Scientific Computing and Differential Equations

Gene Golub and James M. Ortega

• Chapter 1 (Read on your own)

• Chapter 2 Letting it Fly: Initial Value Problem
  
  • 2.1 Examples of Initial Value Problems
    
  • 2.2 One-Step Methods
    
  • 2.3 Polynomial Interpolation
    
  • 2.4 Multistep Methods
    
  • 2.5 Stability, Instability, and Stiff Equations

• Chapter 3 Pinning it Down: Boundary Value Problems
  
  • 3.1 The Finite Difference Method for Linear Problems
    
  • 3.2 Solution of the Discretized Problem

• Chapter 4 More on Linear Systems of Equations
  
  • 4.1 Introduction and Least Squares Problems
    
  • 4.2 Gaussian Elimination
    
  • 4.3 Interchanges
    
  • 4.4 Ill-conditioning and Error Analysis
    
  • 4.5 Other Factorizations

• Chapter 5 Life is Really Nonlinear
  
  • 5.1 Nonlinear Problems and Shooting
    
  • 5.2 Solution of a Single Nonlinear Equation
    
  • 5.3 Systems of Nonlinear Equations

• Chapter 6 Is there more than Finite Differences
  • 6.1 Introduction to Projection Methods
    
  • 6.2 Spline Approximation
    
  • 6.3 Numerical Integration
    
  • 6.4 The Discrete Problem Using Splines

• Chapter 7 N Important Numbers
  • 7.1 Eigenvalue Problems
    
  • 7.2 The QR Method
    
  • 7.3 Other Recursive Methods

• Chapter 8 Space and Time
  
  • 8.1 Partial Differential Equations
    
  • 8.2 Explicit Methods and Stability
    
  • 8.3 Implicit Methods
    
  • 8.4 Semi Discrete Methods

• Chapter 9 The Curse of Dimensionality
  
  • 9.1 Two and Three Space Dimensions
    
  • 9.2 Direct Methods
    
  • 9.3 Iterative Methods