MATH254 DIFFERENTIAL EQUATIONS
| Course Code: | 2360254 |
| METU Credit (Theoretical-Laboratory hours/week): | 4 (4.00 - 0.00) |
| ECTS Credit: | 7.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Lecturer Dr. MUHİDDİN UĞUZ |
| Offered Semester: | Fall Semesters. |
Course Objectives
The objectives of this course are to introduce the student with the concept of a differential equation, basic techniques for solving certain classes of differential equations, especially those which are linear, and making connections between the qualitative features of the equation and the solutions. Connections to problems from the physical world are emphasized. As well as ordinary differential equations, the course aims to introduce the students to certain partial differential equations.
Course Content
Existence and uniqueness theorems. First order equations. Trajectories. Higher order linear equations; undetermined coefficients, variation of parameters and operator methods. Power series solutions. Laplace transform solutions of IVPs. Theory of linear systems. Solutions by operator, Laplace and linear algebra methods. Partial differential equations, separation of variables and Fourier series.
Course Learning Outcomes
By the end of this course, a student will:
- classify and identify different types of differential equations,
- explicitly solve several important classes of ordinary differential equations and interpret their qualitative behavior,
- apply ideas from linear algebra in order to solve single linear ordinary differential equations and systems of such equations,
- model certain physical phenomena using differential equations and reinterpret their solutions physically,
- use power series methods to solve second order linear differential equations
- apply the Laplace transform for solving differential equations,
- use the method of separation of variables in order to solve some basic partial differential equations via Fourier series
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