AEE501 ADVANCED MATHEMATICS FOR ENGINEERS I
| Course Code: | 5720501 |
| 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. Have a solid foundation in advanced mathematical concepts essential for aerospace engineering and related fields.
2. Develop proficiency in linear algebra and matrix operations, including applications in engineering systems.
3. Learn the theory and applications of tensor calculus in continuum mechanics and field theory.
4. Equip with the necessary tools of complex analysis for solving engineering problems involving analytic functions and contour integration.
5. Get the fundamentals of the calculus of variations and its relevance to optimization and dynamical systems in engineering.
6. Apply advanced mathematical methods to formulate and solve engineering problems in a rigorous and systematic way.
Course Content
Linear spaces and operators. Matrix algebra. Tensor fields. Complex analysis. Calculus of variations.
Course Learning Outcomes
By the end of this course, students will be able to:
1. Identify and apply the fundamental properties of vector spaces, linear transformations, and inner product spaces in engineering contexts.
2. Perform advanced matrix operations, including eigenvalue analysis and matrix factorizations, to model and solve linear systems arising in engineering problems.
3. Formulate and manipulate tensor fields in various coordinate systems, and apply tensor calculus to represent physical quantities such as stress and strain.
4. Analyze and solve problems involving complex-valued functions using techniques from complex analysis, including contour integration and residue calculus.
5. Use the principles of calculus of variations to derive governing equations for dynamical systems and optimize engineering functionals.
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. | ✔ | |||