AEE305 NUMERICAL METHODS
| Course Code: | 5720305 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 5.0 |
| Department: | Aerospace Engineering |
| Language of Instruction: | English |
| Level of Study: | Undergraduate |
| Course Coordinator: | Assoc.Prof.Dr. NİLAY SEZER UZOL |
| Offered Semester: | Fall Semesters. |
Course Objectives
At the end of this course the students will have an
- An ability to expand functions into Taylor series and related truncation errors, and round-off errors
- An ability to solve first and higher-order initial value ODEs, and coupled set of initial value ODEs with multi-step (Runge-Kutta) methods
- An ability to solve coupled set of initial value ODEs
- An ability to formulate conservation laws in integral and partial differential forms
- An ability to discretize integral forms of governing equations in finite
volumes - An ability to discretize PDEs in finite differences and perform Fourier stability analysis
- An ability to classify PDEs as elliptic, parabolic and hyperbolic, and make proper choice of numerical methods for their solution
- An ability to write a computer program to solve initial value ODEs in general
- An ability to implement and/or modify finite volume and finite difference
methods in Fortran - An ability to compile and run Fortran programs on computers and analyze results using graphical tools
- An ability to work on teams
- An ability to report homework solutions in technical form
- An ability to make ethical choices
Course Content
Numerical solution of Ordinary Differential Equations (ODE): Initial value problems;
Runge-Kutta methods; Adaptive stepping; Systems of ODEs; Higher order ODEs; Boundary
value problems. Numerical solution of partial Differential Equations (PDE): Finite volume
method; Numerical solution using triangular grids; Finite difference method; Model
equations; Finite difference approximations; Convergence and stability analysis of finite
difference equations; Numerical solutions of parabolic PDEs; Elliptic PDEs; Hyperbolic
PDEs.
Course Learning Outcomes
ABET Criteria a, b, d, e, f, g, j and k are addressed in this course.
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 | ✔ | |||