# 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.