Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab

** 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)

This website is designed & maintained by Ms. Moumita Ganguly (mouganguly09@gmail.com).

Dr. Aniruddha Chakraborty

School of Basic Sciences

Indian Institute of Technology Mandi

Mandi, Himachal Pradesh 175001

India

ph: +(91)1905-237930

achakrab