COURSE OUTLINE
AMSC 460 / CMSC 460 Computational Methods Section 0101
Fall 2007
Introduction, Computer Arithmetic and Errors
(Notes)
(approx. 4 lectures)
course survey
introduction to Matlab
machine arithmetic
error analysis
stability and conditioning
Interpolation
(Chapters 2-3)
(approx. 5 lectures)
polynomial interpolation in two bases
piecewise polynomial interpolation
spline interpolation
Integration
(Chapter 4)
(approx. 3 lectures)
elementary integration formulas (midpoint, trapezoid, etc.)
compound and adaptive integration formulas
Matrix Computations
(Chapter 5)
(approx. 3 lectures)
Solving Linear Systems of Equations
(Chapter 6)
(approx. 4 lectures)
Gaussian elimination
well-conditioning vs. ill-conditioning, matrix and vector norms
sparse systems: direct and iterative methods
Solving Linear Least Squares Problems
(Chapter 7)
(approx. 3 lectures)
data-fitting and least squares
QR factorization
Solving Nonlinear Systems of Equations
(Chapter 8)
(approx. 3 lectures)
bisection, Newton's method, and secant method
methods for systems of equations
Ordinary Differential Equations
(Chapter 9)
(approx. 4 lectures)
ordinary differential equations and Euler's method
adaptive methods for ordinary differential equations
methods for stiff systems
Chapter references are to: Introduction to Scientific Computing by Charles F. van Loan, Prentice Hall.