014006 Introduction to Numerical Analysis

Course Objectives

The course aims to provide tools and methods of linear algebra. Emphasis is given to topics that will be useful in other disciplines. The course includes theoretical discussions (i.e. theorems) and practical implementations of the methods. Many of the theorems will be stated without proofs.

Lecture Topics

  1. Introduction. Taylor series, partial derivatives.
  2. Description of various errors: rounding errors truncating errors
  3. Systems of linear equations
  4. Finding roots of algebraic equations
  5. Nonlinear systems of equations
  6. Optimization of functions without constraints
  7. Interpolation
  8. Curve fitting: least squares approximation, regression
  9. Numerical integration
  10. Numerical derivation
  11. Solution of ordinary differential equations

Prerequisites

104002 – Calculus 2

234112 – Programming C

104131 – Ordinary Differential Equations (may be taken in parallel)

Reading Requirements

  • S.C. Chapra and R.P. Canale, “Numerical Methods for Engineers”, McGraw-Hill, 2002.
  • R.L. Burden and J.D. Faires, “Numerical Analysis”, Brooks Cole, 2004.
  • Auxiliary pages for lectures by Carol Braester, “Introduction to Numerical Methods”, 1998.

Contact Hours

Lecture: 2 hours

Recitation: 2 hours

Credit: 3.0