Courses

Last Updated:
10/03/2019 - 15:02

IAM561 - Introduction to Scientific Computing I

Credit: 3(3-0); ECTS: 8.0
Instructor(s): Hamdullah Yücel
Prerequisites: Consent of Instructor(s)

Course Catalogue Description

Computer Arithmetic; Linear Equations: Gauss elimination, LU decomposition; Linear Least Squares: data fitting, normal equations, orthogonal transformations; Eigenvalue Problems; Singular Value Decomposition; Nonlinear Equations: bisection, fixed-point iteration, Newton’s method, optimization; Interpolation: polynomials, piecewise polynomials; Numerical Differentiation and Integration.

Course Objectives

This course is intended for relatively new graduate students who require knowledge of and background in numerical methods. At the end of this course, the student will:

• understand the errors, source of error and its effect on any numerical computations, and also analyse the efficiency of any numerical algorithms
• learn how to obtain numerical solution of nonlinear equations
• learn how to approximate the functions using interpolating polynomials
• learn how to numerically differentiate and integrate functions
• learn to implement the numerical methods using MATLAB

Course Learning Outcomes

Upon successful completion of this course, the student will be able to:

• determine the effect of round off error and loss of significance
• design and analyze algorithms for solutions of linear equations
• derive appropriate numerical methods to solve algebraic and transcendental equations
• derive appropriate numerical methods to calculate a definite integral
• code various numerical methods using MATLAB

Tentative (Weekly) Outline

1. Computer Arithmetic
2. Linear Equations: Gauss elimination
3. Linear Equations: LU decomposition
4. Linear Least Squares: data fitting, normal equations
5. Linear Least Squares: orthogonal transformations
6. Eigenvalue Problems
7. Singular Value Decomposition
8. Nonlinear Equations: bisection, fixed-point iteration
9. Nonlinear Equations: Newton’s method, optimization
10. Interpolation: polynomials
11. Interpolation: piecewise polynomials
12. Numerical Differentiation
13. Numerical Integration: basic quadrature algorithms
14. Numerical Integration: Gaussian quadrature

Course Textbook(s)

• U. Ascher and C. Greif, A First Course in Numerical Methods, SIAM, 2011.

Supplementary Materials and Resources

• Books:
• M. T. Heat, Scientific Computing, McGraw Hill, 1997
• A. Quarterioni, R. Sacco, and F. Salari, Numerical Mathematics, Springer, 2000.
• Resources:
• MATLAB Student Version is available to download on MathWorks website, http://www.mathworks.com, or METU FTP Severs (Licenced)