MATH381 NUMERICAL ANALYSIS I
| Course Code: | 2360381 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 6.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course, the student will learn:
-
the concepts of convergence, stability, error, and conditioning in numerical computations
-
direct and iterative methods for solving systems of linear equations
-
numerical approaches for eigenvalue and least squares problems
-
root-finding methods for nonlinear equations
Course Content
Convergence, stability, error analysis and conditioning. Solving systems of linear equations: The LU and Cholosky factorization, pivoting, error analysis in Gaussian elimination. Matrix eigenvalue problem, power method, orthogonal factorizations and least squares problems. Solutions of nonlinear equations. Bisection, Newton`s, secant and fixed point iteration methods.
Course Learning Outcomes
Student, who passed the course satisfactorily will be able to:
-
explain convergence, stability, and conditioning in numerical algorithms
-
solve linear systems using LU, Cholesky, and iterative methods
-
analyze error behavior in Gaussian elimination and related methods
-
compute eigenvalues with the power method and solve least squares problems with orthogonal factorizations
-
apply and compare root-finding methods such as bisection, Newton, secant, and fixed-point iteration
Program Outcomes Matrix
| Level of Contribution | |||||
| # | Program Outcomes | 0 | 1 | 2 | 3 |
| 1 | Acquires mathematical thinking skills (problem solving, generating ways of thinking, forming correspondence, generalizing etc.) and can use them in related fields. | ✔ | |||
| 2 | Can produce innovative thoughts and products. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Has a comprehension of mathematical symbols, concepts together with the interactions among them and can express his/her solutions similarly. | ✔ | |||
| 5 | Has a command of Turkish and English languages so that he/she can actively communicate (read, write, listen and speak). | ✔ | |||
| 6 | Contributes to solving global, environmental and social problems either individually or as being part of a social group. | ✔ | |||
| 7 | Respects ethical values and rules; applies them in professional and social issues. | ✔ | |||
| 8 | Can work cooperatively in a team and also individually. | ✔ | |||
| 9 | Is responsive to life-long learning, improving his/her skills and abilities | ✔ | |||
| 10 | Comprehends necessity of knowledge, can define it and acquires it; uses knowledge effectively and shares it with others | ✔ | |||
0: No Contribution 1: Little Contribution 2: Partial Contribution 3: Full Contribution