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Course Code: 
MATH 365
Semester: 
Fall
Course Type: 
Core
P: 
3
Lab: 
0
Laboratuvar Saati: 
0
Credits: 
3
ECTS: 
6
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

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