Course Information
SemesterCourse Unit CodeCourse Unit TitleL+PCreditNumber of ECTS Credits
7MATH481DIFFERENTIAL EQUATIONS WITH NUMERICAL METHODS2+236

Course Details
Language of Instruction English
Level of Course Unit First Cycle
Department / Program MATHEMATICS
Mode of Delivery Face to Face
Type of Course Unit Elective
Objectives of the Course 1. To learn the basic concepts in the numerical solution of PDEs
2. To understand the major mathematical ideas behind the numerical methods for solving differential equations
3. To formulate numerical methods for solving PDEs and study their properties
4. To study the theory of numerical methods for partial differential equations
5. To use MATLAB to implement the numerical methods on computer
Course Content Initial and Boundary Value Problems. Heat Equation. Wave Equation. Elliptic PDE problems. Reaction- Convection-Diffusion Problems. Upwind and Centred Approximation Method. Poisson equation in 2D. Explicit and Implicit methods.
Course Methods and Techniques
Prerequisites and co-requisities None
Course Coordinator None
Name of Lecturers Associate Prof.Dr. ALİ İHSAN NESLİTÜRK
Assistants None
Work Placement(s) No

Recommended or Required Reading
Resources “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
Lecture Notes”, David J. Silvester ,2008.

Course Category

Planned Learning Activities and Teaching Methods
Activities are given in detail in the section of "Assessment Methods and Criteria" and "Workload Calculation"

Assessment Methods and Criteria
In-Term Studies Quantity Percentage
Midterm exams 2 % 60
Quizzes 0 % 0
Homeworks 0 % 0
Other activities 0 % 0
Laboratory works 0 % 0
Projects 0 % 0
Final examination 1 % 40
Total
3
% 100

ECTS Allocated Based on Student Workload
Activities Quantity Duration Total Work Load
Weekly Course Time 1 24 24
Outside Activities About Course (Attendance, Presentation, Midterm exam,Final exam, Quiz etc.) 1 50 50
Application (Homework, Reading, Self Study etc.) 1 24 24
Exams and Exam Preparations 1 125 125
Total Work Load   Number of ECTS Credits 7 223

Course Learning Outcomes: Upon the successful completion of this course, students will be able to:
NoLearning Outcomes
1 1. Ability to solve real world problems arising in the form of differential equations by numerical methods
2 2. Construct appropriate finite-difference approximations to PDEs
3 3. Write programs to solve PDEs by finite difference methods
4 4. Ability to estimate the error a priori
5 5. Verify experimentally the convergence and accuracy of numerical methods


Weekly Detailed Course Contents
WeekTopicsStudy MaterialsMaterials
1 Initial and Boundary Value Problems “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
2 Initial and Boundary Value Problems “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
3 The Heat Equation “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
4 The Wave Equation “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
5 Arasınav 1
6 Elliptic PDE problems “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
7 Sturm-Liouville Theory “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
8 Reaction-Diffusion Problem “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
9 Convection–Diffusion Problem: Upwind Approximation Method “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
10 Arasınav 2
11 Convection–Diffusion Problem: Centered Approximation Method “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
12 Poisson equation in 2D “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
13 Heat Equation: Explicit methods “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
14 Heat Equation: Implicit methods “Elementary Numerical Analysis”, Third Edition, Kendall Atkinson& Weimin Han, 2004.
15 Final 1st week
16 Final 2nd week


Contribution of Learning Outcomes to Programme Outcomes
P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P11 P12 P13 P14
C1 4 4 4
C2 4 4 3
C3 4
C4 4
C5 4 4

Contribution: 0: Null 1:Slight 2:Moderate 3:Significant 4:Very Significant


https://obs.iyte.edu.tr/oibs/bologna/progCourseDetails.aspx?curCourse=163234&lang=en