**Review for Math2574H exam 1**

The exam will be held on Thursday February 18. It is on sections 1.1-2.3 from the book.

Here are some extra questions which I have selected to help you with review for exam 1. These questions are intended to help, not to be a list of things which, by implication, you should or should not know, and also not to be by implication a sufficiently long list. It may be that you need to do more questions to get practice, in which case look at adjacent questions in the book.

Section 1.1: no extra review questions

Section 1.2: 17, 27, 31, 33

Section 1.3: 5, 21, 25

Section 1.4: 15, 19, 25, 33, 44

Section 1.5: 12, 20, 34, 36

Section 1.6: 1, 12, 33, 35, 44, 46

Try the equations in Chapter 1 Review Problems on page 78.

Section 2.1: 7, 9, 17, 26

Section 2.2: 10

Section 2.3: 3, 9, 23, 24

Equations you should be familiar with:

Motion in a line with constant acceleration.

Motion with constant acceleration and resistance proportional to v or the square of v.

Newton's law of cooling

Natural growth and decay

Logistic equation

Acceleration due to gravity with an inverse square law.

I will not test you on Toricelli's equation.

Methods of solution you should be familiar with:

separation of variables,

first order linear (integrating factor)

substition method for homogeneous equations

exact differential equations,

substitution methods to reduce the order of second order equations.

I will not test you on Bernoulli equations or the ad hoc substitutions at the start of 1.6.

If you need one of the unusual integrals that have arisen in order to solve a problem, I will give you the formula on the exam.