ME521 ANALYTICAL METHODS IN ENGINEERING I
| Course Code: | 5690521 |
| 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 differential equation analysis and solution techniques
2. Mathematical functions and transformations common in engineering problems
3. Analytical thinking and conceptualization skills
Course Content
Review of ordinary differential equations: Series solutions; special functions (Bessel, Legendre, Fourier). Boundary and initial value problems (Sturm-Liouville). Laplace and Fourier transforms. Fourier integrals. Introduction to integral equations. Introduction to calculus of variations. Partial differential equations; separation of variables. Transformations. (R)
Course Learning Outcomes
At the end of this course, the students will be able to 1. Use the concepts and methods of standard ODE analysis including linearity, linear independence, homogeneity, constant coefficient and equidimensional equations, system of equations, operator notation and variation of parameters. 2. Develop series solutions for linear second order ODE’s, using regular and singular point expansions. 3. Identify and solve Legendre and Bessel equations using Legendre polynomials and Bessel functions, respectively. 4. Develop Fourier series and Fourier integral representations of given suitable functions. 5. Develop operational skills to use Fourier, Fourier sine and Fourier cosine transforms. 6. Identify and solve Sturm-Liouville problems. 7. Identify and solve parabolic PDE’s, e.g. the heat equation, using separation of variables, Fourier and Laplace transforms. 8. Identify and solve hyperbolic PDE’s, e.g. the wave equation, using separation of variables, D’Alembert’s method and Fourier and Laplace transforms. 9. Identify and solve elliptic PDE’s, e.g. the Laplace equation, using separation of variables and Fourier transform.