PH 401: Mathematic al Physics

Syllabus​

Scalar and vector fields. Vector equations, Differentiations, gradient tangent plane, divergence and curl. Integrations, surface and volume integrals, Green, Gauss, and Stokes theorems and their applications. Transformations of coordinate systems and vector components, metric coefficients, curvilinear coordinate. Expressions for grad. div. and curl. Helmholtz eqn in three dimensions and separation of variables in various coordinate systems. Matrices and determinants. Linear equations of homogenous and inhomogenous types. Linear vector spaces. Scalar product. Linear independence, Change of basis. Schmidt orthogonalisation. Special matrices. Bilinear and quadratic forms. Eigenvalues and Eigenvectors. Transformation of matrices, diagonalization, orthogonal and unitary transformations. Functions of a complex variable, limit, continuity, analytic function, Cauchy formula, Laurent series, isolated and essential singularities. Contour integrations. Conformal transformations. Fourier series. Fourier and Laplace transforms with applications.

Texts/References

  • M.R. Spiegel, Vector Analysis, Schaum’s outline series, Tata McGraw Hill,1979
  • J.W. Brown and R.V. Churchill, Complex variables and applications, 6th ed., McGraw Hill, 1996
  • M.J.Ablowitz, A.S.Fokas, Complex variables, Cambridge Univ. Press., First South Asian paperback edition, 1998
  • H.A. Hinchey, Introduction to Applicable Mathematics, Part I, Wiley Eastern, 1980
  • G. B. Arfken and H.J.Weber, Mathematical methods for physicists, 4th ed. Academic Press, 1995