Math 5070 Material

For Spring 2007

Jay Treiman

The material that will be covered in this class includes the following:

  1. Chapter 1
    1. Basic concepts and Taylor's Theorem
    2. Orders of convergence
    3. Difference equations
  2. Chapter 2
    1. Floating-point numbers and roundoff errors
    2. Absolute and relative errors
    3. Conditioning
  3. Chapter 3
    1. Bisection
    2. Newton's Method
    3. Secant Method
    4. Fixed points
  4. Chapter 4
    1. Matrix Algebra
    2. LU factorization
    3. Pivoting
    4. Norms and analysis of error
  5. Chapter 6
    1. Polynomial interpolation
    2. Divided difference
    3. Hermite interpolation
    4. Spline interpolation
  6. Chapter 7
    1. Numerical Differentiation
    2. Numerical integration via interpolation
    3. Gaussina quadrature
    4. Romberg integration
  7. Chapter 8
    1. Existence and uniqueness of solutions to DE's
    2. Taylor series methods
    3. Runge-Kutta Methods
    4. Multistep methods