Vector algebra and vector calculus. Tensors.
2. Vector spaces
Linear algebra, matrices, Cayley-Hamilton Theorem. Eigenvalues and eigenvectors.
1. Vector and tensor analysis
3. Complex analysis
Elements of complex analysis, analytic functions; Taylor and Laurent series; poles, residues and evaluation of integrals.
4. Differential equations
Linear ordinary differential equations of first & second order, partial differential equations (Laplace, wave and heat equations in two and three dimensions).
5. Special functions
Hermite, Bessel, Laguerre and Legendre functions.
6. Transforms
Fourier series, Fourier and Laplace transforms.
7. Green’s function
8. Probability distributions
Elementary probability theory, random variables, binomial, Poisson and normal distributions. Central limit theorem.
9. Group theory
Introductory group theory: SU(2), O(3).
References
K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical methods for physics and engineering, Third Edition, Cambridge University Press.
George B. Arfken and Hans J. Weber, Mathematical Methods for Physicists: A Comprehensive Guide, Seventh Edition, Academic Press.
Michael Stone and Paul Goldbart, Mathematics for Physics: A Guided Tour for Graduate Students, Cambridge University Press.
Frederick W. Byron and Robert W. Fuller, The Mathematics of Classical and Quantum Physics, Dover.
James Ward Brown and Ruel V. Churchill, Complex Variables and Applications, Eighth Edition, McGraw-Hill Higher Education.
Assignments
Examinations