Mathematics for Physics-
The emphasis of course is to equip students with the mathematical and critical skills required in solving problems of interest to physicists. The skills developed during course will prepare them not only for doing fundamental and applied research but also for a wide variety of careers.
- Vector operations vector Algebra-Component form
- Scalar and vector fields- Differentiation of scalar and vector fields-Del operator-gradient
- divergence, curl-physical interpretation
- Integral calculus -Line integral. Surface integral, volume integral
- fundamental theorem of gradients
- Gauss divergence theorem
- fundamental theorem of curl-stokes theorem
- Divergence less and cur less fields.
Functions and plots
- Periodic functions. Orthogonality of sine and cosine functions
- Dirichlet Conditions. Expansion of periodic functions in a series of sine and cosine functions
- Determination of Fourier coefficients
- Application. Summing of Infinite Series.
- Parseval’s Identity and its application to summation of infinite series
- Addition and Multiplication of Matrices
- Null Matrices. Diagonal, Scalar and Unit Matrices. Upper- Triangular and Lower-Triangular Matrices
- Transpose of a Matrix. Symmetric and Skew-Symmetric Matrices
- Conjugate of a Matrix. Hermitian and Skew Hermitian Matrices
- Singular and Non-Singular matrices. Orthogonal and Unitary Matrices
- Similar Matrices. Trace of a Matrix
- Finding Eigen values and Eigen vectors of a Matrix
- Diagonalization of Matrices