To understand and express the concepts and laws of physics, it is essential that students learn the relevant mathematical techniques. In this course students will study Vector Calculus (Block 1), and Probability and Statistics (Block 2).

The study of vector calculus is of great value in physics. While the use of vectors simplifies the expression of physical concepts, their differentiation and integration is useful in determining the resultant of forces or momenta, determining the work done on a particle moving in any force field, modelling the flow of fluids in pipes, computing the electric field due to a charged conductor, etc. Indeed, the tools of vector calculus discussed in Block 1 find extensive use in mechanics, electromagnetics, quantum mechanics, fluid mechanics, optics, etc.

There is, perhaps, no part of mathematics that is more intimately connected with everyday experiences than probability theory. We all know that the element of chance dominates the physical world. Even the origin of life is itself a chance happening! Probability theory serves as a model for chance phenomena. Along with statistical methods, it enables us to deal with any problem involving large numbers of particles/variables. Knowledge of probability and statistics is required in such diverse areas as the kinetic theory of matter, statistical mechanics, quantum mechanics, atmospheric physics, design of experiments, interpretation of data and error analysis.

If students intend to study physics in depth, they must take this course, particularly because vector calculus is not being discussed in any of the mathematics courses.

Block 1: Vector Calculus:
1. Vector algebra
2. Vector differential calculus
3. Coordinate systems
4. Integration of scalar and vector fields
Appendix: Proof of the vector integral theorems

Block 2: Probability and Statistics:
5. Basic concepts of probability
6. Probability distributions
7. Applications in physics.

Assessment is by one assignment (30%) and a final examination (70%).

Programmes for which this course is required or in which it can be included:
Bachelor of Science.