ES 301- Numerical Methods in Engineering

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. 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)

6.Numerical differentiation

7. Integration of functions, line and surface integrals. (trapezoidal, Simpson's and sequential rules, Romberg's integration, Gauss-Legendre integration)

8.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 )

9. 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, 1997.

                      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, B. P., Teukolsky, S. A., and Vetterling, W., Numerical Recipes-The

                      Scientific Computing, Cambridge University Press, 1992.

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

Grading Policy:    Midterms+Attd+Hw    %65
                             Final                          %35

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.