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  • 7:55 PM, Sunday, 20 Jul 2025

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.

Academic Programmes:

Academic Year:

Text Books: 

  1. Kreyszig, E., Advanced Engineering Mathematics, 10th ed., John Wiley (2011).

Reference: 

  1. Wylie, C.R. and Barrett, L.C., Advanced Engineering Mathematics, McGraw-Hill (2002).

  2. Greenberg, M.D., Advanced Engineering Mathematics, Pearson Education (2007).

  3. James, G., Advanced Modern Engineering Mathematics, 3rd ed., Pearson Education (2005).

  4. Sneddon, I.N., Elements of Partial Differential Equations, McGraw-Hill (1986).

  5. Renardy, M. and Rogers, R.C., An Introduction to Partial Differential Equations, 2nd ed., Springer-Verlag (2004).

  6. McOwen, R.C., Partial Differential Equations: Methods and Applications, 2nd ed., Pearson Education (2003).

  7. Borelli, R.L., Differential Equations: A Modelling Perspective, 2nd ed., Wiley, 2004.

Course Outcomes (COs):

CO1: Evaluate and Understand Fourier transforms and Laplace trasforms

CO2: Understanding Linear First order Partial differential equations and second order PDE

CO3: Evaluate problems using Charpits method, PDEs using separation of variables, second order PDE with constant and variable coefficient

CO4: Understand the concept of maxima and minima of functionals and Isoperimetric problems

Academic Lecture: 
3
Academic Tutorial: 
0
Academic Practical: 
0

Semester Details:

Subject Code: 
MA221
Subject Name: 
Integral Transform, PDE and Calculus of Variations
Academic Credits: 
3