MATH584 PARTIAL DIFFERENTIAL EQUATIONS II
| Course Code: | 2360584 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mathematics |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Assoc.Prof.Dr. KOSTYANTYN ZHELTUKHIN |
| Offered Semester: | Fall Semesters. |
Course Objectives
Introduction of Sobolev space and concept of weak solution. Application of the concept of weak solution to determine solvability of partial differential equation.
Course Content
Sobolev spaces: Weak Derivatives, Approximation by Smooth functions, Extentions, Traces, Sobolev Inequalities, The Space H^-1. Second-order Elliptic Equations: Weak Solutions, Lax-Milgram Teorem, Energy estimates, Fredholm Alternative, Regularity, Maximum Principles, Eigenvalues and Eigenfunctions. Linear Evolution Equations: Second-order Parabolic equations, (Weak solutions, Regularity, Maximum principle), Second-order Hyperbolic Equations (Weak Solutions, Regularity, Propagation of disturbances), Hyperbolic Systems of First-order Equations, Semigroup theory.
Course Learning Outcomes
Use Sobalev spaces and their properties to determine existence and uniqueness weak solutions for Elliptic, Hyperbolic and Parabolic Equations. Determine regularity of weak solutions. Use weak solutions to determine the solvability of a partial differential equation and attained different properties of a solution.
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 | Gains academic maturity through self-study. | ✔ | |||
| 3 | Can design mathematics related problems, devise solution methods and apply them when appropriate. | ✔ | |||
| 4 | Carries out parts of a mathematical research program independently. | ✔ | |||
| 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 | Gets exposed to academic culture through interaction with others. | ✔ | |||
| 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