# Math 274 - Exam 1 - Sp 2018

## Thursday, 1 Feb, 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 is written to take about 85 minutes.

The exam covers Sections 1.1 - 3.2. Expectations from each section are listed below.

- 1.1 - No explicit questions from this section, but the language is used throughout the class/exam.
- 1.2 - Be able to verify a function is/is not a solution to an equation. Know Theorem 1.
- 1.3 - Given a first order equation, sketch the direction field and/or identify the direction field. Given a direction field, be able to sketch solution curves satisfying specified initial data.
- Phase Line Group Project - Be able to identify and classify equilibrium solutions as a sink, source, or node. Be able to use the phase line to predict asymptotic behavior.
- 2.2 - Be able to identify a separable equation and solve via separation.
- 2.3 - Be able to identify a linear equation and solve using the integrating factor. Know Theorem 1.
- 2.4 - Using the given information, identify and solve an exact equation. Be able to to show, using the partial derivative condition, that an equation is/is not exact.
- 2.5 - Not covered.
- 2.6 - Using the given information, identify and make an appropriate substitution to solve an equation.
- 3.2 - Be able to set up and solve a mixing problem, both constant volume and varying volume.
- Complex Numbers - Know the definitions, be able to do the suggested homework #1-3 (#4 and #5 will useful in the future, but not for this exam.)

Particulars.

- The exam is 100 points.
- Roughly a quarter of the exam is composed of homework problems.
- There is at least one question related to each section we discussed, including the notes on Complex Numbers.
- Unless otherwise specified, implicit solutions are acceptable.