Information Package / Course Catalogue - Adnan Menderes University

General Information Unit Staff Academic Information Programme Outcomes Course Structure Diagram Contact Information

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Numerical Solution of Differential Equations

Course Code	: MTK527
Course Type	: Area Elective
Couse Group	: Second Cycle (Master's Degree)
Education Language	: Turkish
Work Placement	: N/A

Theory	: 3
Prt.	: 0
Credit	: 3
Lab	: 0
ECTS	: 8

Objectives of the Course

This course aims to acquaint students with the basic knowledge of numerical solution of some differential equations. Students will be familiar with classification of equations initial and boundary value problems and relation between Volterra and Fredholm integrals. They may easily understand the features of topics used at the area of information other courses. They will be able to make applications related to biology, and other sciences.

Course Content

Introduction to MATLAB and integral theory, Local truncation errors, Butcher table and Runge-Kutta method And Adams methods, Linear and Nonlinear Volterra integral equations of the second kind, Numerical stability of Multi-step methods.

Name of Lecturer(s)

Assoc. Prof. Korhan GÜNEL

Learning Outcomes

1.	To be able to comprehend the importance of the some basic concepts of the integral equations
2.	To be able to write numerical programming with MATLAB.
3.	To be able to design numerical quadrature.
4.	To be able to implement Butcher table and their algorithms.
5.	To be able to use mathematical concepts in solving certain types of problems

Recommended or Required Reading

1.	Clay C. Rose, (2004), Differential Equations, Springer, second edition.
2.	B. R. Hunt, R. L. Lipsman, J. E. Osborn, J. M. Rosenberg, (2005), Differential Equations with MATLAB

Weekly Detailed Course Contents

Week 1 - Theoretical

Introduction of MATLAB and differential equations

Week 2 - Theoretical

Ordinary differential equations., Initial and boundary value problems and solution of methods,

Week 3 - Theoretical

Numerical solution of Volterra integral equations

Week 4 - Theoretical

Stability analysis of numerical solution of Volterra integral equations

Week 5 - Theoretical

Local truncation errors and order of convergence

Week 6 - Theoretical

Linear and non-linear differential equations

Week 7 - Theoretical

Single step methods for differential equations

Week 8 - Theoretical

Linear and Nonlinear Volterra integral equations of the second kind, Midterm exam

Week 9 - Theoretical

Linear and Nonlinear Volterra integral equations of the second kind

Week 10 - Theoretical

Numerical stability of Single step methods

Week 11 - Theoretical

Taylor series and Runge-Kutta methods

Week 12 - Theoretical

Butcher table and Runge-Kutta method And Adams methods

Week 13 - Theoretical

Numerical stability analysis of Multi-step methods

Week 14 - Theoretical

Stability Analysis

Week 15 - Final Exam

FINAL EXAM

Assessment Methods and Criteria

Type of Assessment	Count	Percent
Midterm Examination	1	%30
Final Examination	1	%70

Workload Calculation

Activities	Count	Preparation	Time	Total Work Load (hours)
Lecture - Theory	14	0	3	42
Individual Work	14	0	4	56
Midterm Examination	1	42	3	45
Final Examination	1	54	3	57
TOTAL WORKLOAD (hours)				200

Contribution of Learning Outcomes to Programme Outcomes

	PÇ-1	PÇ-2	PÇ-3	PÇ-4	PÇ-5	PÇ-6	PÇ-7	PÇ-8	PÇ-9	PÇ-10	PÇ-11	PÇ-12	PÇ-13	PÇ-14	PÇ-15
OÇ-1	3	3	3	3								3			4
OÇ-2	4	4	4	4	4		4								4
OÇ-3	4	4	4	4	4		4								4
OÇ-4	4		4									5			3
OÇ-5	4		4	4								4			3

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