ES 361 Computing Methods in Engineering

Course Description:
Numerical solution of linear and nonlinear systems of equations. Interpolating polynomials, Numerical differentiation and integration. Numerical solution of ordinary differential equations.

Prerequisite(s):
None

Textbook(s) and/or Other Required Material:
Chapra, S.C. and Canale, R.P., Numerical Methods for Engineers, McGraw-Hill, 3rd., 1998

The following books are the excellent sources of reference.
Mathews, J.H., Numerical Methods for Mathematics, Science and Engineering, Prentice- Hall, 1992
Kahaner, D., Moler, C. and Nash, S., Numerical Methods and Software Prentice-Hall, 1989
Cheney, W. and Kincaid, D., Numerical Methods and Computing, Brooks - Cole, 1999
Nakamura, S., Applied Numerical Methods in C, Prentice-Hall, 1993
Dahlquist, G. and Bjorck, A.., Numerical Methods Prentice -Hall, 1974
Press, W., Flannery, B.P., Teukolsky, S.A., and Vetterling, W., Numerical Recipes-The Art of Scientific Computing, Cambridge University Press, 1992.

Course Objectives:
The course is designed to equip students, with computational skills and tools needed to perform the analysis in various branches of engineering

Topics Covered:
1. Mathematical preliminaries: aim of the course, some concepts in approximations. The errors due to chopping, rounding, truncation, etc. - 1 week
2. Solution of nonlinear equations: bracketing methods(bisection and regula-falsi methods); open methods (Newton-Raphson and secant methods, successive approximation. - 1 week
3. System of nonlinear equation (Newton-Jacobi, fixed-point iterations). - 1 week
4. Review of linear algebraic equations: direct and iterative methods for solving linear system of equations: Gaussian elimination, LU decomposition, Gauss-Jacobi and Gauss Seidel, successive over-relaxation methods, ill-conditional systems and pivotin g strategies. - 2 weeks
5. Eigensystems: power and inverse power methods - 2 weeks
6. Approximation of functions: base functions and orthogonality, interpolation and extrapolation. (Lagrange approximation, Newton polynomials, interpolation by spline functions and interpolation in two or more dimensions). - 3 weeks
7. Numerical differentiation. - 1 week
8. Integration of functions, line and surface integral (trapezoidal, Simpson's and sequential rules, Romberg's integration, Gauss-Legendre integration). - 2 weeks
9. Numerical solution of ordinary differential equations: initial value problems (Taylor, Euler, Heun and Runge-Kutta methods), boundary value problems (shooting, finite difference and superposition methods) - 3 weeks
10. Special topics (such as modeling of data, partial differential equations, numerical transform techniques, and etc., - 1 week

Class/Laboratory Schedule:
The course has three hours. Each lecture hour is 50 minutes.

Computer Usage: Fortran and Mathcad versions of example computer programs are on the web site of the course. The students are required to use these programs.

Contribution of Course to Meeting the Professional Component:
Mathematics and Basic Sciences: 3 Credits
Engineering Design: None
Engineering Sciences: None
Humanities and Social Sciences: None

Relationship of Course to Program Objectives:
This course intends to satisfy the first objective of the Department of Aeronautical Engineering.

Prepared By:
Turgut Tokdemir
11-26-1999