# 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 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.