MECH521 ANALYTICAL METHODS IN ENGINEERING I
| Course Code: | 3650521 |
| 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: | Masters |
| Course Coordinator: | Assoc.Prof.Dr. ANAR DOSIEV |
| Offered Semester: | Fall Semesters. |
Course Objectives
By the end of this course, a student will learn:
- basic tools of complex analysis (power series expansions, Laurent series, complex integration and residue caclulus, etc.)
- standard facts from linear algebra, linear independence, determinants, eigenvalues and eigenvectors, Jordan forms. inner product spaces.
- basic linear algebra needed to find eigenvalues and eigenvectors
- system of linear differential equations, basic theory, fundamental matrices, higher order linear differential equations, mechanical vibrations, resonance phenomenon, correspondence between linear second order differential equations and physical spring systems
- computation of Laplace transforms, and use to solve differential equations with discontinuous forcing functions, distributions and delta functions.
- Fourier series expansions, Fourier integral, Fourier transform.
- partial diffrential equations, heat conduction problem
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.
Course Learning Outcomes
By the end of this course, a student will:
- classify and identify different types of complex singularities,
- explicitly solve linear system of algebraic equations, find spectrum of a matrix and related eigenvectors, calculate Jordan forms and functions of a matrix,
- apply ideas from linear algebra in order to solve linear systems of ordinary differential equations and find various fundamental matrices,
- model certain physical phenomena using differential equations and reinterpret their solutions physically,
- apply the Laplace transform for solving differential equations, use distributions to solve initial value problems
- use the method of Fourier transform in order to solve some basic partial differential equations.