Mathematics of Approximation

  • Johan de Villiers

Part of the Mathematics Textbooks for Science and Engineering book series (MTSE, volume 1)

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Johan de Villiers
    Pages 1-24
  3. Johan de Villiers
    Pages 25-35
  4. Johan de Villiers
    Pages 37-70
  5. Johan de Villiers
    Pages 71-83
  6. Johan de Villiers
    Pages 85-98
  7. Johan de Villiers
    Pages 99-125
  8. Johan de Villiers
    Pages 127-165
  9. Johan de Villiers
    Pages 167-231
  10. Johan de Villiers
    Pages 233-287
  11. Johan de Villiers
    Pages 289-399
  12. Back Matter
    Pages 401-406

About this book


The approximation of a continuous function by either an algebraic polynomial, a trigonometric polynomial, or a spline, is an important issue in application areas like computer-aided geometric design and signal analysis. This book is an introduction to the mathematical analysis of such approximation, and, with the prerequisites of only calculus and linear algebra, the material is targeted at senior undergraduate level, with a treatment that is both rigorous and self-contained. The topics include polynomial interpolation; Bernstein polynomials and the Weierstrass theorem; best approximations in the general setting of normed linear spaces and inner product spaces; best uniform polynomial approximation; orthogonal polynomials; Newton-Cotes , Gauss and Clenshaw-Curtis quadrature; the Euler-Maclaurin formula ; approximation of periodic functions; the uniform convergence of Fourier series; spline approximation,with an extensive treatment of local spline interpolation,and its application in quadrature. Exercises are provided at the end of each chapter


Best approximation Fourier series Polynomial approximation Quadrature Spline approximation

Authors and affiliations

  • Johan de Villiers
    • 1
  1. 1., Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

Bibliographic information