AMCS/MATH 603:  Introduction to Numerical Analysis I

Spring 2021
Instructor: Charles L. Epstein

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The Course

Numerical Analysis is a study of the interface between the idealized world of continuum mathematics and the realities of finite, discrete numerical computation. The principal motivation for most numerical analysis was to develop methods for approximately solving equations, ODEs and PDEs. There are a variety of topics that mirror those occuring in continuum mathematics. Most of the course will focus on the 1d-case, though of course most  current research in the field focuses on higher dimensional problems. Indeed, "Machine Learning" is largely devoted to the problem of approximating functions of many variables.  We will take material from a variety of sources, among them:
  1. Rivlin, T., An Introduction to the Approximation of Functions, Dover Press    Rivlin
  2. Stoer and Bullirsch, Introduction to Numerical Analysis, Springer                   S & B
  3. Trefethen, L.N., Approximation Theory and Approximation Practice, SIAM  ATAP
  4. Trefethen, L.N., Spectral Methods in MATLAB, SIAM                                     SMM

A problem set will be assigned every other week on Tuesday, which will be due two weeks hence. The problem sets appear at the bottom of this web-page. Everything will be posted on the AMCS 603 Canvas page.


  1. Representing functions (Rivlin Chapters 1,2, 4, and ATAP  Chapters 6-10, for practical aspects of the subject)
  2. Interpolation (S &B Chapter 1,  ATAP 1-5, 10-16)
  3. Calculus: (S&B Chapter 3 and 5, ATAP Chapters 18, 19, 21, SMM Chapters 1-6, 12)
  4. Applications to ODEs and PDEs (S & B Chapter 7,  SMM 7-10)(As time permits)


Problem sets

Online resources

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