Interpolation, Numerical Integration and Differentiation, Initial Value Problems for Ordinary Differential Equations, Boundary Value Problems for Ordinary Differential Equations, Partial Differential Equations, Fast Fourier Transform.

For further information see the academic catalog: IAM562

Course Objectives

At the end of this course, the student will learn:

  • how to interpolate functions, especially by using polynomials as well as piecewise polynomials (Splines)
  • how to numerically differentiate and integrate functions
  • how to discretise and solve initial as well as boundary value problems for ordinary differential equations
  • how to discretise and solve initial and boundary value problems for partial differential equations
  • what a fast Fourier transform is and how to apply it in specific problems

Course Learning Outcomes

Student, who passed the course satisfactorily will be able to:

  • interpolate functions or data and extract information from measurements
  • apply numerical differentiation and integration of functions
  • solve initial value problems for ODEs
  • solve initial, boundary value problems for PDEs
  • apply fast Fourier transform method

Tentative (Weekly) Outline

  • Interpolation
  • Numerical Differentiation
  • Numerical Integration
  • Initial Value Problems for Ordinary Differential Equations
  • Boundary Value Problems for Ordinary Differential Equations
  • Partial Differential Equations
  • Fast Fourier Transform

Course Textbook(s)

  • M.T. Heat, "Scientific Computing", McGraw Hill, 1997
  • A. Quarteroni, R. Sacco, F. Saleri, " Numerical Mathematics", Springer, 2000
  • C. F. van Loan, Introduction to Scientific Computing, Prentice Hall, 1999
  • A. Quarterioni, F. Saleri, Scientific Computing with MATLAB and Octave, Springer-Verlag, 2006