
Section 5.1: Background for programming projects, introduction to the
solution of initial value problems 

Section 5.2: Derivations of Euler's method, definition of
convergence 

Section 5.25.3: Error bounds and
asymptotic error estimate for Euler's method, local truncation error, global
error 

Section 5.25.4: Convergence proof for
Euler's method, derivation of Rungekutta methods 

Section 5.4: RungeKutta methods cont,
derivation of the general second order RungeKutta methods 

Section AS: Timestep estimation, model
problem analysis, intervals of absolute stability 

Section AS: Timestep estimation for
general equations 

Section 5.11: Implicit methods
(Trapezoidal rule, Backward Euler), comparison of ODE methods 

Section 5.11: Implicit methods,
solving the implicit equations, stiff differential equations 

Section 5.6: Overview of multistep
methods 

Section 5.9: Numerical methods for
systems of ODE's 

Section 5.9: Results on numerical
methods for systems, convergence results, error bounds, asymptotic error
estimates, regions of absolute stability. 

Section 11.3: Two point boundary
values problems, finite difference approximation 

Section 7.1 11.3: Review of vector and
matrix norms, error estimates for linear twopoint boundary value problem 

Section 11.4: Programming
consideration for two point boundary value problems 

Section 7.3: Iterative methods for the
solution of linear systems of equations, GaussJacobi method 

Section 7.3: Iterative methods cont,
GaussSeidel methd, error analysis for iterative methods 

Section 7.14: Error analysis for
iterative methods cont, relationship between error and the residual,
stopping criterion 

Section 7.34: Convergence results for
iterative methods, condition number 

Section 8.1: Discrete least squares approximation,
construction of the normal equations 

Section 8.1, DLS: Derivation of the normal
equations, matrix/vector formulation of the discrete least squares
problem 

Section DLS: Using the QR decomposition to solve
normal equations, relation of QR to GramSchmidt. 

Section 8.5: Introduction to discrete Fourier
approximation 

Section 8.5: Fourier approximation cont, complex
form of the discrete Fourier approximation 

Section 8.6: The fast Fourier transform 