Course Content
The text book for this course is
`Applied Numerical Analysis' by Curtis F. Gerald and Patrick O. Wheatley,
seventh edition, Addison-Wesley, 2003.
In addition, consult
the lecture notes on special topics by Floyd Hanson.
Some supplemental materials to the lectures will be posted below.
0. Preliminaries
L-1 What is numerical analysis?
L-2 Bisection; Errors
L-3 Floating-Point Arithmetic
L-4 Floating-Point Arithmetic (continued); Measuring Efficiency
1. Solving Nonlinear Equations
L-5 The secant method
L-6 Newton's method and fixed-point iterations
L-7 Convergence rates and Aitken Acceleration
L-8 Roots of Polynomials
L-9 The Golden Section Search method
2. Solving Sets of Equations
L-10 Introduction to Linear Algebra
L-11 Elimination Methods
L-12 LU factorization
L-13 Cholesky decomposition and the cost of elimination
L-14 Improve numerical stability of LU by pivoting
L-15 LU with row pivoting continued
L-16 Condition Numbers
L-17 Multidimensional Newton Method
3. Interpolation and Curve Fitting
L-20 Lagrange and Neville interpolation
L-21 Review of Chapters 0,1, and 2.
L-22 Exam I
L-23 Divided Differences
L-22 Splines
L-23 Least Squares Approximation
L-24 Conditioning and Errors
4. Approximation of Functions
L-25 Chebyshev polynomials
L-26 Padé approximations
5. Numerical Differentiation and Numerical Integration
L-27 Interpolation for Derivatives and Integrals
L-28 Extrapolation and Newton-Cotes integration formulas
L-29 Composite Integration Formulas
L-30 Romberg Integration
L-31 Gaussian Quadrature
L-32 Review for Exam II
with answers
6. Numerical Solution of Ordinary Differential Equations
L-34 Taylor Series and Euler Methods
L-35 Runge Kutta and Multistep Methods
L-36 predictor-corrector methods
L-37 Higher order equations; Stability and Convergence
L-38 The shooting method
L-39 Finite Differences
L-40 Characteristic Value Problems
Review
L-41 Review of Chapters 0, 1, and 2
L-42 Review of Chapters 3, 4, and 5
L-43 Review of Chapter 6
The web pages for
the MCS 471 Spring 2005 Course Content
are still available.