| Credit Hours: |
3-0-3 |
| Prerequisites: |
Graduate standing in engineering or a related discipline |
| Catalog Description: |
Numerical methods for solution of engineering problems; initial, eigenvalue, and boundary value problems; computational stability for ordinary and linear partial differential equations. |
| Textbooks: |
J. Douglas Faires and Richard L. Burden; Numerical Methods, 7th Edition, Brooks/Cole, 2000. |
| Instructors: |
Cassiano de Oliveira |
| References: |
A. Jennings; Matrix Computation for Engineers and Scientists, John Wiley
S. Crandall; Engineering Analysis, McGraw-Hill
Hornbeck; Numerical Methods, Prentice Hall
Collatz; Numerical Treatment of Differential Equations, Springer
Conte; Elementary Numerical Analysis
Carnahan, Luther, and Wilkes; Applied Numerical Methods
Froberg; Introduction to Numerical Analysis |
| Goals: |
To introduce the student to a number of numerical methods needed for solution to mechanical engineering problems; method for solution appropriate to static or steady state problems, vibration or stability problems and initial value or transient problems are considered. |
| Topics: |
- Solution to Simultaneous Equations
- Direct Methods: Gaussian Elimination
- Decomposition Methods
- Symmetric Systems
- Iterative Methods: Jacobi
- Finite Difference Approximations
- Ordinary Differential Equations
- Partial Differential Equations
- Order of Error
- Eigenvalue Problems
- Orthogonality Principal
- Expansion Theorem
- Inverse Power Method
- Jacobi Method
- Mid-Term Exam
- Lectures 18-23, Initial Value Methods
- Euler, Central Difference and Trapezoidal Methods
- Stability Issues
- Systems of First Order Nonlinear Equations
- Newmark Method for Second Order Dynamic Problems
- Initial Value Partial Differential Equations
- Parabolic Systems
- Hyperbolic Systems
- Final Exam
|
| Delivery Mode (%): |
Lecture |
100 |
Literature Study |
|
Term Project |
|
|
| Grading Scheme (%): |
Homework |
20 |
Midterm |
30 |
Final |
50 |
|
