Time and place: MWF 12:20--1:10, 112 Engr B. Building.

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

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

Please let me know if you have questions or comments about the homework.
The grader is not allowed to change your homework grade once it was assigned.

Syllabus: MATH 455 (CMPSC 455) Introduction to Numerical Analysis I

• Introduction: Computer arithmetic and Error Analysis (ch.1 and 2),
  • Floating point arithmetic and roundoff errors,
  • Error propagation, loss of significance,
  • Stable and unstable computations, conditioning
• Numerical rootfinding (ch. 3),
  • Bisection and secant methods,
  • Newton's method,
  • Examples of simple codes and algorithms,
  • Iterative methods, fixed points, and convergence rates.
• Direct methods for linear systems (ch. 4: 4.1--4.5)
  • Vectors, norms, and matrix algebra
  • Error analysis, condition number, and convergence,
  • Gaussian elimination,
  • Choleski factorization,
  • Direct methods for banded and sparse matrices (if time permits).
• Interpolation (ch. 6)
  • Polynomial interpolation,
  • Errors in polynomial interpolation,
  • Splines.
• Numerical quadrature (ch. 7),
  • Numerical differentiation,
  • The Trapezoid rule and Romberg's algorithm,
  • Simpson's rule,
  • Gaussian quadrature formulae.

Students may take only one course for credit from MATH 451 and MATH 455.

Prerequisites: CMPSC 201 and CMPSC 202; or CMPSC 121; or MATH 220 and MATH 230; or MATH 231.

Textbook: Kincaid and Cheney, Numerical Analysis, Mathematics of Scientific Computing, third edition.

Grade: 50% homeworks and projects (weekly, due one week after assignement, will usually involve writing some short code), 25% quizes (four, at the end of chapters 2, 3, 4, and 6), 25% final (comprehensive).