Course
PostgraduateSemester
Sem. ISubject Code
MA615Subject Title
Advanced Engineering MathematicsSyllabus
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. Functional and their differentiation, Euler-Lagrange equation, Boundary value problems, Variational principles, Rayleigh-Ritz Methods
Text Books
Same as Reference
References
1. Advanced Engineering Mathematics, Kreyszig, E., 9th edition, John Wiley, 2005.
2. Complex analysis for Mathematics and Engineering, Mathews, J. H. and Howell, R., Narosa, 2005.
3. Numerical Linear Algebra, V. Sundarapandian, Prentice-Hall, 2008.
4. Numerical Analysis, R. L. Burden and J. D. Faires, Brooks/Cole, 2001.
5. Calculus of Variations, I. M. Gelfand and S. V. Fomin, Prentice Hall, 1963.
6. Calculus of Variations with Applications, A. S. Gupta, Prentice Hall, 1997.
7. Advanced Engineering Mathematics, Jain, R. K. and Iyengar, S. R. K., Narosa, 2005.
8. Advanced Engineering Mathematics, Greenberg, M. D., Pearson Education, 2007.
9. Complex Variables and Applications, Churchill, R. V. and Brown, J. W., 6th ed., McGraw-Hill, 2004.
Course Outcomes (COs):
CO1: Understand fundamental concepts and theorems related to complex numbers, analytic functions, elementary functions, complex integration, and power series.
CO2: Know how to utilize residue theory to evaluate contour integrals, improper integrals, and integrals over the real line, and also know about the concept of conformal mapping and its applications.
CO3: Demonstrate how fundamental concepts of interpolation, numerical differentiation, and integration can be used for achieving better approximation and its analysis.
CO4: Acquire comprehensive understanding of linear algebraic systems, eigenvalues, eigenvectors, and various methods for solving linear systems
CO5: Utilize MATLAB programming to evaluate linear algebraic systems.