NUMERICAL ANALYSIS

Course Code:

MATH 365

Course Type:

Area Elective

P:

3

Lab:

0

Laboratuvar Saati:

0

Credits:

3

ECTS:

7

Course Language:

English

Course Objectives:

Getting know and examine different numerical methods for various type of caluculations.

Course Content:

Introduction and background. Iterative solution of non-linear equations, bisection method, fixed point iteration, Newton’s and the secant method. Polynomial, divided differences and finite differences interpolations. Systems of linear equations, Gaussian elimination, LU decomposition, iterative methods. Numerical differentiation and integration.

Course Methodology:

1: Lecture, 2: Problem Solving, 3: Question-answer, 4: Homework

Course Evaluation Methods:

A: Written examination, B: Homework

Vertical Tabs

Course Learning Outcomes

Learning Outcomes	Program Learning Outcomes	Teaching Methods	Assessment Methods
1) can determine roots of higher order equations numerically.		1,2,3,4	A
2) have a basic knowledge of numerical interpolation and approximation of functions		1,2,3,4	A
3) have a basic knowledge of numerical integration and differentiation.		1,2,3,4	A
4) is familiar with numerical solution of ordinary differential equations [		1,2,3,4	A
5) can do error analysis		1,2,3,4	A

Course Flow

Week	Topics	Study Materials
1	Basic definitions, Taylor polynomials,	Course book:Chapter 1,3
2	Rootfinding, bisection method	4.1
3	Newton`s method, fixed point iteration	4.2, 4.4
4	Polynomial interpolation, Divided differences, Error in polynomial interpolation	5.1,5.2,5.3
5	Approximation problems, error	Chapter 6
6	Numerical integration, the trapezoidal and Simpson rules,	7.1
7	error formulas. Gaussian numerical integration method.	7.2,7.3
8	Numerical differentiation, Differentiation by interpolation,	7.4
9	MIDTERM
10	An introduction to numerical solutions to differential equations	9.1
11	Euler’s method, convergence.	9.2, 9.3
12	Taylor and Runge-Kutta methods	9.4
13	Cont.	9.4
14	review

Recommended Sources

Textbook

K. E. Atkinson, W. Han, Elementary

Numerical Analysis, 3Ed. John Wiley, 2004.

Additional Resources

Material Sharing

Documents
Assignments
Exams

Assessment

IN-TERM STUDIES	NUMBER	PERCENTAGE
Mid-terms	1	100
Quizzes	-
Assignments	-
Total		100
CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE		50
CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE		50
Total		100

COURSE CATEGORY

Expertise/Field Courses

Course’s Contribution to Program

No	Program Learning Outcomes	Contribution
No	Program Learning Outcomes	1	2	3	4	5
1	The ability to make computation on the basic topics of mathematics such as limit, derivative, integral, logic, linear algebra and discrete mathematics which provide a basis for the fundamenral research fields in mathematics (i.e., analysis, algebra, differential equations and geometry)					X
2	Acquiring fundamental knowledge on fundamental research fields in mathematics			X
3	Ability form and interpret the relations between research topics in mathematics		X
4	Ability to define, formulate and solve mathematical problems					X
5	Consciousness of professional ethics and responsibilty			X
6	Ability to communicate actively	X
7	Ability of self-development in fields of interest					X
8	Ability to learn, choose and use necessary information technologies				X
9	Lifelong education				X

ECTS

Activities	Quantity	Duration (Hour)	Total Workload (Hour)
Course Duration (14x Total course hours)	14	3	42
Hours for off-the-classroom study (Pre-study, practice)	14	2	28
Mid-terms (Including self study)	1	15	15
Quizzes
Assignments	11	3	33
Final examination (Including self study)	1	25	25
Total Work Load			143
Total Work Load / 25 (h)			5,72
ECTS Credit of the Course			6

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