Course Code	Semester	Course Name	LE/RC/LA	Course Type	Language of Instruction	ECTS
MB0071		Numerical Analysis II	2/2/0	DE	Turkish	5

Course Goals	To introduce 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)	Numerical Analysis I
Corequisite(s)	-
Special Requisite(s)	-
Instructor(s)	Assist. Prof. Dr. M. Fatih Uçar
Course Assistant(s)	-
Schedule	-
Office Hour(s)	Monday 13:00-15:00 3A-04
Teaching Methods and Techniques	-Lecture and laboratory 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	Taylor Polynomials for the functions in two variable, Numerical solutions of initial value problems: Picard Method, Euler Method	Lecture and laboratory recitation
2. Week	Numerical solutions of initial value problems: Runge-Kutta Methods	Lecture and laboratory recitation
3. Week	Numerical solutions of system of ordinary differential equations	Lecture and laboratory recitation
4. Week	Numerical solutions of higher order differential equations	Lecture and laboratory recitation
5. Week	Finite difference methods for the solution of linear problems	Lecture and laboratory recitation
6. Week	Finite difference methods for the solution of nonlinear problems	Lecture and laboratory recitation
7. Week	Numerical methods for the system of linear equation: LU-QR Factorization	Lecture and laboratory recitation
8. Week	Numerical methods for the system of linear equation: Jacobi method, Gauss-Seidel method and SOR	Lecture and laboratory recitation
9. Week	Numerical methods for finding eigenvalues and eigenvectors of a matrix.	Lecture and laboratory recitation
10. Week	Numerical methods for finding eigenvalues and eigenvectors of a matrix.	Lecture and laboratory recitation
11. Week	Interpolation: Spline interpolations; linear, quadratic and cubic splines	Lecture and laboratory recitation
12. Week	Interpolation: Curve fitting, discrete least squares method and orthogonal polynomials.	Lecture and laboratory recitation
13. Week	Interpolation: Rational interpolation, Padé approximation and error analysis	Lecture and laboratory recitation
14. Week	Chebyshev polynomials and error analysis	Lecture and laboratory recitation
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	20
Final Exam	1	50

Program Outcomes PO-1 Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science. PO-2 Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science. PO-3 Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence. PO-4 Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline. PO-5 Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science. PO-6 Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish. PO-7 Using time effectively in inventing solutions by implementing analytical thinking. PO-8 Understanding professional ethics and responsibilities. PO-9 Having the ability to behave independently, to take initiative, and to be creative. PO-10 Understanding the importance of lifelong learning and developing professional skills continuously. PO-11 Using professional knowledge for the benefit of the society.

Learning Outcomes LO-1 Set up second order Taylor polynomials for the functions in two variables. LO-2 Calculate numerical solution of initial value problems. LO-3 Find numerical solutions to system of ordinary differential equations. LO-4 Construct finite differences to solve linear and nonlinear equations. LO-5 Uses several methods to solve system of linear equations. LO-6 Apply some methods for approximation theory.

Course Assessment Matrix:

	PO 1	PO 2	PO 3	PO 4	PO 5	PO 6	PO 7	PO 8	PO 9	PO 10	PO 11