# Math 274 - Exam 2 - Sp 2018

## Thursday, 1 March, 6:10 - 8:00 pm

You are responsible for all prerequisite information, this is a partial list.

The following information will be given.

The exam covers Sections 4.1 - 4.7, 4.9, 7.2-7.3.  Expectations from each section 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.
• Complex Method of Undetermined coefficients - you will not be required to use complex methods.
• 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.
• 7.2 - Know the definition of the Laplace transform and be able to compute a transform using the definition.  Know the Laplace transform is linear.  Know the definition of exponential order, piecewise continuity, and the theorem on existence of the transform (Theorem 2).
• 7.3 - The important properties are included on the given information.  Be able to use them.

Particulars.

• 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.
• About 20% of the exam involves Laplace transforms.