Course | Dual Degree (B. Tech + Master of Science / Master of Technology) |
Semester | Sem. IV |
Subject Code | MA221 |
Subject Title | Integral transforms, PDE, and Calculus of Variations |
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 rarefactions – solution of heat, wave, and Laplace equations using separable variable techniques and Fourier series.
Calculus of Variations: optimization of functional – Euler‐Lagranges equations – first variation – isoperimetric problems – Rayleigh‐Ritz method.
1. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).