Mathematical Physics
B.Sc. pt II (hons) course
B.Sc. pt II (hons) course
Syllabus | In classes | Links | References
Dates and timings:
Wednesday and Thursday, 12:00 PM – 01:00 PM (IST)
Friday, 10:00 AM – 12:00 PM (IST)
Starting date:
Revision of pre-requisites from August 3,
new course material from August 19, 2016
Reference Books: Mathematical Methods for Physics and Engineering by Riley-Hobson-Bence (Cambridge University Press)
There were classes in January 2017 too, couldn't get updated on the website.
Orthogonal Curvilinear co-ordinate system. Scale factors, expression for gradient, divergence and curl and their applications to Cartesian, circular, cylindrical and spherical polar co-ordinate systems.
Co-ordinate transformation and Jacobian. Transformation of Covariant, Contravariant and Mixed Tensors. Addition, Multiplication and Contraction of Tensors. Metric tensor and its use in transformation of tensors. Dirac Delta Function and its properties.
Fourier series: Fourier theorem and computation of Fourier coefficients. Even and odd functions, half range expansion, sums and scale changes, forced oscillations, Expansion Techniques: integration and differentiation. Introduction to Fourier transform and its simple applications.
Solution of differential equations - Series method: Properties of power series, solution of ordinary differential equation: Legendre's Equation, Legendre Polynomials and Functions, Hermite Polynomials.
The method of Frobenius: Solution about regular singular points, The Gamma function, the Bessel-Clifford equation.
Roots differing by an integer: Series method, Solution of Bessel equation for:
Basic identities involving Bessel Functions. Basic properties like orthogonality recurrence relation and generating functions of Bessel, Hermite, Legendre, and associated Legendre's function (simple applications)
Solution of partial differential by separation of variable technique and its application to following Boundary Value Problems:
Matrices: Inverse of a matrix, adjoint, Hermition adjoint, Solution of linear equations using matrix.
Normas and inner products, orthogonal sets and matrices, the Gram Schmidt process and the Q-R factorization theorem. Projection matrices. Least square fit of data. Eigen values and Eigen vectors, diagonalization of matrices. Examples involving up to 3×3 matrices and for the case of real symmetric and simple matrices. Solution of linear differential equations for the homogeneous and non-homogeneous cases.
On wikipedia
Other sites
ocw.mit.edu