Last | Top | Next

Differential Equations (92.236)
Review Guide for Exam #1

Exam #1 will include all the material from Chapter 1 of your text. Each section emphasizes a particular method or possibly a few related methods. In particular, the necessary skills that you should have upon completion of Chapter 1 are summarized as follows:

From Chapter 1, you should be able to
Verify that a given function is a solution to a given ODE.
Use initial conditions to determine the arbitrary constants within the general solution.
Solve ODEs of the form y' = f(x) by simple integration.
Sketch solution curves for a first-order ODE given the slope field.
Apply Theorem 1 to address the uniqueness and existence of solutions to IVPs.
Solve separable ODEs of the form g(y)dy = f(x)dx.
Solve linear ODEs of the form y' + p(x)y = q(x).
Identify if an ODE in the form, Mdx + Ndy = 0, is exact.
Solve exact ODEs of the form Mdx + Ndy = 0.
Find integrating factors for non-exact ODEs (if appropriate).
Use a variety of substitution methods to convert a given ODE into a form that is easier to solve.
Classify a given ODE into one of the groups discussed above and identify an appropriate method for solving the given ODE.

In addition to the specific analytical solution techniques noted above, several practical applications involving 1st-order ODEs were integrated throughout Chapter 1 of your text. Several additional detailed application examples were also made available, including problems related to Newton's 2nd Law of Motion, Radioactive Decay, Compound Interest, Newton's Law of Cooling, Torricelli's Law, Mixing Problems, among others. From a physical description of a system related to one of the example application areas, you should be able to

  1. Formulate the basic balance equations appropriate for a given physical situation,
  2. Solve the resultant balance equations, and
  3. Analyze and interpret the solutions to the physical problems.

This latter sequence of objectives is the real goal for taking this course in Differential Equations.

PS. Note that the handout, Summary Information for Exam #1, along with a set of Integral Tables and Laplace Transforms will be available during the exam. You should be very familiar with all the material on these summary sheets.

Last updated by Prof. John R. White (January 2007)

Last | Top | Next

Main | Current Activities | Courses | Research | Vitae | Misc. Goodies