M.Sc. (Physics) curriculum, Tribhuvan University 2073

37

PHY603: Math Physics II 3 CH (45L+15T) Nature of the course: Theory Full Marks: 75 Pass Marks: 37.5 Course Description:

This course contains different areas of mathematics that are used extensively in the study of physics.

Objectives:

The objective of this course is to train the students to use the methods of mathematics to formulate and solve problems in physics, and make them capable to apply this knowledge in higher studies and research.

Course Contents:

1. Complex Variables: [15 hours] 1.1 Complex variables and functions, 1.2 Cauchy – Riemann conditions: analytic functions, 1.3 Derivatives of analytic functions, 1.4 Cauchy integral theorem, formula and applications; 1.5 Laurent expansion, 1.6 Singularities: poles, branch points, analytic continuation, 1.7 Calculus of residues and applications 1.8 Evaluation of definite integrals, 1.9 Evaluation of sums, 1.10 Mapping and conformal transformations, 1.11 Method of steepest descents, 1.12 Dispersion relations.

2. Probability and Statistics: [15 hours]

2.1 Review of probability, 2.2 Random variables: discrete Probability, mean and variance, 2.3 Moments of probability, 2.4 Covariance and correlation, marginal and conditional probability, 2.5 Distribution functions: binomial, Poisson and Gauss normal distributions, 2.6 Transformation of random variables, 2.7 Error propagation, 2.8 Fitting curves to data,

2.9 The distribution, 2.10 Student-t- distribution, 2.11 Confidence intervals, 2.12 Error analysis

3. Curvature & Field Equation: [15 hours]

3.1 The Riemann Tensor, 3.2 Properties of Riemann Tensor, 3.3 Riemannian Curvature, 3.4 The Ricci Tensor, 3.5 Zero Curvature and Euclidian Metric,

M.Sc. (Physics) curriculum, Tribhuvan University 2073

38

3.6 Flat Riemannian Spaces, 3.7 Normal Coordinates, 3.8 Schur’s Theorem, 3.9 The Einstein Tensor, 3.10 The Einstein Field Equation.

Textbooks:

1. Arfken G.B., Weber H.J. and Harris F.E – Mathematical Methods for Physicists, 7th Edn.,

Academic Press, Amsterdam (2013).

2. Spiegel Murray R. – Theory and Problems of Statistics (Schaum Series), McGraw Hill,

London (1992).

3. Key D. K – Tensor Calculus, Schaum Series, McGraw Hill, London (1988).

Reference Books:

1. Mathew, J. & Walker, R. – Mathematical Methods in Physics, Benjamin, Menlo Park,

Second Edition (1970).

2. Riley K.F., Hobson M.P. and Bence S. J., Mathematical Methods for Physics and

Engineering, 3rd Edn., Cambridge University Press, New York (2006).

3. Copson, E.T. – An Introduction to the Theory of Functions of Complex Variable, Oxford

Clarendon Press (1935).

4. Margenu & Murphy – Mathematics for Physicist and Chemist, East, West Press Pvt. Ltd.,

New Delhi (1964).

5. Morse, P.M. & Feshbach H. – Methods of Theoretical Physics, Part I & II, McGraw Hill, New

York (1953).