Course Details:
This course is aimed to provide knowledge of fundamental Mathematics to chemistry discipline students.
Module 1: Vectors
Vectors, vector components, scalar products, other vector combinations, orthogonality, projection operators, orthogonalization of coordinates, vector calculus.
Module 2: Function Spaces
The function as a vector, scalar products & orthogonality, linear independence, orthogonalization of basis function, differential operators, generation of special functions, function resolution in a set of basis functions, Fourier series.
Module 3: Matrices
Vector rotations, Special Matrices, Matrix equations & Inverses, Determinants, Rotation of Coordinate Systems, Principal Axes, Eigenvalues and Characteristic Polynomials, Eigenvectors, Characteristic Polynomial.
Module 4: Similarity Transforms and Projections
The similarity transform, simultaneous diagonalization, generalized characteristic equation, Matrix decomposition using eigenvectors, degenerate eigenvalues, matrix Functions & equations, diagonalization of tridiagonal matrices.
Module 5: Introduction to Group Theory
Vectors and symmetry operations, Matrix Representations of symmetry operations, Group operations, Properties of irreducible representations, Direct Product of Group elements, Direct Products and Integrals.
Module 6: Integral Transforms
Brief Historical Introduction, basic concepts and definitions, Fourier Transforms, Laplace Transform, Hankel Transform, Mellin Transform, Wavelet Transform.
Module 7: Complex Analysis
The complex plane, analytical functions, line integrals, complex integrations, power series, Laurant series, residue calculus, fractional calculus.
References:
1. Methods of Theoretical Physics, Morse and Feshbach.
2. Mathematical Methods of Physics, Mathews and Walker.
3. Mathematical Methods for Physicists, G. Arfken.
4. Handbook of Differential Equations, Zwillinger.
5. Fourier Transfoms, I. N. Sneddon.
6. Visual Compelx Analysis, T. Needham.
7. Methods of Mathematical Physics (Vol:1 & II), R. Courant & D. Hilbert.