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Course Code : AMAT 22282
Title : Numerical Methods II
Pre-requisites : AMAT 12253
Learning Outcomes:
At the end of the course, the student should be able to;
define vector norm, matrix norm, and their general properties
use numerical methods for differentiation and integration
find numerical solutions to a system of equations using iterative methods
calculate approximate solutions to ordinary differential equations using numerical methods
discuss the convergence and stability of the solution.
Course Contents:
Numerical Linear Algebra:
Vector Norms, Matrix norms, General properties of vector and matrix norms, norm convergence.
Numerical Differentiation and Integration:
Numerical differentiation, open and closed Newton-Cotes formulae, Trapezoidal, Simpson’s 1/3 and 3/8 rules, Romberg integration method, Gaussian quadrature.
Solving Linear Systems of Equations (Iterative):
Relative error bound, condition number, iterative and relaxation methods: Jacobi, Gauss-Seidel methods and their convergence, Richardson, SOR Iterative methods. Conjugate Gradient Method.
Numerical Solutions of Ordinary Differential Equations:
Explicit and Implicit numerical schemes, Taylor- Series method, Picard’s method of successive approximations, Euler’s method, Heun’s method, Midpoint method, Runge-Kutta methods, computation of error bound, stability of methods, predictor-corrector methods: Adams - Moulton, Adams-Bashforth, Milne’s methods, global and local truncations errors.
Method of Teaching and Learning : A combination of lectures and tutorial discussions.
Assessment : Based on tutorials, tests, presentations and end of course examination.
Recommended Reading :
1. Burden, R.L., Faires, J.D, Burden, M.L. (10th Ed., 2016). Numerical Analysis, Cengage Learning.
2. Trefethen, L.N. & Bau, D. (1997). Numerical Linear Algebra, Philadelphia, USA.
3. Golub, H., Vanloan, C.F. (2013). Matrix computations, JHU Press.
4. Kreyszig, E. (10th Ed., 2010). Advanced Engineering Mathematics, John Wiley.
5. Sauer, T. (2012). Numerical Analysis, Pearson.
6. Epperson, J.F. (2013). An Introduction to Numerical Methods and Analysis, Wiley.
7. Faul, A.C. (2016). A Concise Introduction to Numerical Analysis, Chapman and Hall/CRC.
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