This course aims to familiarise the student with a variety of mathematical techniques which every student of physics should be conversant with. Having taken the course you should be comfortable with casting a wide variety of physics problems in mathematical language and being able to analyse and solve them subsequently. The course will also include an introduction to programming with Python. Within the physics curriculum at Ashoka university, this course is an essential prerequisite for Classical Mechanics and Electricity and Magnetism in Light of Relativity offered in the third semester.
Recommended course content:
Brief review of basic calculus: Differentiation and integration, derivative as a rate of change, setting up a differential equation for physical problems. Taylor series. Basic ideas of vector spaces and linear algebra: Eigenvalues and eigenvectors. Characteristic equation, completeness and orthonormality. Functions of more than one variable: Basic idea of partial derivatives. Line, surface, and volume integrals. Vector Analysis: Gradient, Divergence and Curl, Differential Vector identities. Applications to Electromagnetism.
Pre-requisites: Students who have not done mathematics at the 12th-grade level are required to take Calculus I.
Taught at the level of: Basic Multivariable Calculus (J E Marsden, A Tromba, and A Weinstein), Vector Analysis (M Spiegel, M Lipschutz), Mathematical Methods for Scientists and Engineers (D A McQuarrie).