MAT 423 - Numerical Analysis I Fall 2006, TTh 12:15-1:30, ECG G236

Instructor: Rosemary Renaut Office: GWC 652, Phone: 965-3795

Office Hours: Wed 9:30-10:30, Th 10:30-11:30

Textbooks:
• "Numerical Mathematics" by A. Quarteroni, R. Sacco and F. Saleri, Springer Verlag, New York, Berlin 2000
• "Matlab Guide" by Desmond J. Higham and Nicholas J. Higham, Second Edition, SIAM, Philadelphia 2005
• "Numerical Computing with Matlab" by Cleve B. Moler, SIAM, Philadelphia 2004
Syllabus
• Principles of Numerical Mathematics
• Well-posedness and Condition Number of a Problem
• Stability of Numerical Methods
• The Floating-point Arithmetic
• Direct Methods for the Solution of Linear Systems
• Stability Analysis of Linear Systems
• Solution of Triangular Systems
• The Gaussian Elimination Method (GEM) and LU Factorozation
• Pivoting
• Sparse Matrices (Matlab Routines)
• Linear Least Squares Problems
• Existence and Uniqueness
• Sensitivity and Conditioning
• Orthogonalization Methods
• Approximation of Eigenvalues and Eigenvectors
• Geometrical Location of Eigenvalues
• The Power Method
• The QR Iteration
• The QR Method with Single and Double Shift
• Nonlinear Systems and Numerical Optimization
• Solution of Systems of Nonlinear Equations
• Unconstrained Optimization
• Basic Introduction to Constrained Optimization



Tests, Final Exam, Programming Assignments
Class Participation	5% (in class programming, attending class)
Midterm Exam	25% (four problems)announced one week in advance
Homework and Programming assignments	35% (in Matlab programming language)
Final Exam	35% (four problems), comprehensive
GRADING POLICY A: 90% and above; B: 80%-90%; C: 70%-80%; D: 60%-70%; E: below 60%.