The goal of this course is to provide a solid foundation in the study of classical
boundary value problems that arise in engineering and physics. In addition, the student will learn how to
utilize a computer algebra package such as Matlabin problem solving a crucial skill for today’s
applied mathematician.
Prerequisite(s)
None.
Corequisite(s)
None.
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)
Assist. Prof. Dr. Canan Akkoyunlu
Course Assistant(s)
None.
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Yrd. Doç. Dr. Hikmet ÇAĞLAR, AK/3-A-09.
Teaching Methods and Techniques
Lecturing and problem solving.
Principle Sources
Numerical Methods for viscosity solutions and applications, Falcone M., Makridakis C., 2001
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
Introducing Ordinary Differential Equations
Lecture
2. Week
Introduction to MATLAB and practical numerical analysis
Lecture
3. Week
Approximate solutions of the nonlocal boundary value problems for PDE mixed types.
Lecture
4. Week
Finite difference schema.
Lecture
5. Week
Finite difference schema.
Lecture
6. Week
Understand numerical basic concepts.
Lecture
7. Week
Introduction to Numerical Methods:
Lecture
8. Week
Midterm Exam
Midterm Exam
9. Week
Solution of Non-linear boundary value problems
Lecture
10. Week
Computer applications.
Lecture
11. Week
Solution of linear boundary value problems with local condition
Lecture
12. Week
Solution of linear boundary value problems with local condition(Cont.)
Lecture
13. Week
Solution of linear boundary value problems with non-local condition
Lecture
14. Week
Solution of linear boundary value problems with non-local condition(Cont.)
Lecture
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have scientific research in mathematics and computer science in the level of theoretical and practical knowledge.
PO-2
On the basis of undergraduate level qualifications, develop and deepen the same or a different areas of information at the level of expertise, and analyze and interpret by using statistical methods
PO-3
Develop new strategic approaches for the solution of complex problems encountered in applications related to the field and unforeseen and take responsibility for the solution.
PO-4
Evaluate critically skills acquired in the field of information in the level of expertise and assess the learning guides.
PO-5
Transfer current developments in the field and their work to the groups inside and outside the area supporting with quantitative and qualitative datas as written, verbal and visual by a systematic way.
PO-6
Use information and communication technologies with computer software in advanced level.
PO-7
Develop efficient algorithms by modeling problems faced in the field and solve such problems by using actual programming languages.
PO-8
Respect to social, scientific, cultural and ethical values at the stages of data collection related to the field, interpretation, and implementation.
PO-9
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-10
Establish and discuss in written, oral and visual communication in an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
At the end of this unit the students will have acquired the concept of approximate solutions of both ordinary and partial differential boundary value problems by finite difference methods and be able to analyse the matrices which arise from the discretization procedures.
LO-2
To learn the single step methods for the numerical solution of ordinary differantial equation
LO-3
To learn finite difference methods for ordinary differential equation
LO-4
: To learn the numerical solution of high degree differential equation and systems of equations
LO-5
To demostrate applications id different discipline