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September 23, 2023

## Duration:

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**FREE**

## This course includes:

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### Description

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**)

### Course Curriculum

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

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