Understanding the basic concepts of Numerical Solution of Integral Equations.
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. Hikmet ÇAĞLAR
Course Assistant(s)
None.
Schedule
Will be announced in the forthcoming term.
Office Hour(s)
Yrd. Doç. Dr. Hikmet ÇAĞLAR, AK/3-A-15.
Teaching Methods and Techniques
Lecture and homeworks.
Principle Sources
Handbook of Integral Equations 2008, Andrei D. Polyanin, Alexander V. Manzhirov
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction and background material
Lecture and homework
2. Week
An incomplete list of matrices possessing a reduced-in-complexity matrix-
vector product
Lecture and homework
3. Week
Integral operators for the Parabolic problem (Heat equation) and the fast
Gauss transform
Lecture and homework
4. Week
Integral operators for the Elliptic problem (Poisson and Helmholtz equation)
Lecture and homework
5. Week
The Fast Multipole Method for the 2D Poisson problem
Lecture and homework
6. Week
The Fast Multipole Method for the 3D Poisson problem
Lecture and homework
7. Week
The Fast Multipole Method for the 2D Helmholtz problem
Lecture and homework
8. Week
Midterm
Midterm
9. Week
The Fast Multipole Method for the 3D Helmholtz problem
Lecture and homework
10. Week
Fast Methods for the electromagnetism: the Maxwell problem
Lecture and homework
11. Week
Kernel-free Fast Multipole Methods
Lecture and homework
12. Week
Integral operators for the Hyperbolic problem and related
fast methods
Lecture and homework
13. Week
An outline on preconditioning of boundary elements linear systems
Lecture and homework
14. Week
Calderon preconditioning techniques
Lecture and homework
15. Week
Final exam
16. Week
Final exam
17. Week
Final exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
50
Final Exam
1
50
Program Outcomes
PO-1
Have ability to develop new mathematical ideas and methods by using high-level mental processes such as creative and critical thinking, problem solving and decision-making.
PO-2
Follow the current developments in the field of mathematics, and make the critical analysis, synthesis and evaluation of new and complex ideas.
PO-3
Understand the interdisciplinary interaction related to Mathematics and play a role in an effective manner in environments that require with the resolution of problems encountered in this process.
PO-4
Defend original views on the discussion of the issues in the field of mathematics with experts and communicate to show competence in oral and written.
PO-5
Do research with high-level national and international scientific working groups, and acquire the responsibility to contribute to the literature by publishing original works in respected scientific journals.
PO-6
Use computer software to solve problems effectively by following the developments in information and communication technologies.
PO-7
Contribute to the solution of social, scientific, cultural and ethical problems encountered issues related to the field and support the development of these values.
PO-8
To solve problems related to the field, establish functional interacts by using strategic decision making processes.
PO-9
Establish and discuss in written, oral and visual communication at an advanced level by using at least one foreign language.
Learning Outcomes
LO-1
Learn basic techniques
LO-2
The learning basic skills of modeling and solving Integral Equations are the major goals of this course.
LO-3
Understand in the science and engineering fields, many physical phenomena can be mathematically modeled and yield to Integral Equations.
LO-4
Understand the statements of basic theories of existence.
LO-5
Understand the statements of basic theories uniqueness, and stability for Integral Equations.
