ME 6758 Numerical Methods In Mechanical Engineering

ME 6758: Numerical Methods In Mechanical Engineering
Offered Every Fall and Spring

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. Crosslisted with NRE and HP 6758.
Textbook:	J. Douglas Faires and Richard L. Burden; Numerical Methods, 7th Edition, Brooks/Cole, 2000.
Instructor:	Cassiano de Oliveira (Spring 2004)

References:	A. Jennings; Matrix Computation for Engineers and Scientists, John Wiley S. Crandall; Engineering Analysis, McGraw-Hill
Other References:	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:
I. Solution to Simultaneous Equations
A. Direct Methods: Gaussian Elimination
Decomposition Methods
Symmetric Systems
B. Iterative Methods: Jacobi
Gauss-Seidel
SOR
II. Finite Difference Approximations: A. Ordinary Differential Equations; B. Partial Differential Equations; C. Order of Error
III. Eigenvalue Problems: A. Orthogonality Principal; B. Expansion Theorem; C. Inverse Power Method; D. Jacobi Method
IV. Mid-Term Exam
V. Lectures 18-23, Initial Value Methods: A. Euler, Central Difference and Trapezoidal Methods; B. Stability Issues; C. Systems of First Order Nonlinear Equations; D. Newmark Method for Second Order Dynamic Problems
VI. Initial Value Partial Differential Equations: A. Parabolic Systems; B. Hyperbolic Systems
VII. Final Exam


Delivery Mode:	Lecture 100%

Grading Scheme:

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Revised June 2004