Integral Transforms: The Fourier transform pair - algebraic properties of Fourier transform – convolution, modulation, and translation – transforms of derivatives and derivatives of transform – inversion theory. Laplace transforms of elementary functions – inverse Laplace transforms – linearity property – first and second shifting theorem – Laplace transforms of derivatives and integrals – Laplace transform of Dirac delta function – applications of Laplace transform in solving ordinary differential equations.

Partial Differential Equations: introduction to PDEs – modeling problems related and general second order PDE – classification of PDE: hyperbolic, elliptic and parabolic PDEs – canonical form – scalar first order PDEs – method of characteristics - Charpits method – quasi- linear first order equations – shocks and rare factions – solution of heat wave and Laplace equations using separable variable techniques and Fourier series.

Calculus of Variations: optimization of functional – Euler- Lagrange equations – first variation – is operimetric problems – Rayleigh - Ritz method.