**[Cr:4, Lc:3, Tt:1, Lb:0]**

- Fourier series: General properties, applications of Fourier series, properties of Fourier series, Gibbs phenomenon, discrete Fourier transform, relation with fast Fourier transforms.
- Integral transforms: Fourier integral, Fourier transforms, inversion theorem, Fourier transform of derivatives, convolution theorem, Laplace transform and its relation to Fourier transform. Laplace transform solution to differential equations. convolution theorem, Inverse Laplace transform.
- Introduction to integral equations: Integral transforms, generating functions, Neumann series, separable Kernels, Hilbert-Schmidt theory.
- Calculus of Variations: One dependent and an independent variable, Euler's equations, several dependent variables, several independent variables, Lagrangian multipliers, variation with constraints.

- H. J. Weber and G. B. Arfken, Essential Mathematical Methods for Physicists, Academic Press (2004).
- D. A. McQuarrie, Mathematical Methods for Scientists and Engineers, Viva Books (2009).
- Mary L. Boas, Mathematical Methods in the Physical Sciences, Wiley (2005).