At the end of this course, the students; 1) Learn scientific computing basic principles in engineering problems. 2) Have an ability for commenting on error analysis and their results. 3) Formulate measurements that depend on physiological parameters in biomedical field. 4) Applying course units in homeworks on MATLAB or similar programs.

MODE OF DELIVERY

Face to face

PRE-REQUISITES OF THE COURSE

No

RECOMMENDED OPTIONAL PROGRAMME COMPONENT

None

COURSE DEFINITION

Interpolation and polynomial approximation, the divided differences, Hermit interpolation, polynomial numerical differentivation, curve fifting, Interpolation by spline functions, Richardson's extrapolation, Numerical Integraiton, Romberg integration, finite element method, finite difference method, boundary element method. MATLAB applications.

COURSE CONTENTS

WEEK

TOPICS

1^{st} Week

Introduction. Approximations in scientific computing, computer arithmetics

2^{nd} Week

Linear Equations. Linear system properties, sensitivity, solving linear systems, special types of linear sysems,iterative methods used in solving linear equations

3^{rd} Week

Linear Equations. Linear system properties, sensitivity, solving linear systems, special types of linear sysems,iterative methods used in solving linear equations

4^{th} Week

Linear Equations. Linear system properties, sensitivity, solving linear systems, special types of linear sysems,iterative methods used in solving linear equations

5^{th} Week

Linear Least Squares Problems and Properties. Problem transformation, orthogonalization methods, singular value decomposition

6^{th} Week

Linear Least Squares Problems and Properties. Problem transformation, orthogonalization methods, singular value decomposition

7^{th} Week

Eigenvalue Problems. Eigenvalues nad eigenvectors, properties, problem transormations, eigenvalue and eigenvector calculations

8^{th} Week

Midterm Exam

9^{th} Week

Eigenvalue Problems. Eigenvalues nad eigenvectors, properties, problem transormations, eigenvalue and eigenvector calculations

10^{th} Week

Nonlinear Equations.Properties of nonlinear system, convergense rate, stopping criteria, nonlinear euations in one plane.

11^{th} Week

Nonlinear Equations.Properties of nonlinear system, convergense rate, stopping criteria, nonlinear euations in one plane.

12^{th} Week

Optimization. Optimization problems, properties, optimization in one plane, unconstrained optimization, constrained optimization

13^{th} Week

Optimization. Optimization problems, properties, optimization in one plane, unconstrained optimization, constrained optimization

14^{th} Week

Interpolation and Properties. Polinomial interpolation, piecewise polinomial interpolation

RECOMENDED OR REQUIRED READING

(1)Scientific Computing, An Introductory Survey, Micheal T. Heath, 1997, McGraw-Hill Companies Inc. (2)Steven C. Chapra ve Raymond P. Canale, Numerical Methods for Engineers (4th Edt.), 2002, McGraw-Hill Companies Inc

PLANNED LEARNING ACTIVITIES AND TEACHING METHODS

Lecture,Problem Solving

ASSESSMENT METHODS AND CRITERIA

Quantity

Percentage(%)

Mid-term

1

35

Assignment

1

20

Total(%)

55

Contribution of In-term Studies to Overall Grade(%)

55

Contribution of Final Examination to Overall Grade(%)

45

Total(%)

100

ECTS WORKLOAD

Activities

Number

Hours

Workload

Midterm exam

1

72

72

Preparation for Quiz

1

12

12

Individual or group work

2

3

6

Preparation for Final exam

1

24

24

Course hours

14

3

42

Preparation for Midterm exam

1

11

11

Laboratory (including preparation)

0

0

0

Final exam

1

96

96

Homework

1

24

24

Total Workload

287

Total Workload / 30

9,56

ECTS Credits of the Course

10

LANGUAGE OF INSTRUCTION

Turkish

WORK PLACEMENT(S)

No

KEY LEARNING OUTCOMES (KLO) / MATRIX OF LEARNING OUTCOMES (LO)