Numerical Analysis

Course ID:  B5603S01

Credits: 3

Objective: 

1. Understanding the basics of the numerical techniques 

2. Communicating the results of a numerical method effectively 

3. Knowing the strengths and limitations of the numerical techniques 

4. Developing fundamental skills for further applications

Course Prerequisites: Basic knowledge of programming

Outline:

0. Fundamentals 

1.1 Bisection Method 

1.2 Fixed Point Iteration 

1.4 Newton’s Methods 

1.5 Root Finding Without Derivatives 

2.1 Gaussian Elimination 

2.2 The LU Factorization 

2.5 Iterative methods 

2.7 Nonlinear systems of equations 

3.1 Data and interpolating functions 

3.2 Interpolation error 

3.3 Chebyshev Interpolation 

3.4 Cubic Splines 

4.1 Least squares and the normal equations 

4.2 Linear and nonlinear models 

4.3.1 Gram-Schmidt Orthogonalization 

5.1 Numerical Differentiation 

5.2 Newton-Cotes formulas for numerical integration 

5.3 Romberg Integration 

5.4 Adaptive Quadrature 

5.5 Gaussian Quadrature 

6.1 Initial value problems 

6.2 Analysis of IVP solvers 

6.4 Runge-Kutta methods and applications 

6.7 Multi-step methods 

6.3 Systems of ordinary differential equations 

9.1 Random numbers (Option) 

9.2 Monte-Carlo simulation (Option) 

12.1 Eigenvalues (Option)

Teaching Method:  Lecture notes and exercises

Reference:  

1. T. Sauer, Numerical Analysis, 2nd ed. Pearson 

2. R. L. Burden, J. D. Faires, Numerical Analysis, 9th ed. Cengage Learning