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  • 9:28 PM, Saturday, 16 Oct 2021

Course Undergraduate
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 in- tegrals – 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-Lagrange equations – first variation – isoperimetric problems – Rayleigh-Ritz method.

Text Books

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


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 , 3 rd 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 , 2 nd ed., Springer-Verlag (2004).

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

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