Lecture 1 of Numerical methods for differential equations (CTB2400)

• The following subjects are discussed:
  
  
  • Taylorpolynomial and remainder term
  • Order symbol of Landau + rules to combine them
  • Absolute and relative error
  • Floating point numbers and rounding errors
    
    
  Corresponding pages in the book: pages 1-10. The lecture is also available via collegerama. At 1.11 the presentation of a Senior Installation Engineer from Seaway7 starts. The slides are also available.
  
  
• Historical remarks
  
  
• Easy exercises of Chapter 1.
  
  
• Exercises 1-4 of page 10 can be made ( answers).
  
  
• Additional information
  
  
  • English explanation of the Taylor polynomial with a nice Java example.
  • Introduction and information about Numerical Analysis.
  • Disasters caused by numerical errors
  • Numerical Mathematics in the WorldWideWeb offers you the possibility of testing a lot of methods from numerical computing and optimization interactively. You will need only minimal programming knowledge for using this.
  • Numerical simulation is used in many civil engineering applications. One application is the SWAN package developed at the TUDelft to compute random, short-crested wind-generated waves in coastal regions and inland waters. Also in the Traffic flow theory and simulation group of Prof.dr.ir. Serge Hoogendoorn many numerical methods are used.