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  • 10:42 AM, Friday, 24 Jan 2020


Course Postgraduate
Semester Sem. I
Subject Code MA615
Subject Title Advanced Engineering Mathematics

Syllabus

Complex integration: Cauchy-Goursat Theorem (for convex region), Cauchy's integral formula, Higher order derivatives, Morera's Theorem, Cauchy's inequality and Liouville's theorem, Fundamental theorem of algebra, Maximum modulus principle, Taylor’s theorem, Schwarz lemma.

Laurent's series, Isolated singularities, Meromorphic functions, Rouche's theorem, Residues, Cauchy's residue theorem, Evaluation of integrals, Riemann surfaces.

Direct and iterative methods for linear systems, eigen value decomposition and QR/SVD factorization, stability and accuracy of numerical algorithms, sparse and structured matrices, Gradient method for optimization.

Finite element method: Finite element formulation of boundary value problems, one and two dimensional finite element analysis.

Functionals and their differentiation, Euler-Lagrange equation, Boundary value problems, Variational principles, Rayleigh-Ritz Methods

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
  3. V. Sundarapandian, Numerial linear algebra, Prentice-Hall, 2008.
  4. R.L.Burden and J.D.Faires, Numerical Analysis, Brooks/Cole, 2001
  5. I.M.Gelfand and S.V.Fomin, Calculus of Variations, Prentice Hall, 1963
  6. A.S.Gupta, Calculus of Variations with Applications, Prentice Hall, 1997
  7. Jain, R. K. and Iyengar, S. R. K., Advanced Engineering Mathematics, Narosa (2005).
  8. Greenberg, M. D., Advanced Engineering Mathematics, Pearson Education (2007).
  9. Churchill, R. V. and Brown, J. W., Complex Variables and Applications, 6th ed., McGraw-Hill (2004).
References

Same as Textbooks