Spring 06 / M. Z. Aşık, Office: MM903, e-mail: azulfu@metu.edu.tr, Web Page: http://www.metu.edu.tr/~azulfu

**
ES 305- Computing Methods in Engineering for CE Students**

Course outline

1. Mathematical preliminaries: aim of the course, some concepts in approximations. The errors due to chopping, rounding, truncation, etc.

2. Solution of nonlinear equations : bracketing methods (bisection and regula-falsi methods); open methods (Newton-Raphson and secant methods, successive approximations)

3. System of nonlinear equations (Newton-Jacobi, fixed-point iterations.)

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 methods, Successive Over-Relaxation methods, ill-conditioned systems and pivoting strategies.

5. Eigensystems: power and inverse power methods.

6. Approximation of functions: base functions and orthogonality, interpolation and extrapolation. (Lagrange approximation, Newton polynomials, interpolation by spline functions, least squares)

7. Numerical differentiation

8. Numerical integration.. (trapezoidal, Simpson's and sequential rules, Romberg's integration, Gauss-Legendre integration)

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 )

10. Special topics (such as modelling of data, partial differential equations, numerical transform techniques, and etc.,)

Textbook :

Chapra, S. C. and
Canale, R. P., Numerical Methods for Engineers, McGraw-Hill, 3^{rd} Ed.,
1998.

(Or: Mathews J. H., Numerical Methods for Mathematics, Science and Engineering, Prentice Hall, 1992.)

References:

Burden, Richard L. and Faires, J. Douglas, Numerical Analysis, Brooks-Cole.

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.

Dahlquist, G. and Bjorck, A., Numerical Methods, Prentice-Hall, 1974

Press, W., Flannery, BP, Teukolsky, SA, and Vetterling, W, Numerical Recipes-The
Art of Scientific

Computing, Cambridge University Press, 1992.

Nakamura, S., Applied Numerical Methods In C, Prentice-Hall, 1993.

Grading Policy:

Midterms+HW+Att %65

Final %35

Exam Dates:

March 22, 2012 and May 3, 2012.

Please note that: If a student misses any of the exams without a legal reason he/she receives zero for that exam; however, if the student has a legal reason, he/she must take the makeup exam which will be given after the final.