Prof. Tim Davis, P.O. Box 116120 University of Florida Gainesville, FL 32611-6120 phone (352) 392-1481, fax (352) 392-1220 email: my last name AT cise.ufl.edu

COT 4501: Numerical Analysis, a Computional Approach, Fall 2008

• Class time:
  • Tues 5th-6th periods (11:45am to 1:40pm) and Thurs 6th period (12:50pm to 1:40pm), in CSE E220.
  • Final exam: 7:30am to 9:30am, Thursday, Dec. 18, in CSE E220. Don't say I didn't warn you...
• Textbook and other resources:
  • Scientific Computing: An Introductory Survey, by Michael Heath (required).
  • MATLAB Primer, 7th edition, by Tim Davis and Kermit Sigmon (optional).
  • Numerical Computing with MATLAB, by Cleve Moler (a useful and free on-line reference, not required - just suggested if you want to read more about MATLAB for numerical methods)
• Syllabus:
  You're reading it.
• Class pictures:
  I will take pictures of each student in the class so that I can get to know you. Do not put your UF ID on any paper or assignment - I shouldn't need it.
• Laptops in class:
  Do not use laptops in class. They are distracting, to both the instructor and your fellow students. Also do not read The Alligator (etc) in class...
• Office hours:
  My office hours are just after class, until 2:45pm (or later if there's still a line out my door).
• TAs:
  To be determined.

Topics covered (subject to modification):

• Chapter 1: Scientific Computing
  • 1.1 Introduction
  • 1.2 Approximations in Scientific Computation
  • 1.3 Computer Arithmetic
  • 1.4 Mathematical Software
  • 1.5 Historical Notes and Further Reading
• Chapter 2: Systems of Linear Equations
  • 2.1 Linear Systems
  • 2.2 Existence and Uniqueness
  • 2.3 Sensitivity and Conditioning
  • 2.4 Solving Linear Systems
  • 2.5 Special Types of Linear Systems
  • 2.6 Iterative Methods for Linear Systems
  • 2.7 Software for Linear Systems
  • 2.8 Historical Notes and Further Reading
• Chapter 3: Linear Least Squares
  • 3.1 Linear Least Squares Problems
  • 3.2 Existence and Uniqueness
  • 3.3 Sensitivity and Conditioning
  • 3.4 Problem Transformations
  • 3.5 Orthogonalization Methods
  • 3.6 Singular Value Decomposition
  • 3.7 Comparison of Methods
  • 3.8 Software for Linear Least Squares
  • 3.9 Historical Notes and Further Reading
• Chapter 4: Eigenvalue Problems
  • 4.1 Eigenvalues and Eigenvectors
  • 4.2 Existence and Uniqueness (covered lightly)
  • 4.3 Sensitivity and Conditioning
  • 4.5 Computing Eigenvalues and Eigenvectors (covered lightly)
  • 4.6 Generalized Eigenvalue Problems (skip)
  • 4.7 Computing the Singular Value Decomposition (skip)
  • 4.8 Software for Eigenvalue Problems (skip)
  • 4.9 Historical Notes and Further Reading
• Chapter 5: Nonlinear Equations
  • 5.1 Nonlinear Equations
  • 5.2 Existence and Uniqueness
  • 5.3 Sensitivity and Conditioning
  • 5.4 Convergence Rates and Stopping Criteria
  • 5.5 Nonlinear Equations in One Dimension
  • 5.6 Systems of Nonlinear Equations
  • 5.7 Software for Nonlinear Equations (skip)
  • 5.8 Historical Notes and Further Reading
• Chapter 6: Optimization
  • 6.1 Optimization Problems
  • 6.2 Existence and Uniqueness
  • 6.3 Sensitivity and Conditioning
  • 6.4 Optimization in One Dimension
  • 6.5 Multidimensional Unconstrained Optimization (skip)
  • 6.6 Nonlinear Least Squares (skip)
  • 6.7 Constrained Optimization (skip)
  • 6.8 Software for Optimization (skip)
  • 6.9 Historical Notes and Further Reading
• Chapter 7: Interpolation
  • 7.1 Interpolation
  • 7.2 Existence, Uniqueness, and Conditioning
  • 7.3 Polynomial Interpolation
  • 7.4 Piecewise Polynomial Interpolation
  • 7.5 Software for Interpolation (skip)
  • 7.6 Historical Notes and Further Reading
• Chapter 8: Numerical Integration and Differentiation
  • 8.1 Integration
  • 8.2 Existence, Uniqueness, and Conditioning
  • 8.3 Numerical Quadrature (partial coverage)
  • 8.4 Other Integration Problems (skip)
  • 8.5 Integral Equations
  • 8.6 Numerical Differentiation
  • 8.7 Richardson Extrapolation (skip)
  • 8.8 Software for Numerical Integration and Differentiation (skip)
  • 8.9 Historical Notes and Further Reading
• Chapter 9: Initial Value Problems for Ordinary Differential Equations
  • 9.1 Ordinary Differential Equations
  • 9.2 Existence, Uniqueness, and Conditioning
  • 9.3 Numerical Solution of ODEs (lightly covered)
  • 9.4 Software for ODE Initial Value Problems (skip)
  • 9.5 Historical Notes and Further Reading
• Chapter 10: Boundary Value Problems for Ordinary Differential Equations (skip)
• Chapter 11: Partial Differential Equations (skip)
• Chapter 12: Fast Fourier Transform
  • 12.1 Trigonometric Interpolation
  • 12.2 FFT Algorithm
  • 12.3 Applications of DFT
  • 12.4 Wavelets (skip)
  • 12.5 Software for FFT (skip)
  • 12.6 Historical Notes and Further Reading
• Chapter 13: Random Numbers and Stochastic Simulation (skip)