## Courses

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## 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

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

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