Time and place: MWF 2:30--3:20, 111 Sacket Bldg.

Office Hours: MWF 1:20--2:20 (or by appt.)
My office is in McAllister, room 235 ( Contact)

This course is a prerequisite for Mathematics 524.

Homeworks: Homework 1, Homework 2, Homework 3, Homework 4, Homework 5, Homework 6, Homework 7, Homework 8, Homework 9, Homework 10 (due Wednesday).

Syllabus and catalog description: MATH 523 NUMERICAL ANALYSIS I

• Introduction: Computer arithmetic and Error Analysis (ch.1)
  • Floating point arithmetic and roundoff errors,
  • Error propagation, loss of significance,
  • Stable and unstable computations, conditioning.
• Numerical solutions of nonlinear equations (ch. 5)
  • Bisection and secand methods,
  • Newton's method,
  • Examples of simple codes and algorithms,
  • General iterative methods and fixed points,
  • Convergence theorems,
  • Newton's method for systems.
• Systems of linear equations(ch. 4),
  • Norms, error analysis, and condition numbers,
  • Gaussian elimination,
  • Choleski factorization,
  • Least squares,
  • Neumann series and an introduction to the main iterative methods,
  • Eigenvalue problems,
  • Direct methods for banded and sparse matrices.
• Approximation and interpolation (ch.2)
  • Polynomial approximation and error analysis,
  • Least squares polynomial approximation,
  • Piecewise polynomial approximation and interpolation (inc. splines),
  • The Fast Fourier Transform,
  • The multipole method for special dense matrix vector products.
• Numerical quadrature (ch. 3),
  • Basic quadrature formulas,
  • The Peano Kernel Theorem,
  • Richardson extrapolation,
  • Asymptotic error expansions,
  • Romberg integration,
  • Gaussian quadrature,
  • Adaptive quadrature,
  • Monte Carlo methods for higher dimensional integrals.
• Numerical solutions of nonlinear systems and optimization: conclusion (ch. 5).

Textbook: Stoer and Bulirisch, Introduction to Numerical Analysis, third edition.

Grade: 50% homework and 50% projects (code that illustrates the methods that we learn).