COURSE DESCRIPTION
This course aims at introducing the methods of mathematics applicable in the various areas of chemistry research to chemistry majors,first year integrated and regular Ph.D students in the Chemistry department. A semi-rigorous introduction to the theory of methods followed by illustration of their use in chemistry and related areas shall be targeted. This is a mandatory course for 3rd year BS-MS and 1st year M.Sc. students in Chemistry. It is also an elective from Chemistry Ph.D. students.
Contents: Linear algebra: Linear vector spaces, linear independence of vectors, basis sets, inner products, properties of linear operators and their algebra, the eigenvalue problem, matrices and their algebra, determinants, matrix eigenvalue problems, coordinate transformations. Complex numbers and variables: Representations of complex numbers, complex algebra, functions of a complex variable. Multivariable calculus: Functions of two or more variables, partial derivatives, maxima, minima, and saddle points, Lagrange multipliers, line integrals, surface integrals, Green’s theorem. Vector calculus: Gradient and the directional derivative, divergence, continuity equation, curl, Stokes’ and Gauss’ theorems. Special Integrals and Integral transforms: Gamma functions, Gaussian integrals, Fourier series, Fourier and Laplace transforms and their applications. Ordinary differential equations: First order equations and their applications. Separation of variables, equations reducible to separable form. Second-order linear differential equations: homogeneous with constant coefficients. Introduction to probability and statistics.
Prerequisites: MTH 101, MTH 102 or equivalent; Currently the course is not open for majors from other disciplines. The course
Text Books:
- McQuarrie, D. A., Mathematical methods for scientists and engineers, University Science Books, 2003.
- G. Arfken, H. Weber, and F. Harris, Mathematical Methods for Physicists, 7th Ed, Academic Press 2012
- M. L. Boas, Mathematical Methods for the Physical Sciences, 3rd Ed, Kaye Pace 2006.
- Goodson, D. Z., Mathematical Methods for Physical and Analytical Chemistry, Wiley, 1st Ed., 2011.
- K. F. Riley, M. P. Hobson, S. J. Bence, Mathematical Methods for Physics and Engineering, 3rd Ed, Cambridge University Press, 2006.
- J. Matthews and R. L. Walker, Mathematical Methods of Physics, 2nd Ed, Addison Wesley Longman 1971
COURSE ASSESSMENT
This course will feature assignments (5%), 2 quizzes (15%), a mid-semester exam (30%) and an end-semester exam (50%).
TUTORIALS
N.A.
ANNOUNCEMENTS
[05.08.2024] Welcome (back) to IISER Bhopal!
[02.09.2024] Assignment 1 uploaded. Due on 11/9/24.
[15.09.2024] Solutions to Assignment 1 uploaded. Contact TAs for any issues.
[15.09.2024] Assignment 2 uploaded. Due on 26/9/24.
[26.09.2024] Quiz 1 solutions uploaded.
[02.10.2024] Assignment 3 uploaded. Due on 11/11/24 in class.