AEE502 ADVANCED MATHEMATICS FOR ENGINEERS II
| Course Code: | 5720502 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Aerospace Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. SERKAN ÖZGEN |
| Offered Semester: | Fall Semesters. |
Course Objectives
By taking this course, the students will:
1. Develop a solid understanding of ordinary and partial differential equations, including their classification, formulation, and solution techniques.
2. Apply power series methods to solve linear differential equations and gain familiarity with special functions such as Bessel, Legendre, and Hermite functions.
3. Solve boundary-value problems using appropriate analytical and semi-analytical methods.
4. Utilize transform techniques, including Laplace and Fourier transforms, to analyze and solve engineering problems involving differential equations.
5. Construct and use Green’s functions to solve linear inhomogeneous differential equations with specified boundary conditions.
6. Analyze and solve classical partial differential equations of parabolic, elliptic, and hyperbolic types relevant to various engineering applications.
7. Apply perturbation methods, including regular and singular perturbation techniques, to obtain approximate solutions to complex or multiscale problems.
8. Strengthen mathematical modeling and analytical skills essential for solving advanced engineering problems across multiple disciplines.
Course Content
General consideration on differential equations. Power series solutions and special functions. Boundary-value problems. Transform methods. Green's functions. Partial differential equations. Perturbation methods.
Course Learning Outcomes
By the end of this course, students will be able to:
1. Classify and formulate ordinary and partial differential equations relevant to engineering problems.
2. Solve linear differential equations using power series expansions and identify the resulting special functions.
3. Analyze and solve boundary-value problems using appropriate analytical techniques.
4. Apply Laplace and Fourier transform methods to solve differential equations and interpret their physical meaning.
5. Construct and interpret Green’s functions for linear differential equations with given boundary conditions.
6. Identify and solve parabolic, elliptic, and hyperbolic partial differential equations using classical methods.
7. Apply regular and singular perturbation techniques to derive approximate solutions to engineering problems with small parameters.
8. Translate physical systems into mathematical models and critically evaluate the solutions in the context of engineering applications.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | An ability to identify, formulate, and solve complex engineering problems by applying principles of engineering, science, and mathematics | ✔ | |||
| 2 | An ability to apply engineering design to produce solutions that meet specified needs with consideration of public health, safety, and welfare, as well as global, cultural, social, environmental, and economic factors | ✔ | |||
| 3 | An ability to communicate effectively with a range of audiences | ✔ | |||
| 4 | An ability to recognize ethical and professional responsibilities in engineering situations and make informed judgments, which must consider the impact of engineering solutions in global, economic, environmental, and societal contexts | ✔ | |||
| 5 | An ability to function effectively on a team whose members together provide leadership, create a collaborative and inclusive environment, establish goals, plan tasks, and meet objectives | ✔ | |||
| 6 | An ability to develop and conduct appropriate experimentation, analyze and interpret data, and use engineering judgment to draw conclusions | ✔ | |||
| 7 | An ability to acquire and apply new knowledge as needed, using appropriate learning strategies | ✔ | |||