### Courses

##### Last Updated:
29/11/2019 - 15:23

## 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

#### 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)