Course contents:

Linear Algebra : Vector spaces over R and C, Subspaces, Basis and Dimension, Matrices and determinants, Rank of a matrix, System of linear equations, Gauss elimination method, Linear transformations, Rank-nullity theorem, Change of basis, Eigen values, Eigen vectors, Diagonalization of a linear operator, Inner product spaces. Spectral theorem for real symmetric matrices, application to quadratic forms.

Integral Transforms: Laplace transforms of elementary functions, Inverse Laplace transforms and applications, Fourier series, Fourier transforms, Fourier cosine and sine integrals, Dirichlet integral, Inverse Fourier transforms, Special Functions: Gamma and Beta functions, Error functions.

Textbook & reference books:

1. Stephen H. Friedberg,‎ Arnold J. and Insel , Lawrence E. Spence, Linear Algebra, Pearson, 4th Edition, 2002.
2. Serge Lang, Linear Algebra, Springer 2nd edition, 3nd ed. 2004.
3. Gilbert Strang, Linear Algebra and its applications, Brooks, 4th Edition 2006.
4. Lokenath Debnath and Dambaru Bhatta, Integral Transforms and Their Applications, Chapman Hall, 3nd edition, 2010.
5. Andrews Larry and Shivamoggi Bhimsen K., Integral Transforms for Engineers, Prentice Hall India, 2003 edition, 2010.
6. Goyal J K and Gupta K P, Laplace And Fourier Transforms, PRAGATI PRAKASHAN, 2nd edition (2016)
7. W. Bell, Special Functions for Scientists and Engineers, Dover Publications Inc, 2004 Edition, 2004.