**Lecturer:**Professor Floyd B. Hanson, 718 SEO, X3-2142:**E-Mail:**hanson@uic.edu- Time: 11AM, Days: MWF, Room: 306 AH, CallNumber: 59680
**Office Hours:**1+PM MWF 718 SEO, but starting after class in 320TH**Class Web Page (this page):**http://www.math.uic.edu:~hanson/mcs471syllabus.html/

**E-Mail:**Hanson@uic.edu

- Introduction, finite floating point arithmetic, catastrophic cancellation, chopping and rounding errors. ---- 3 hours.
- Solution of nonlinear equations; bisection method, secant method, Newton's method, fixed point iteration, Muller's method. ---- 4 hours.
- Numerical optimization; Method of golden section search (see class notes), Newton's method optimization. ---- 2 hours.
- Solutions of linear algebraic equations; forwarding Gaussian elimination, pivoting, scaling, back substitution, LU-decomposition, norms and errors, condition numbers, iterations, Newton's method for systems, computer implementation. ---- 11 hours.
- Interpolation; Lagrange interpolation, Newton interpolation, inverse interpolation. ---- 4 hours.
- Numerical Integration; finite differences, Newton cotes rules, trapezoidal rule, Simpson's rule, extrapolation, Gaussian quadrature. ---- 8 hours.
- Numerical solution of ordinary differential equations; Euler's method, Runge-Kutta method, multi-step methods, predictor-corrector methods, rates of convergence, global errors, algebraic and shooting methods, for boundary value problems, computer implementation. ---- 10 hours.
- Leeway and exams. ---- 3 hours.
- Total. ---- 45 hours.

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