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Course Co-ordinated by IIT Kharagpur
Coordinators
 
Prof. Samudra Roy
IIT Kharagpur

 

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Mathematical Methods in Physics- I 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. In the first part, we learn different aspects of the linear vector space which is the essential mathematical tool for quantum mechanics and can be applicable for many physical systems outside the domain of quantum mechanics. In the second part, we cover complex analysis whose general application is vast. 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
Week

Topics

1.

Concept of Set, Binary composition, Group, Ring, Field, Vector Space, Examples of vector space in Euclidean space (•’3), Metric Space

2.

Linearly dependent & independent vectors, Dimensions, Basis, Span, Linear Functional, Dual space, Inner Product, Normed Space, Schwarz inequality, Gram-Schmidt orthonormalization, Completeness

3.

Linear Operator, Matrix representation, Transformation of axis, Change of Basis, Unitary transformation, Similarity transformation, Eigen value & Eigen vectors, Matrix decomposition

4.

Elementary Matrices,Rank, Subspace with examples. Diagonalization of matrix, The Cayley-Hamilton theorem, Function, mapping, Function space, Linearly dependent & independent function, Examples, Wronskian, Gram-determinant

B.Sc,M.Sc,

1. Matrices and Tensors in Physics by A.W Joshi
2. Mathematical Methods for Physicists by G. Arfken
3. Mathematical Methods for Physics by J. Mathews & R.L Walker
4. Mathematics for Physicists by P. Dennery & A. Krzywicki
5. Mathematics for Quantum Mechanics by J.D Jackson
6. Vector space and Matrix in Physics by M.C Jain
7. A first course in Complex Analysis by D.G. Zill & P.D. Shanahan
8. Complex Variable (Schaums Series) By M.R Spiegel
9. Complex Variable and Application by R.V Churchill and J.W Brown
10. Mathematical Methods in the Physical Sciences by M.L.Boas

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