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