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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 03 - Span, Linear Combination of Vectors

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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.)