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 | Possesses advanced knowledge in one or more subfields of aerospace engineering and applies this knowledge effectively in engineering practices and solution processes. | ✔ | |||
| 2 | Follows current scientific and technological developments in the field, identifies research problems, generates solutions using appropriate methods, and interprets the results. | ✔ | |||
| 3 | Employs analytical thinking and numerical methods in solving complex engineering problems and, when necessary, develops and applies appropriate experimental approaches. | ✔ | |||
| 4 | Uses appropriate modeling, analysis, simulation, and experimental methods for complex engineering problems, evaluates the results, and makes engineering decisions. | ✔ | |||
| 5 | Clearly and systematically communicates scientific and technical knowledge in written and oral form, works effectively in intra-disciplinary and interdisciplinary teams, and assumes leadership when necessary. | ✔ | |||
| 6 | Acts with professional ethics and awareness of social and environmental responsibility and evaluates the possible impacts of engineering solutions. | ✔ | |||
| 7 | Understands the importance of lifelong learning and effectively uses methods to access new knowledge. | ✔ | |||
| 8 | Is aware of fundamental engineering problems related to national aerospace, defense, and energy technologies and possesses the competence to contribute to these areas. | ✔ | |||