MCS 471 Numerical Analysis

Course Coordinator: Professor F. B. Hanson, 718 SEO, X3-2142 (X6-3041msg)

• E-Mail: Hanson@uic.edu
• Class Web Page: MCS 471 Home Page

Catalog description: Introduction to numerical analysis; floating point arithmetic, computational linear algebra, interpolation, numerical integration, numerical solution of ODEs, computer subroutine packages (including Maple and Matlab/Octave).

Prerequisites (REVISED): A grade of C or better in MCS 360 Structured Programming II or EECS 270 Introduction to Programming languages or MCS190 Introduction to Scientific Computing or EECS 170 Fortran Programming for Engineers or MCS 260 Introduction to Computer Science I or EECS 171 Introduction to Programming.

Semester Credit hours: 3U4G

List of Topics: ---- Hours:

• 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. ---- 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, 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.

List of Topics by Lectures: (click here)

Text: C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, 5th Ed., Addison-Wesley, 1994.

Prior Semester MCS471 Courses: (click here)

Supplementary References: (click here)

Class Notes: (click here)

Help for Numeric and Symbolic Computational Tools: (click here)

(Gateway to MathLab, Maple, Octave, UNIX, and Numerics Pages)

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