Math 230 - Chapter 8-9 Study Guide

  1. Find the general solution of the system X'=AX. These are all 2×2 systems. Three parts.
  2. Use Variation of Parameters to solve. These are both 2×2 systems. The fundamental matrix Φ is given. Two parts.
  3. Use the eigenvalues and eigenvectors from Maxima to write the general solution with real coefficients. These are both 3×3 systems. Two parts.
  4. Use RREF() on your calculator to find the general solution of the 3×3 system. The eigenvalues are given. Two parts.
  5. The formulas for the constants (k1, k2, k3, k4) for the Euler, Improved Euler, and Runge-Kutta 4 methods are given. Use them to find the next y value. You will need to know the formula for the next y value (including the weighting).
  6. Find the eigenvalues for a 3×3 system.
  7. Find the Matrix Exponential using Laplace Transforms and then find the general solution to the 2×2 system X'=AX.
  8. Take Home: Use the Euler, Improved Euler, and RK4 methods to approximate the given value. Graph the actual solution and the approximations on the same graph.


Points per problem

# 1 2 3 4 5 6 7 8 Total
Pts 24 16 12 12 12 6 8 10 100