Mathematical Methods in Physics I
Mathematical Methods in Physics I. Instructor: Prof. Samudra Roy, Department of Physics, IIT Kharagpur. This is a basic course in physics for M.Sc (and/or B.Sc 3rd year) students which provides an overview of the essential mathematical methods used in different branches of physics. This course is mainly divided into two parts. Students in 3rd year B.Sc or 1st year M.Sc are encouraged to take this course. All the assignments and the final examination will be of objective type.
(from nptel.ac.in )

Lecture 32 - Roots of a Complex Number
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Lecture 01 - Set, Group, Field, Ring
Lecture 02 - Vector Space
Lecture 03 - Span, Linear Combination of Vectors
Lecture 04 - Linearly Dependent and Independent Vector, Basis
Lecture 05 - Dual Space
Lecture 06 - Inner Product
Lecture 07 - Schwarz Inequality
Lecture 08 - Inner Product Space, Gram-Schmidt Ortho-nomalization
Lecture 09 - Projection Operator
Lecture 10 - Transformation of Basis
Lecture 11 - Transformation of Basis (cont.)
Lecture 12 - Unitary Transformation, Similarity Transformation
Lecture 13 - Eigenvalue, Eigenvectors
Lecture 14 - Normal Matrix
Lecture 15 - Diagonalization of a Matrix
Lecture 16 - Hermitian Matrix
Lecture 17 - Rank of a Matrix
Lecture 18 - Cayley-Hamilton Theorem, Function Space
Lecture 19 - Metric Space, Linearly Dependent-Independent Functions
Lecture 20 - Linearly Dependent-Independent Functions (cont.), Inner Product of Functions
Lecture 21 - Orthogonal Functions
Lecture 22 - Delta Function, Completeness
Lecture 23 - Fourier Series
Lecture 24 - Fourier Series (cont.)
Lecture 25 - Parseval Theorem, Fourier Transform
Lecture 26 - Parseval Relation, Convolution Theorem
Lecture 27 - Polynomial Space, Legendre Polynomial
Lecture 28 - Monomial Basis, Factorial Basis, Legendre Basis
Lecture 29 - Complex Numbers
Lecture 30 - Geometrical Interpretation of Complex Numbers
Lecture 31 - de Moivre's Theorem
Lecture 32 - Roots of a Complex Number
Lecture 33 - Set of Complex Number, Stereographic Projection
Lecture 34 - Complex Function, Concept of Limit
Lecture 35 - Derivative of Complex Function, Cauchy-Riemann Equation
Lecture 36 - Analytic Function
Lecture 37 - Harmonic Conjugate
Lecture 38 - Polar Form of Cauchy-Riemann Equation
Lecture 39 - Multi-valued Function and Branches
Lecture 40 - Complex Line Integration, Contour, Regions
Lecture 41 - Complex Line Integration (cont.)
Lecture 42 - Cauchy-Goursat Theorem
Lecture 43 - Application of Cauchy-Goursat Theorem
Lecture 44 - Cauchy's Integral Formula
Lecture 45 - Cauchy's Integral Formula (cont.)
Lecture 46 - Series and Sequence
Lecture 47 - Series and Sequence (cont.)
Lecture 48 - Circle and Radius of Convergence
Lecture 49 - Taylor Series
Lecture 50 - Classification of Singularity
Lecture 51 - Laurent Series, Singularity
Lecture 52 - Laurent Series Expansion
Lecture 53 - Laurent Series Expansion (cont.), Concept of Residue
Lecture 54 - Classification of Residue
Lecture 55 - Calculation of Residue for Quotient From
Lecture 56 - Cauchy's Residue Theorem
Lecture 57 - Cauchy's Residue Theorem (cont.)
Lecture 58 - Real Integration using Cauchy's Residue Theorem
Lecture 59 - Real Integration using Cauchy's Residue Theorem (cont.)
Lecture 60 - Real Integration using Cauchy's Residue Theorem (cont.)