This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Prerequisite(s)
-
Corequisite(s)
-
Special Requisite(s)
-
Instructor(s)
Assist. Prof. Dr. M. Fatih Uçar
Course Assistant(s)
-
Schedule
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Office Hour(s)
Monday 13:00-15:00 3A-04
Teaching Methods and Techniques
-Lectures and recitation.
Principle Sources
-Richard L. Burden and J. Douglas Faires Numerical Analysis, ninth edition, Brooks/Cole, Cengage Learning 2011, ISBN-13:978-0-538-73564-3.
Other Sources
*K. Atkinson and W. Han, Elementary Numerical Analysis, John Wiley, 3rd edition.
*A. Ralston and P.Rabinowitz, A First Course in Numerical Analysis, Dover Publications Inc.
*C.F. Gerald and P.O. Wheatly, Applied Numerical Analysis, Addison-Wesley Publishing Company
* James Payne, Beginning Python : Using Python 2.6 and Python 3.1, Wiley Publishing Inc., Indianapolis, Indiana, 2010.
Course Schedules
Week
Contents
Learning Methods
1. Week
Mathematical structure and error analysis; source of errors, stability and convergence analysis
Oral presentation and Laboratory
2. Week
Root finding problems and methods
Oral presentation and Laboratory
3. Week
Weierstrass approximation theorem, higher order Taylor theorem, minimax approximation
Oral presentation and Laboratory
4. Week
Spline interpolation; linear, quadratic and cubic splines
Oral presentation and Laboratory
5. Week
Rational interpolation, Padé approximations and error analysis
Oral presentation and Laboratory
6. Week
Chebyshev polynomials and error analysis
Oral presentation and Laboratory
7. Week
Curve fitting and least squares
Oral presentation and Laboratory
8. Week
Numerical methods for the solution of system of linear equations; LU-QR Decomposition, Jacobi Method, Gauss Seidal Method and SOR
Oral presentation and Laboratory
9. Week
Numerical methods to find eigenvalue and eigenvector of a matrix
Oral presentation and Laboratory
10. Week
Ordinary differential equations; existence and uniquness of the solution
Oral presentation and Laboratory
11. Week
Numerical solution for the initial value problems; Picard Method, Euler Method, Runge-Kutta Methods
Oral presentation and Laboratory
12. Week
Discritization and numerical solution for the higher order differential equations
Oral presentation and Laboratory
13. Week
Discritization and numerical solution for the partial differential equations
Oral presentation and Laboratory
14. Week
Stability and convergence analysis
Oral presentation and Laboratory
15. Week
Final exam
Exam
16. Week
Final exam
Exam
17. Week
Final exam
Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
30
Homework / Term Projects / Presentations
2
30
Final Exam
1
40
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
Approximate functions using first and second order Taylor polynomials, and calculates an upper bound of the error in these approximations.
LO-2
Solve initial value problems numerically.
LO-3
Solve systems of ordinary differential equations via numerical methods.
LO-4
Approximate linear and nonlinear equations with finite difference method.
LO-5
Approximate solution of systems of linear equations numerically.
