Methods of Mathematical PhysicsII: Course Outline (PHY321)
Course Outline
Fourier Series and Integral Transforms: Definition and general properties, Fourier Series of Various Physical Functions, Uses and Applications of Fourier Series, Fourier Transforms, Convolution Theorems, Laplace transforms and applications.
Tensor Analysis: Vector calculus (differentiation, integration, space curves, multivariable vectors, surfaces, scalar and vector fields, gradient, divergence and curl, cylindrical and spherical coordinates, general curvilinear coordinates), change of basis, Cartesian tensor as a geometrical object, order/rank of a tensor, tensor algebra, quotient law, pseudotensors, Kronecker delta and Levicevita, dual tensors, physical applications, integral theorems for tensors, nonCartesian tensors, general coordinate transformations and tensors.
Group Theory and Representations for finite groups: Transformations, groups – definitions and examples, subgroups and Cayley’s theorem, cosets and Lagrange’s theorem, conjugate classes, invariant subgroups, factor groups, homomorphism, direct products, mappings, linear operators, matrix representations, similarity transformation and equivalent matrix representations, group representations, equivalent representations and characters, construction of representations and addition of representations, invariance of functions and operators, unitary spaces and Hermitian matrices, operators: adjoint, selfadjoint, unitary, Hilbert space, reducibility of representations, Schur’s lemmas, orthogonality relations, group algebra, expansion of functions in basis of irreducible representations, Kronecker product, symmetrized and antisymmetrized representations, adjoint and complexconjugate representations, real representations
Text Books

Mathematical methods for physicists a comprehensive guide byCall Number: 515.02453 ARFISBN: 9789381269558
Reference books

Mathematical Methods for Physicists byCall Number: 530.15 CHOISBN: 0521652278Publication Date: 20000727

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ISBN 9781904602804
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