 Mathematical Physics

# Mathematical Physics ## CSIR NET 2020 Syllabus

• Fourier series, Fourier and Laplace transform.
• Vector algebra and vector calculus. Linear algebra, matrices
• Elements of complex analysis, analytic functions;
• Linear ordinary differential equations of first & second order, Special functions (Hermite, Bessel, Laguerre and Legendre functions).
• Dimensional analysis.
• Vector algebra and vector calculus.
• Linear algebra, matrices,
• Cayley-Hamilton Theorem. Eigenvalues and eigenvectors.
• Taylor & Laurent series; poles, residues and evaluation of integrals.
• Elementary probability theory, random variables, binomial, Poisson and normal distributions.
• Central limit theorem.

## GATE 2020

• Linear vector space: basis, orthogonality and completeness;
• matrices; vector calculus; linear differential equations; elements of complex analysis:
• Cauchy- Riemann conditions, Cauchy’s theorems, singularities, residue theorem and applications;
• Laplace transforms, Fourier analysis;
• elementary ideas about tensors: covariant and contravariant tensor, Levi-Civita and Christoffel symbols.

## The Best Reference book for Mathematical Physics

### 1. Mathematical methods in physical sciences by M. L. Boas

(Recommendation for beginners )
Mathematical methods in physical sciences by M. L. Boas is one of the standards and thorough book and at the same time very easy to read.
I think it lacks Group Theory, but that's still not enough reason to not use the book extensively.

### 2. G.B Arfken,  H.J Weber and F.E. Harris Mathematical Methods for Physicists

It is neither too hard nor too simple as far a good book for beginners
Deep understanding of the mathematical concepts which are the cornerstone of modern physics and are considered essential for researchers and students interested in advance theoretical physics.

### 3. Mathematical Physics by H.K.Das

(Recommendation for Indian Students)
The textbook contains 49 chapters on all major topics in an exhaustive endeavour to cover syllabuses of all major universities

### 4. Mathematics of classical and quantum physics (Addison-Wesley series in advanced physics)

( Recommendation for the Advance learner )

### 5. A Guided Tour of Mathematical Methods for the Physical Sciences by Roel Snieder, Kasper van Wijk

(Recommendation for Competitive exam preparation)

This book provides a comprehensive tour of the mathematical knowledge and techniques that are needed by students across the physical sciences

### 6. Mathematical Methods for Physics and Engineering by Ken F. Riley, Mike P. Hobson, Stephen J. Bence

(Recommendation for Engineering Students )

The third edition of this highly acclaimed undergraduate textbook is suitable for teaching all the mathematics for an undergraduate course in any of the physical sciences 