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  • 9:15 PM, Tuesday, 26 Oct 2021


Course Dual Degree (B. Tech + M.S / M.Tech)
Semester Sem. IV
Subject Code MA221
Subject Title Partial Differential Equations, Calculus of Variations and Complex Analysis

Syllabus

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 – RayleighRitz method.

Complex Analysis: complex numbers and their geometrical representation – functions of complex variable – limit, continuity and derivative of functions of complex variable – analytical functions and applications – harmonic functions – transformations and conformal mappings – bilinear transformation – contour integration and Cauchy’s theorem – convergent series of analytic functions – Laurent and Taylor series – zeroes and singularities – calculation of residues – residue theorem and applications.

Text Books

1. Kreyszig, E., Advanced Engineering Mathematics, 9th ed., John Wiley (2005).

2. Mathews, J. H. and Howell, R., Complex Analysis for Mathematics and Engineering, Narosa (2005).

References

1. Churchill, R. V. and Brown, J. W., Complex Variables and Applications, 6th ed., McGrawHill (2004). 

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

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

4. James, G., Advanced Modern Engineering Mathematics, Pearson Education (2004).

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

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

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