Math 230 - Chapters 1-3 Study Guide

  1. State the order of the given ordinary differential equation and determine whether it is linear or non-linear. Look at problems 1.1.1-8.
  2. Verify that the indicated family of functions is a solution of the differential equation. Look at problems 1.1.21-24.
  3. Given the general solution and initial conditions to a differential equation, find the solution to the initial value problem. Look at problems 1.2.1-14.
  4. Given the graph of the solution to a differential equation, determine which set of initial conditions was used. Look at problems 1.2.35-38. Multiple choice.
  5. Given a direction field, sketch a solution curve that passes through the indicated point. Look at problems 2.1.1-4.
  6. Given a graph of several solution curves to an autonomous differential equation, identify the critical points, create a phase portrait, and classify each critical point as an attractor, repeller, or semi-stable. Finally, write an equation that could have the solutions shown. Look at problems 2.1.21-28 and figure 2.6.
  7. Solve the differential equation using separation of variables. Look at problems 2.2.1-22.
  8. Solve the differential equation using the intergrating factor. Look at problems 2.3.31-24.
  9. Verify that the differential equation is exact and then solve it. Look at problems 2.4.1-20.
  10. The graph of a series circuit is shown. Setup and solve the differential equation. Look at problems 3.1.27 and 3.1.29 and example 6 in section 3.1. Be sure you know formulas 7 and 8 in section 3.1.
  11. Solve the differential equation by making an appropriate substitution. Look at problems 2.5.1-10.
  12. Solve the Bernoulli equation by making an appropriate substitution. Look at problems 2.5.15-20.
  13. Solve the differential equation by making an appropriate substitution. Look at problems 2.5.23-28.
  14. Write a differential equation to model the described situation. Do not solve the differential equations, only set them up. Two parts. Look at problems 1.3.1-15

Take Home Exam

There is a take home exam for the problems in chapter 3. These problems are due the day of the in-class exam. Each problem is worth 5 points.

  1. Problem 3.1.12
  2. Problem 3.1.18
  3. Problem 3.1.36
  4. Problem 3.2.4
  5. Problem 3.2.24
  6. Problem 3.3.6

Notes:

Points per problem

# 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total
Pts 3 3 3 3 4 6 6 6 6 6 6 6 6 6 70