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 | 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 | ✔ | |||