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  • 12:29 AM, Friday, 15 Nov 2019


Course Undergraduate
Semester Sem. IV
Subject Code MA221
Subject Title Integral Transforms, PDE and calculus of variations

Syllabus

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 usingseparable variable techniques and Fourier series.

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

Text Books

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

References

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