# M 274 - Fall 2017 - Midterm Exam

## Tuesday 10 Oct - 6:10-8:00

 Instructor Section Class time Midterm Exam Tuesday 10 Oct 6:10 - 8:00 pm Malo 01 8 am Reid 103 Markman 02 11 am Reid 104 Pitman 03 12 pm Barnah 103 Pitman 04 1:10 pm Barnah 103 Malo 05 9 am Reid 103 Markman 06 10 am Reid 104 Ashland 07 9 am Reid 108 Ashland 08 2:10 pm Reid 108

### The exam is comprehensive, in particular:

In addition to the sections previously described, the Chapter 4 expectations are listed below.

• 4.1 and 4.9 - Mass-Spring Systems - Be able to classify a system as critically damped, underdamped, or overdamped.  Be able to sketch a graph of solutions.
• 4.2 and 4.3 - Know how to find general solutions to homogeneous linear equations using the auxiliary/characteristic equation.  Know Theorem 1 - Existence/Uniqueness.  Know how to compute a Wronskian (it comes up in Variation of Parameters, among other places) and how the Wronskian is related to Linear Dependence/Independence (See Lemma 2).
• 4.4 and 4.5 - Know how to find the proper form and complete the necessary algebra to solve for the unknown coefficients, see the provided equation sheet.
• 4.6 - The integral equations for Variation of Parameters will be given, the 4.7 form is used, see the equation sheet above.  Review integration.
• 4.7 - Know how to find general solutions to Cauchy-Euler equations using the auxiliary/characteristic equation. The Reduction of Order formula is given, be able to apply it if needed.

Particulars.

• There are 3 problems very similar to the first exam.
• There are homogeneous constant coefficient equations and Cauchy-Euler equations.
• There are nonhomogeneous equations that you will be asked to specify the form of a solution suggested by the Method of Undetermined Coefficients.
• There are nonhomogeneous equations that you must solve; expect to use both methods - Method of Undetermined Coefficients or Variation of Parameters.
• There are questions involving Mass-Spring systems.