ME540 ANALYTICAL METHODS IN ENGINEERING II
| Course Code: | 5690540 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. IŞIK HAKAN TARMAN |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
This course aims to instill/promote the following knowledge, behaviors and skills in the students
1. Advanced level complex calculus techniques and applications
2. Advanced level variational calculus techniques and applications
3. Advanced level integral equation analysis and solution techniques
4. Analytical thinking and conceptualization skills
Course Content
Laplace transforms. Integral equations. Integro-differential equations. Calculus of variations. Singularity functions. Fundamentals of matrix algebra and applications in engineering. Introduction to tensor calculus. Complex functions and contour integrals. (R)
Course Learning Outcomes
At the end of this course, the students will be able to 1. Use the concepts and methods of complex numbers, complex functions, multi-valuedness, branch points and branch cuts, complex differential calculus, analytic functions, complex integral calculus, Laurent series and series expansions, residue theory and applications to real integrals, Laplace and Fourier transform inversions, Conformal mapping. 2. Use the concepts and methods of variational calculus, extremalization of functionals, essential and natural boundary conditions, extremalization of functionals with constraints, method of Lagrange multipliers, extremalization of functionals with variable boundaries, weak form of differential equations, Rayleigh-Ritz method. 3. Use the concepts and methods of integral equations, classifications, Fredholm and Volterra type integral equations, integral equations with separable (degenerate) kernel, solution techniques, Fredholm alternative.
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Acquires the fundamental scientific knowledge required to analyze and solve advanced-level problems in the field of mechanical engineering. | ✔ | |||
| 2 | Gains the competence to utilize advanced engineering mathematics methods in the formulation, analysis, and solution of engineering problems. | ✔ | |||
| 3 | Conducts literature reviews using printed and online sources, analyzes the collected literature, and identifies the current state-of-the-art in the relevant scientific field. | ✔ | |||
| 4 | Demonstrates the ability to prepare and deliver a seminar on a technical subject. | ✔ | |||
| 5 | Develops the ability to conduct independent research on a specific topic and solve advanced engineering problems. | ✔ | |||
| 6 | Contributes to the national and/or international body of knowledge through original research. | ✔ | |||
| 7 | Gains the competence to effectively communicate the process and results of research conducted on a specific subject through scientifically structured written reports and oral presentations. | ✔ | |||
| 8 | Acquires the ability to publish research findings as articles in national and/or international scientific journals and/or present them as papers at conferences. | ✔ | |||
| 9 | Acts in accordance with universal principles of research and publication ethics. | ✔ | |||