Dr. Aniruddha Chakraborty

Course details                                                                                 <<back

Weekly Lecture Hours: 3
Weekly Tutorial Hours: 1
Subject Code: Not Decided
Examination Duration (Hours): 3
Relative Weightage: Tutorial: 4%, End Term Exam: 60%, Quizzes: 36 %.
Credits: 4
Semester: 8-th
Pre-Requisite: M.Sc. in Physics and Chemistry
Venue: Lecture Hall 1
Timings: Monday (8.00-9.00), TuesDay (9.00-10.00), Wednesday (10.00-11.00).
Instructors: Dr. Aniruddha Chakraborty.
Objective: To provide knowledge of fundamental Mathematics and to make the scientific background stronger for chemistry discipline students.

Unit 1: Vectors:

Vectors, Vector Components, Scalar Products, Other Vector Combinations, Orthogonality, Projection Operators, Orthogonalization of Coordinates, Vector Calculus.

Unit 2: Function Spaces:

The function as a vector, Function Scalar Products and Orthogonality, Linear independence, Orthogonalization of Basis Functions, Differential Operators, Generation of Special Functions, Function Resolution in a set of Basis Functions, Fourier Series.

Unit 3: Matrices:

Vector Rotations, Special Matrices, Matrix equations and Inverses, Determinants, Rotation of Coordinate Systems, Principal Axes, Eigenvalues and Characteristic Polynomials, Eigenvectors, Characteristic Polynomial.

Unit 4: Similarity Transforms and Projections

The similarity transform, simultaneous diagonalization, Generalized characteristic equation, Matrix decomposition using Eigenvectors, Degenerate Eigenvalues, Matrix Functions and Equations, Diagonalization of Tridiagonal Matrices.

Unit 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.

Unit 6: Integral Transforms:

Brief Historical Introduction, basic concepts and definitions, Fourier Transforms, Laplace Transform, Hankel Transform, Mellin Transform, Wavelet Transform.

Unit 7: Complex Analysis:

The complex plane, Analytic functions, Line Integrals, Complex integrations, Power Series, Laurent series, Residue calculus, Fractional Calculus.

References:

 1. Morse and Feshbach: Methods of Theoretical Physics.
 2. Mathews and Walker: Mathematical Methods of Physics.
 3. Arfken : Mathematical Methods for Physicists.
 4. Zwillinger :Handbook of Differential Equations.
 5. I. N. Sneddon: Fourier Transfoms
 6. T. Needham: Visual Compelx Analysis
 7. R. Courant and D. Hilbert: Methods of Mathematical Physics (Vol:1 & II)