Mathematical Methods in Physics 1 CGVQBB8RSE

URI	`m2://res/CGVQBB8RSE`
Kind	course
Creators	Auditya Sharma (instructor)
Date	2021-01-04
Scope	in

Expressions

e1: edition

Language	en
Date	2021-01-04

m1: page, IISER Bhopal (record). nptel 111106148
m2: page, 2021-01-04 (record). nptel 111106148

Contents

part 1: Week 1
session 1: Vectors
session 2: Linear vector spaces
session 3: Linear vector spaces: immediate consequences
session 4: Dot product of Euclidean vectors
session 5: Inner product on a Linear vector space
session 6: Cauchy-Schwartz inequality for Euclidean vectors
session 7: Cauchy-Schwartz inequality for vectors from LVS
session 8: Applications of the Cauchy-Schwartz inequality
session 9: Triangle inequality
session 10: Linear dependence and independence of vectors
session 11: Row reduction of matrices
session 12: Rank of a matrix
part 2: Week 2
session 13: Rank of a matrix: consequences
session 14: Determinants and their properties
session 15: The rank of a matrix using determinants
session 16: Cramer's rule
session 17: Square system of equations
session 18: Homogeneous equations
session 19: The rank of a matrix and linear dependence
session 20: Span, basis, and dimension of a LVS
session 21: Gram-Schmidt orthogonalization
session 22: Vector subspaces
session 23: Linear operators
session 24: Inverse of an operator
session 25: Adjoint of an operator
part 3: Week 3
session 26: Projection operators
session 27: Eigenvalues and Eigenvectors
session 28: Hermitian operators
session 29: Unitary operators
session 30: Normal operators
session 31: Similarity and Unitary transformations
session 32: Matrix representations
session 33: Eigenvalues and Eigenvectors of matrices
session 34: Defective matrices
session 35: Eigenvalues and eigenvectors: useful results
session 36: A class of invertible matrices
session 37: Diagonalization of matrices
session 38: Diagonalizability of matrices
session 39: Functions of matrices
part 4: Week 4
session 40: SHM and waves
session 41: Periodic functions
session 42: Average value of a function
session 43: Piecewise continuous functions
session 44: Orthogonal basis: Fourier series
session 45: Fourier coefficients
session 46: Dirichlet Conditions
session 47: Complex Form of Fourier Series
session 48: Other intervals: arbitrary period
session 49: Even and Odd Functions
session 50: Differentiating Fourier series
session 51: Parseval's theorem
session 52: Fourier series to Fourier transforms
session 53: Fourier Sine and Cosine transforms
session 54: Parseval's theorem for Fourier series
part 5: Week 5
session 55: Ordinary Differential equations
session 56: First order ODEs
session 57: Linear first order ODEs
session 58: Orthogonal Trajectories
session 59: Exact differential equations
session 60: Special first order ODEs
session 61: Solutions of linear first-order ODEs
session 62: Revisit linear first-order ODEs
session 63: ODEs in disguise
session 64: 2nd order Homogeneous linear equations with constant coefficients
session 65: The use of a known solution to find another
session 66: An alternate approach to auxiliary equation
part 6: Week 6
session 67: Inhomogeneous second order equations
session 68: Methods to find a Particular solution
session 69: Successive Integration of two first order equations
session 70: Illustrative examples.
session 71: Variation of Parameters
session 72: Vibrations in mechanical systems.
session 73: Forced Vibrations.
session 74: Resonance
session 75: Linear Superposition
part 7: Week 7
session 76: Laplace Transform (LT)
session 77: Basic Properties of Laplace Transforms
session 78: Step functions, Translations, and Periodic functions
session 79: The Inverse Laplace Transform
session 80: Convolution of functions
session 81: Solving ODEs using Laplace transforms
session 82: The Dirac Delta function
session 83: Properties of the Dirac Delta function
part 8: Week 8
session 84: Green's function method
session 85: Green's function method: Boundary value problem
session 86: Power series method
session 87: Power series solutions about an ordinary point
session 88: Initial value problem: power series solution
session 89: Frobenius method for regular singular points

Catalogue records

nptel: 111106148 (manifestation)
nptel_video: 111106148 (manifestation)