NOC:Mathematical Methods in Physics 1

Lecture 1 - Vectors

Lecture 2 - Linear vector spaces

Lecture 3 - Linear vector spaces: immediate consequences

Lecture 4 - Dot product of Euclidean vectors

Lecture 5 - Inner product on a Linear vector space

Lecture 6 - Cauchy-Schwartz inequality for Euclidean vectors

Lecture 7 - Cauchy-Schwartz inequality for vectors from LVS

Lecture 8 - Applications of the Cauchy-Schwartz inequality

Lecture 9 - Triangle inequality

Lecture 10 - Linear dependence and independence of vectors

Lecture 11 - Row reduction of matrices

Lecture 12 - Rank of a matrix

Lecture 13 - Rank of a matrix: consequences

Lecture 14 - Determinants and their properties

Lecture 15 - The rank of a matrix using determinants

Lecture 16 - Cramer's rule

Lecture 17 - Square system of equations

Lecture 18 - Homogeneous equations

Lecture 19 - The rank of a matrix and linear dependence

Lecture 20 - Span, basis, and dimension of a LVS

Lecture 21 - Gram-Schmidt orthogonalization

Lecture 22 - Vector subspaces

Lecture 23 - Linear operators

Lecture 24 - Inverse of an operator

Lecture 25 - Adjoint of an operator

Lecture 26 - Projection operators

Lecture 27 - Eigenvalues and Eigenvectors

Lecture 28 - Hermitian operators

Lecture 29 - Unitary operators

Lecture 30 - Normal operators

Lecture 31 - Similarity and Unitary transformations

Lecture 32 - Matrix representations

Lecture 33 - Eigenvalues and Eigenvectors of matrices

Lecture 34 - Defective matrices

Lecture 35 - Eigenvalues and eigenvectors: useful results

Lecture 36 - Transformation of Basis

Lecture 37 - A class of invertible matrices

Lecture 38 - Diagonalization of matrices

Lecture 39 - Diagonalizability of matrices

Lecture 40 - Functions of matrices

Lecture 41 - SHM and waves

Lecture 42 - Periodic functions

Lecture 43 - Average value of a function

Lecture 44 - Piecewise continuous functions

Lecture 45 - Orthogonal basis: Fourier series

Lecture 46 - Fourier coefficients

Lecture 47 - Dirichlet Conditions

Lecture 48 - Complex Form of Fourier Series

Lecture 49 - Other intervals: arbitrary period

Lecture 50 - Even and Odd Functions

Lecture 51 - Differentiating Fourier series

Lecture 52 - Parseval's theorem

Lecture 53 - Fourier series to Fourier transforms

Lecture 54 - Fourier Sine and Cosine transforms

Lecture 55 - Parseval's theorem for Fourier series

Lecture 56 - Ordinary Differential equations

Lecture 57 - First order ODEs

Lecture 58 - Linear first order ODEs

Lecture 59 - Orthogonal Trajectories

Lecture 60 - Exact differential equations

Lecture 61 - Special first order ODEs

Lecture 62 - Solutions of linear first-order ODEs

Lecture 63 - Revisit linear first-order ODEs

Lecture 64 - ODEs in disguise

Lecture 65 - 2nd order Homogeneous linear equations with constant coefficients

Lecture 66 - The use of a known solution to find another

Lecture 67 - An alternate approach to auxiliary equation

Lecture 68 - Inhomogeneous second order equations

Lecture 69 - Methods to find a Particular solution

Lecture 70 - Successive Integration of two first order equations

Lecture 71 - Illustrative examples

Lecture 72 - Variation of Parameters

Lecture 73 - Vibrations in mechanical systems

Lecture 74 - Forced Vibrations

Lecture 75 - Resonance

Lecture 76 - Linear Superposition

Lecture 77 - Laplace Transform (LT)

Lecture 78 - Basic Properties of Laplace Transforms

Lecture 79 - Step functions, Translations, and Periodic functions

Lecture 80 - The Inverse Laplace Transform

Lecture 81 - Convolution of functions

Lecture 82 - Solving ODEs using Laplace transforms

Lecture 83 - The Dirac Delta function

Lecture 84 - Properties of the Dirac Delta function

Lecture 85 - Green's function method

Lecture 86 - Green's function method: Boundary value problem

Lecture 87 - Power series method

Lecture 88 - Power series solutions about an ordinary point

Lecture 89 - Initial value problem: power series solution

Lecture 90 - Frobenius method for regular singular points