# InfoCoBuild

## 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 44 - Cauchy's Integral Formula

Go to the Course Home or watch other lectures:

 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.)