditya Sharma (instructor)
Date	2021-07-09
Scope	in

Expressions

e1: edition

Language	en
Date	2021-07-09

m1: page, IISER Bhopal (record). nptel 111106152
m2: page, 2021-07-09 (record). nptel 111106152

Contents

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

Catalogue records

nptel: 111106152 (manifestation)
nptel_video: 111106152 (manifestation)