Course
UndergraduateSemester
ElectivesSubject Code
AE456Subject Title
Numerical Methods for Scientific ComputingSyllabus
Mathematical review and computer arithmetic – numbers and errors; Nonlinear equations; Direct methods for linear systems; Iterative methods for linear systems; Eigenvalues and eigenvectors power method, inverse power method, QR method; Approximation theory – norms, orthogonalization, polynomial approximation, piecewise polynomial approximation, trigonometric approximation,rational approximation, wavelet bases; Numerical differentiation; Numerical integration – Romberg integration, Gauss quadrature, Adaptive quadrature; Numerical ordinary differential equations - single step and multi-step methods, Runge-Kutta method, predictor-corrector method, stiffness, stability, shooting methods; Introduction to parallel programming – system architectures, shared and distributed memory programming, performance.
Text Books
- Same as Reference
References
1. Trangenstein, J. A., Scientific Computing: Vol. I - Linear and Nonlinear Equations, Springer (2017).
2. Trangenstein, J. A., Scientific Computing: Vol. II - Eigenvalues and Optimization, Springer (2017).
3. Trangenstein, J. A., Scientific Computing: Vol. III - Approximation and Integration, Springer (2017).
4. Moin, P., Fundamentals of Engineering Numerical Analysis, Cambridge Univ. Press (2010).
5. Chapra, S. C., Applied Numerical Methods with MATLAB for Engineers and Scientists, 3rd ed., (2011).
6. Gander, W., Gander, M. J., and Kwok, F., Scientific Computing: An Introduction using Maple and MATLAB, Springer (2014).
7. Ackleh, A. S., Allen, E. J., Hearfott, R. B., and Seshaiyer, P., Classical and Modern Numerical Analysis: Theory, Methods and Practice, CRC Press (2009).
8. Gilat, A. and Subramaniam, V., Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB, 3rd ed., (2013).