Syllabus ( MATH 214 )

Basic information


Course title: 
Numerical Analysis 
Course code: 
MATH 214 
Lecturer: 
Prof. Dr. Mansur İSGENDEROĞLU (İSMAİLOV)

ECTS credits: 
5 
GTU credits: 
3 (3+0+0) 
Year, Semester: 
2, Spring 
Level of course: 
First Cycle (Undergraduate) 
Type of course: 
Compulsory

Language of instruction: 
Turkish

Mode of delivery: 
Face to face

Pre and corequisites: 
none 
Professional practice: 
No 
Purpose of the course: 
Teaching the error concepts and numerical programming techniques concerning the basic mathematical operations (interpolation, derivative, integral solution of linear algebraic equations and non linear equations) computation of which are performed by means of computer. 



Learning outcomes


Upon successful completion of this course, students will be able to:

develop numerical solutions for basic mathematical operations (interpolation, derivative, integral solution of linear algebraic equations and non linear equations etc.)
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

compute errors in numerical solutions
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam

write computer programming code for numerical solutions
Contribution to Program Outcomes

Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.

Describing, formulating, and analyzing reallife problems using mathematical and statistical techniques.

Having improved abilities in mathematics communications, problemsolving, and brainstorming skills.

Using technology as an efficient tool to understand mathematics and apply it.
Method of assessment

Written exam


Contents


Week 1: 
Number systems and errors: Representation of integers and fractions. 
Week 2: 
Floating point arithmetic, loss of significance and error propagation. 
Week 3: 
Interpolation by polynomial:Polynomial forms, existence and uniqueness of interpolating polynomial. 
Week 4: 
Interpolation by polynomial: Divided difference table, the error of interpolating polynomial. 
Week 5: 
Numerical differentiation, numerical integrationsome basic rules and Gauss rules. 
Week 6: 
Numerical integration: Composite rules, adaptive quadrature. 
Week 7: 
The solution of nonlinear equations: A survey of iterative methods, fixed point iteration. 
Week 8: 
The solution of nonlinear equations:Convergence acceleration for fixed point iteration, convergence of Newton and Secant methods. 
Week 9: 
The solution of nonlinear equations: Polynomial equations real roots, complex roots Müller method. 
Week 10: 
Midterm exam and solutions 
Week 11: 
Matrices and Systems of Linear Equations: Properties of matrices, the solution of linear systems by elimination. 
Week 12: 
Matrices and Systems of Linear Equations:Pivoting strategies, the triangular factorization. 
Week 13: 
Matrices and Systems of Linear Equations:Error and residual of an approximate solution; norm. 
Week 14: 
Matrices and Systems of Linear Equations:Backwarderror analysis and iterative improvement, Determinants and the eigenvalue problem. 
Week 15*: 
 
Week 16*: 
Final exam 
Textbooks and materials: 

Recommended readings: 
Elementary Numerical Analysis  An algorithmic Approach, S.D. Conte, Carl de Boor, McGraw Hill, International Series in Pure and Applied Mathemeatics 

* Between 15th and 16th weeks is there a free week for students to prepare for final exam.




Assessment



Method of assessment 
Week number 
Weight (%) 

Midterms: 
10 
40 
Other interm studies: 

0 
Project: 

0 
Homework: 

0 
Quiz: 

0 
Final exam: 
16 
60 

Total weight: 
(%) 



Workload



Activity 
Duration (Hours per week) 
Total number of weeks 
Total hours in term 

Courses (Facetoface teaching): 
3 
14 

Own studies outside class: 
3 
14 

Practice, Recitation: 
0 
0 

Homework: 
0 
0 

Term project: 
0 
0 

Term project presentation: 
0 
0 

Quiz: 
0 
0 

Own study for midterm exam: 
10 
1 

Midterm: 
3 
1 

Personal studies for final exam: 
20 
1 

Final exam: 
3 
1 



Total workload: 



Total ECTS credits: 
* 

* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)



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