Contents
1. Vector space and matrices:
Vector space: Axiomatic definition, linear independence, bases, Gram-Schmidt orthogonalisation. Matrices: Introduction as representation of linear transformations; Eigenvalues and eigen-vectors; Commuting matrices with degenerate eigenvalues; Orthonormality of eigenvectors.
2. Complex analysis:
Complex numbers, triangular inequalities, Schwarz inequality. Function of a complex variable: limit and continuity; Differentiation, Cauchy-Riemann equations and their applications;Analytic and harmonic function; Classification of singularities, Branch point and branch cut;Complex integrals, Cauchy’s theorem and its converse, Cauchy’s Integral Formula; Taylor and Laurent expansion; Residue theorem and evaluation of some typical real integrals using this theorem.
3. Inhomogeneous differential equations:
Green’s functions
References:
1. Schaum's outline of theory and problems of complex variables with an introduction to conformal mapping and its applications - Murray R. Spiegel, McGraw-Hill.
2. Complex Analysis – L. V. Ahlfors - McGraw-Hill Education
3. Complex Variables and Applications - R V Churchill and J W Brown – Tata McGraw-Hill
4. Methods for Physicists - G. B. Arfken - Elsevier
5. Mathematical methods of Physics - Mathews and Walker - W. A. Benjamin
6. Mathematical Methods for Physicists an Engineers – K. F. Riley, M. P. Hobson and S. J. Bence - Cambridge University Press
7. Mathematics for Physicists - M L Boas - Wiley
8. Advanced Engineering Mathematics – E. Kreyszig - Wiley
9. Theory of functions of complex variables - Shanti Narayan - S. Chand
10. Differential equations –Simmons - McGraw-Hill
11. Group theory & its application to Physical Sciences - M. Hamermesh – Dover
12. Group theory for Physicists - A. W. Joshi – New Age
13. Higher Engineering Mathematics - B. S. Grewal - Routledge