Scheduling Information: 
Time: Friday, February, from 10:3011:20 (our regular class time)
Location: CUC McConomy.
Review Session:
Thursday, February 20, from 7:308:50 in DH 2210.


Topics Covered:

Introduction to Differential Equations. (Section 1.1 and 1.2)
Separable Differential Equations. (Section 2.2)
Some Basic Mathematical Models. (Sections 1.3)
Linear First Order Differential Equations. (Section 2.3)
Existence and Uniqueness Theorems. (Section 1.2, Examples 4 and 5)
Autonomous Differential Equations. (Section 2.1.2, Section 3.1, and Section 3.2. )
Direction Fields. (Section 2.1.1)
Phase Line. (Section 2.1.2, Section 3.1, and Section 3.2.)


Review Questions:


What is a differential equation?

What is a solution to a differential equation?

How can you determine if a particular function is a solution to a given
differential equation?

What is an ordinary differential equation (ODE)? A partial differential
equation (PDE)?

What is the order of a differential equation?

What is a linear first order differential equation?

What is a separable differential equation?

How can you find the general solution to a separable differential
equation? [1. constant solutions, 2. other solutions]

What is the domain of a solution to an initial value problem?

What are the three steps in building a mathematical model? [1. science
(assumptions); 2. Notation & units; 3. mathematics (translate assumptions
into a mathematical statement)]

What are the assumptions that lead to Newton's Law of cooling?

What is the differential equation that describes Newton's law of
cooling?

How to we find a mathematical model for mixing problems [ {stuff
in}{stuff out} ]

What is a linear first order differential equation?

What is an integrating factor for a linear first order differential
equation? What does it allow us to do?

How do we find the integrating factor?

How do we find the solution? [I recommend multiplying the equation,
integrating both sides, and solving for "y(x)" over memorizing a formula.
Strongly!]

What is the direction field for a differential equation?

What are the isoclines of a first order differential equation

How can a direction field give you information about solutions to a differential equation?

What type of questions can a direction field help you answer? What type of question is it not so good at answering?

What is meant by "existence and uniqueness" of solutions to an initial value problem?

We have a theorem about existence and uniqueness for linear first order equations. What are the hypotheses of that theorem? What are the conclusions?

We have another theorem about existence and uniqueness that applies to all first order equations. What are the hypotheses of that theorem? What are the conclusions?

What do these theorems imply about the graphs of solutions in regions where the hypotheses are satisfied?

What is an autonomous differential equation?

What can be said about the isoclines of an autonomous equation?

What is the phase line of an autonomous differential equation? What information does it show about the differential equation?

What is the exponential growth model? On what assumptions is this model based? How does this model predict that populations will behave?

What is the logistic growth model? On what assumptions is this model based? How does this model predict that populations will grow?


Exercises:

Section 1.1: #3, 5, 7, 11, 13, 17, 21, 23, 43, 51, 55
Section 1.3 #5, 9, 11, 13, 17.
Section 2.3 #3, 5, 7, 13, 17, 25, 27, 31, 35.
Section 1.2 #19, 21, 31, 47, 50.
Section 2.1 #1, 3, 15, 21, 25, 39,
Section 3.1 #3, 13, 17, 23, 25, 41, 42,
Section 3.2 #5(a), 21.


Old Exam Problems:

Here is a large collection of exam problems I've
given to Differential Equations students in previous semesters. Not all the
problems are appropriate for this exam. I would recommend the following
problems: 13, 56, 10, 1213, 1528, 3033, 3540, 4246, 4849, 51, 5354, 5663,
6569, 71, 7375, 7782. Some problems on this list are repeated. Sorry about
that. I'll try to cull the repeated problems and repost this, but I wanted to
make them available for you to start your studying.
Before the questions come in  no, I don't have solutions available for these
problems. You have a large number of problems from the text with answers,
and it's important for you to get used to working on problems where the answers
are not available.

