Homework                               

Each homework set will consist of reading assignments of one or more sections of the text, a
set of problems for that section.  Quizzes will be given at approximately two week intervals
that will usually consist of 2 problems. The quiz problems  will be similar to (and in some cases, identical to)
particular homework problems, so that if you do all the assigned homework, you should be well
prepared for a quiz. Since the assigned homework is not being collected for grading, you should
not hesitate to seek assistance with any that you are having difficulties with during office hours.

Calculators and showing your work: You  will be  permitted to use calculators during quizzes (and on exams).
However, you must  show all work required to justify your answers by providing
relevant calculus and algebraic calculations for each step. There is a judgment call as to when a calculation is
so simple that the answer is `obvious'. My instructions to the grader will be that an unjustified answers
should lose credit if the unjustified portion of the answer would  not be obvious to him/her without a
pencil-and-paper calculation. You may use calculators
to check your answers, or as a way of obtaining hints about what the correct answer
should look like. In certain problems in which numerical answers are required, calculators
may of course be used to evaluate functions numerically. In most problems, you may also use graphing calculators to
obtain information about the behavior of graphs of functions, unless sthe statement of the problem specifically
asks you to justfiy such answers with an analytical calculation.


Homework 1: 
Section 1.1 : 2, 3, 5, 10, 11, 15 a,b
Section 1.2 : 1, 5, 7, 9, 25, 27, 29, 33
quiz 1 solutions:  p1  p2
Homework 2: 
Read: sections: 1.5, 1.3   
Remarks: The material in section 1.5 discusses some theoretical results
(in a descriptive, non-rigorous manner) that are important to know about, but
do not in themselves figure directly into many  calculations in the assigned coursework. I
will give a  brief discussion of the issues in Section 1.5  following the presentation of
section 1.2 in the lectures,  since they have a bearing on both the
material on separable equations and on slope fields. In Section 1.3,
the initial discussion of slope fields in  "The geometry of  f(t,y)" is the
most important new material and you  should focus on the methods and
examples presented  here on the first reading. The following
dicussion, "analytic vs qualitative methods" is a rehash of the material
in 1.2 and slope fields in the context of physical applications. It is good to
look at to solidify your understanding of the precedeing sections, but doesn't cover
new mathematical material. The book's CD may be quite useful in getting a feel for
how to graph slope fields, and it is suggested that you take a look at the CD's software
that can be used for this. 
homework problems:
Section 1.5: 14, 17;
Additional problem: Find the explicit solution y(t)  of the initial value problem:
y' = (y-1)(y-2),  y(0)=0.
Determine the interval of existence of y(t). In particular, explain why the formula derived
for the solution y(t) shows that this interval
Section 1.3:  1,3,5, 7a,b ,15
SOLUTIONS TO QUIZ 2: p1 p2

Homework 3
Read sections 1.6, 1.7, 1.8,1.9. As noted mentioned in class, there material
in sections 1.6 and 1.7 is mostly concerned with a conceptual way to obtain
graphical, qualitative information about the behavior of solutions- there is
litttle in the way of computation methods here. It is worth reading a bit
of the texts discussion here,  but these lenghty sections can be skimmed through
for the most part. Section 1.8 is a "warm-up" for the solution of linear
equations (in 1.9). Section 1.9 should be read carefully: it introduces an important
computational technique.
Problems:
Section 1.6:  problems 3,7,12,33,34
Section 1.7: problem 4,9
Section 1.8 problems 3,5,7,9
Section 1.9 problems 1,3, 7,11, 21
SOLUTIONS TO QUIZ 3 p1 p2
Homework 4
Reading: read section 2.1, 2.2, (2.3 skim) in the text.
This chapter introduces a new conceptual framework
for studying systems of differential equations in terms of
a vector field on (two)-dimensiona l vector space.
The most important material is introduced in section 2
in which the direction field associated two 2 DE's is
introduced, and the geometric study of 2-dimensional
phase planes through an analysis of the direction field
associated to  a given set of 2 coupled.  DE's.  Section 2.3
is a "warm-up" for Chapter 3, in which some
examples of particularly simple 2-d systems are solved by
elementary methods that can be used when the equations have
a  special form. General methods of solution are studied in Ch 3.
In the lectures, will will start in on Ch. 3 after section 2.2.
sec 2.1 Problems: 2.2: 2,3,4,7
sec 2.2 Problems: 3,5,9,11,17,18, 21 (for 17,18, just find the equilibria. It would be a good idea
to use the CD provided with the disk to investigate the behavior of these equations numerically).

Homework 4  (continued)
Reach Chapter 3, Sections 1,2
Problems:
Section 3.1 number 5, 8,15,17,24, 26,31
Section 3.2 number  1,2,6 ,7,11,13,15,16,19
There will be a quiz on Friday, April 4 covering the material in Sec 2.1, 2.2, 3.1,3.2
however,it will focus on the most important aspects of the above sections: the location of equilibria
of 2-D systems , using the null sets of the components of the vector field of rate
functions to make rough plots of the direction field of a system in 2-D,   the  vector form of
linear 2-dimensional systems of DE's, and the description of the solution set in terms
of eigensolutions (ie.e. straight line solutions. The quiz will have problems similar to problems done in class
and/or assigned problems from the text:  # 11 and 13-18 in Sec 2.2,
problems 5-9 in section 3.1 , or problems 11-14 in Section 3.2. You should be working through all the the assigned problems,
however, as the quiz cannot cover all types of assigned problems.
Solutions quiz 4 question 1 question 2


Homework 5
 Read chapter 3, section 3.3, 3.4
Problems:
3.3:  numbers 1,3,5,7,9,11,13,15,21
3.4: numbers  1,3,5,7, 9,11,15,21

 Homework 6
 Read sections 3.5, 3.6
3.5  numbers 5.11,13,17,18,21,23
3.6 numbers  2,3,9,12,35,36
problem a, b,c

There will be a quiz (quiz 6) on Friday, May 2 covering the
material in sections 3.4 and 3.5. I've decided not
to put the material we began today (Monday) on
the quiz this week. This material will be on the final
exam. Quiz 6 will be the last quiz of the semester.
 
Final exam review problems: p1  p2  p3
These are intended to provide a guide to the topics and types of
questions that will be on the final exam. Additional problems
can be obtained (with the exception of the variation of parameters
problem on p2) from the text in sections 2.1,2,2,3.1 through 3.6,   and 4.1, 4.2.
Although we will have a brief discussion of the Laplace transform method on the last day of
class, this topic will not be on the final exam since it comes at the end of the semeseter.
The review problems will be discussed during a review session
that will be led by Garett Cahill on Wed, May 14 from 6 to 8 pm in LGRT 204.
I will also post a solution sheet to the review problems within the next few days.