# 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 |
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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:

- 30% will cover material very similar to the first exam. Questions are similar to and/or inspired by questions on the first exam. Please review exam 1, the exam 1 expectations, and the exam 1 solutions.
- 70% will cover Chapter 4 material, see information below.
- The following information will be given.

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.