The unifying theme this course is linear algebra. This course demonstrates the far reaching ideas of linear algebra in physics while building necessary mathematical foundations for other physics courses.
The course will begin with a review of basic algebra of complex numbers and matrices. It will then progress into linear transformations of vectors by matrices to illustrate the ideas of linear algebra: linear independence, decomposition of a vector into orthonormal basis vectors and eigenvectors of linear transformations. Fourier series will be introduced as an infinite dimensional generalisation of decomposition of a vector, thereby generalizing the ideas of linear vector spaces to infinite dimensions.
Finally, differential equations will also be cast in the linear algebra language, and we will look at transformations of functions by linear differential operators, and solutions of linear differential equations as functions in a linear vector space.