# M 274 - Fall 2017 - Exam 1

## In class Friday 22 Sept

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

• In particular you must evaluate trigonometric functions at known angles.

The exam is written to take 40 to 45 minutes.  Use your time wisely.  For example, it is likely not in your interest to spend 25 minutes on a 10 point problem.  If you get stuck, move on and come back if you have time.  Read each problem completely before getting started; many problems include simplifications and additional information.

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.
• 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 75 points.
• There is a short matching section.
• There is a short true/false section.
• There is a question asking you to verify a function is a solution to an initial value problem.
• There is a phase line question.
• There is a separable equation, a linear equation, an exact equation, and a substitution.  Some of which are initial value problems, i.e. you will have to solve for c.
• There is a mixing problem.
• Unless otherwise specified, implicit solutions are acceptable.