HP 6758 - Numerical Methods In Mechanical Engineering
Offered Every Fall and Spring

Credit Hours: 3-0-3
Prerequisite: Graduate standing in Mechanical Engineering or consent of the school
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 ME and NRE 6758.
Textbooks: J. Faires and Richard L. Burden, Numerical Methods; Third Edition, Brooks/Cole, 2002.
Instructor: Robert E. Fulton (Fall 2003)
References: A. Jennings; Matrix Computation for Engineers and Scientists, John Wiley
  S. Crandall; Engineering Analysis, McGraw-Hill
Goals/Objectives:
 
 
 		 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:
Topic
 
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
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
   
Delivery Mode: Lecture 100%

Grading Scheme:

Homework 20%
Mid Term Exam 30%
Final Exam 50%

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Revised July 2004