
Math 20D (Introduction to Differential Equations)
Course Topics: Ordinary Differential Equations
Instructor: Prof. Michael Holst
(5739 AP&M, mholst@math.ucsd.edu;
Office Hours: MW 10:00am11:00am)
Term: Fall 2004
Main Class Webpage:
http://ccom.ucsd.edu/~mholst/teaching/ucsd/20d_f04/index.html
Computer Lab Webpage:
http://www.math.ucsd.edu/~math20d/.
Textbook(s):
 Stewart,
Calculus: Early Transcendentals,
5th Edition, Brooks/Cole, 2003, Chapter 11;
 Conrad,
Differential Equations: A Systems Approach,
1st Edition, Prentice Hall, 2003, Chapters 17.
Other books: (Suggested reading if you find Conrad lacking.)
 Boyce and Diprima,
Elementary Differential Equations,
8th Edition, John Wiley and Sons, 2004, Chapters 19.
TA(s):
 Matt Cecil
(mcecil@math.ucsd.edu),
APM 6402, Office Hours: Wed 10am12pm.
FINALS WEEK: Mon 13pm, Wed 35pm.
 Ryan TullyDoyle
(rtullydo@math.ucsd.edu),
APM 6402, Office Hours: Mon 11am1pm.
FINALS WEEK: By appointment.
 Jake Wildstrom
(dwildstr@math.ucsd.edu),
APM 2250, Office Hours: Mon 34pm, Tue 121pm, Wed 12pm, Fri 121pm.
FINALS WEEK: By appointment.
Lecture (A00): 9:00a9:50a MWF,
PCYNH/MULTI 106
Discussion Sections and Computer Labs:
(DIS=WLH 2112; LAB1=APM B337/B349;
LAB2=NW Mezzanine lab in CLICS)
 510270 (A01/A50): 08:00a08:50a Tu (LAB1)  Thu (DIS);
TA: Matt Cecil.
 510271 (A02/A51): 09:00a09:50a Tu (LAB1)  Thu (DIS);
TA: Matt Cecil.
 510272 (A03/A52): 10:00a10:50a Tu (LAB2)  Thu (DIS);
TA: Jake Wildstrom.
 510273 (A04/A53): 11:00a11:50a Tu (LAB2)  Thu (DIS);
TA: Jake Wildstrom.
 510274 (A05/A54): 12:00p12:50p Tu (LAB2)  Thu (DIS);
TA: Ryan TullyDoyle.
 510275 (A06/A55): 01:00p01:50p Tu (LAB2)  Thu (DIS);
TA: Ryan TullyDoyle.
CATALOG DESCRIPTION:
20D. Introduction to Differential Equations (4)
Infinite series.Ordinary differential equations:exact,separable,
and linear; constant coefficients, undetermined coefficients,
variations of parameters. Series solutions. Systems, Laplace transforms,
technique for engineering sciences. Computing symbolic and graphical
solutions using Matlab. Formerly numbered Math. 21D. May be taken as
repeat credit for Math. 21D.
Prerequisite: Math 20C (or Math 21C) with a grade of C or better.
LECTURES, READING, HOMEWORKS:
The list of lecture topics each week and the corresponding theory
homeworks problems assigned each week will be posted on the Main Class
Webpage that you are currently reading.
You should read the relevant sections in the text before
the lectures in order to get the most from the lectures.
The lectures will highlight the important parts of the material,
but there will not be time in lecture to cover all of the material
in each section in detail.
Therefore, having access to, and reading, the textbook
is an important component of the course.
Below is a list of the topics for each of the lectures during the quarter.
(Sections numbered 11.* refer to the Stewart book, whereas the
remaining sections refer to the Conrad book.)
Date 
Lecture 
Section(s) 
Topics Covered 
WEEK 0 
Fri 9/24 
1 
11.1 
Sequences: Concepts, Squeeze Thm, Monotonic Seq Thm 
WEEK 1 
Mon 9/27 
2 
11.211.3 
Geometric and Harmonic Series, Integral Test 
Wed 9/29 
3 
11.411.5 
Comparison and Alternating Series Tests 
Fri 10/1 
4 
11.6 
Absolute convergence, Ratio and Root Tests 
WEEK 2 
Mon 10/4 
5 
11.811.9 
Power series, radius of convergence, examples 
Wed 10/6 
6 
11.10 
Taylor series and remainder estimate 
Fri 10/8 
7 
11.12 
Applications of Taylor series and remainder estimate 
WEEK 3 
Mon 10/11 
8 
1.11.2 
Introduction to ODE and linear growth/decay models 
Wed 10/13 
9 
1.3 
Linear firstorder ODE 
Fri 10/15 
10 
2.12.2 
Separable ODE, Exact form and integrating factors 
WEEK 4 
Mon 10/18 
11 
2.3 
Graphical analysis of ODE 
Wed 10/20 
12 
2.4
& Review 
Initial Value Problems in ODE (IVP);
REVIEW for Midterm 1 
Fri 10/22 
 
Midterm 1 
TOPICS COVERED: HW1HW3
(Stewart 11.111.12, Conrad 1.11.2).

WEEK 5 
Mon 10/25 
13 
2.5 
Nonlinear growth models and asymptotic behavior 
Wed 10/27 
14 
3.13.2 
Systems of ODE and the phase plane 
Fri 10/29 
15 
3.43.5 
Autonomous systems; Interacting population models 
WEEK 6 
Mon 11/1 
16 
4.1 
IVP for linear systems of ODE 
Wed 11/3 
17 
4.2 
Systems with constant coefficients 
Fri 11/5 
18 
4.3 
Systems wth oscillating solutions 
WEEK 7 
Mon 11/8 
19 
4.4 
General solution of a linear system 
Wed 11/10 
20 
4.4, 2.2 
Examples from 4.14.4; second look at 2.2 
Fri 11/12 
21 
5.1 
IVP for 2ndorder ODEs 
WEEK 8 
Mon 11/15 
22 
5.25.3 
Homogeneous equations,
and the case of constant coefficients 
Wed 11/17 
23 
5.5
& Review 
Inhomogeneous equations (method of undetermined coefs);
REVIEW for Midterm 2 
Fri 11/19 
 
Midterm 2 
TOPICS COVERED: HW4HW7 (Conrad 1.34.4).

WEEK 9 
Mon 11/22 
24 
5.8 
Variation of constants/parameters 
Wed 11/24 
25 
6.1, 6.3 
Definition and properties of the Laplace transform 
Fri 11/26 
 
Holiday 
Thanksgiving 
WEEK 10 
Mon 11/29 
26 
6.4 
Inverse transforms of rational functions 
Wed 12/1 
27 
7.17.2 
Series solutions of ODE at a regular point. 
Fri 12/3 
 
Review 
REVIEW for Final Exam 
FINALS WEEK 
Thu 12/9 
 
Final Exam 
TOPICS COVERED: HW8HW10 (Conrad 5.17.2)
AND Commulative.

GRADES, EXAMS, DATES:
Your scores on the theory and computer homeworks each count for 10%
of your grade, making the combined homeworks count for
20% of your final grade.
The remaining 80% of your grade will be calculated from your
performance on two midterm exams and one final exam, to
be given on the dates below.
EXAM DATES:
 Midterm 1: Friday Oct 22, in class.
Covers HW1HW3 (Stewart 11.111.12, Conrad 1.11.2);
20% of grade.
 Midterm 2: Friday Nov 19, in class.
Covers HW4HW7 (Conrad 1.34.4);
20% of grade.
 Final: Thursday Dec 9, 8:0011:00am, PCYNH/MULTI 106.
Covers HW8HW10 (Conrad 5.17.2) and Commulative;
40% of grade.
OTHER IMPORTANT DATES:
 First lecture: Fri, Sep 24
 Last lecture: Fri, Dec 3
 Finals week: MonSat, Dec 611
 Holiday: Thu, Nov 11 (Veterans Day Holiday 
No discussion on Thu 11/11)
 Holiday: ThuFri, Nov 2526 (Thanksgiving Holiday 
No discussion on Thu 11/25, no lecture on Fri 11/26)
COMPUTER HOMEWORKS:
Each week you will be assigned some computer problems
that compliment the lectures and theory homeworks for that week.
Your TA will explain exactly how to use the computers allocated to the
class for this purpose, and will give you the laboratory time and
location information for our particular class.
The computer laboratory time is for your benefit; your TA will be
available during that hour to help you with the computer problem sets
each week.
You should be able to complete the problem set for that week during
the hour allocated.
Some people have conflicts with other courses during the computer
laboratory time; you do not have to attend the laboratory sessions,
but you will have to make other arrangements to get access to a computer
with MATLAB to complete the computer problem set each week.
You should read the homework over before going to the lab
each week, otherwise you will not be able to take advantage of the
time you have in that hour with the TA.
Your TA will explain exactly how to print out results to turn in
each week.
Complete information about the computer laboratories can be found at the
computer homework website
mentioned at the top of this page.
Here is a list of topics for each of the laboraties during the quarter:
 Introduction to MATLAB Using Sequences and Series
 Taylor Series
 Modeling With ODEs
 Direction Fields with DFIELD
 The Phase Plane and Solution Curves for Systems of ODEs
 Solution of Linear Systems Using Eigenvalues and Eigenvectors
 Numerical Methods for ODEs and Systems of ODEs
 The Laplace Transform
WEEKLY THEORY HOMEWORK ASSIGNMENTS:
The weekly homeworks assigned below are to be turned in to the TA by the
deadlines posted below.
The discussion sections are for your benefit; your TA will
help you work the assigned homework problems, which is the best way
to help you prepare for the midterms and final exams.
I do not mind if you work with other students in the class
on the homework problems each week (in fact, I encourage it), but
everyone must write up and turn in a separate homework.
If you can do the homework problems well, you will be
wellprepared for the exams.
Below are the assigned homework problems for each week during the quarter.
WARNING: I sometimes make minor changes to the problem sets (deleting or
adding a problem here and there) to reflect how far we get in the lectures,
so please check this page often for updated homework assignments.
 HW1: Due 4pm Fri Oct 1:
[Solutions are here]
 11.1 (Stewart): 1, 12, 19, 22, 56, 62, 68
 11.2 (Stewart): 2, 6, 19, 26, 37, 59, 61
 11.3 (Stewart): 3, 22, 28, 32
 HW2: Due 4pm Fri October 8:
[Solutions are here]
 11.4 (Stewart): 1, 2, 16, 30, 37, 46
 11.5 (Stewart): 8, 15, 24
 11.6 (Stewart): 7, 16, 33, 37
 11.8 (Stewart): 2, 12, 29, 36
 11.9 (Stewart): 7, 16, 26, 35
 HW3: Due 4pm Fri October 15:
[Solutions are here]
 11.10 (Stewart): 7, 19, 40, 42, 59, [Optional: 61]
 11.12 (Stewart): 2, 27, 35, [Optional: 37]
 1.1 (Conrad): 9, 12, 15, 17
 1.2 (Conrad): 8, 12, 16, 17
 MIDTERM 1 (HW 13): Friday October 22
(Sample Midterm 1
and
Score Histogram)

 HW4: Due 4pm Fri October 22:
[Solutions are here]
 1.3 (Conrad): 1, 5, 13, 24c, 24f
 2.1 (Conrad): 5, 8, 12, 16
 2.3 (Conrad): 18, 21, 25, 26
 2.4 (Conrad): 2, 22
 HW5: Due 4pm Fri October 29:
[Solutions are here]
 2.5 (Conrad): 5, 6, 7, 8, 10, 20, 29
 3.1 (Conrad): 5, 7, 8
 3.2 (Conrad): 6, 10, 14
 HW6: Due 4pm Fri November 5:
[Solutions are here]
 3.4 (Conrad): 8, 15, 16
 3.5 (Conrad): 1, 5
 4.1 (Conrad): 2, 4, 14, 15
 4.2 (Conrad): 3, 4, 8, 15, 16
 HW7: Due 4pm Fri November 12:
[Solutions are here]
 4.3 (Conrad): 1, 3, 5, [Optional: 7, 9]
 4.4 (Conrad): 4, 8a, 8b, 10a, 11, [Optional: 6, 7, 10c]
 2.2 (Conrad): 1, 2, 15, 16, 22, 23
 MIDTERM 2 (HW 47): Friday November 19
(Sample Midterm 2
and
Score Histogram)


Solutions to the actual Midterm 2 are here

 HW8: Due 4pm Mon November 22:
[Solutions are here]
 5.1 (Conrad): 1, 2, 7
 5.2 (Conrad): 1, 10, 14
 5.3 (Conrad): 3, 5, 13, 17
 5.5 (Conrad): 3, 4, 11, 15, 21
 HW9: Due 4pm Mon November 29:
[Solutions are here]
 5.8 (Conrad): 1, 7, 17
 6.1 (Conrad): 1, 5, [Optional: 10]
 HW10: Due 4pm Fri December 3:
[Solutions are here]
 6.3 (Conrad): 1, 13, 31, 41, 44, [Optional: 30]
 6.4 (Conrad): 1, 3, 9, 11, 19, [Optional: 33]
 7.1 (Conrad): 3, 11, 16, [Optional: 19]
 7.2 (Conrad): 3, 15, 25, 31, [Optional: 4]
 FINAL (HW 810 and Cummulative): Thu December 9
(Some Sample Final Problems and Solutions.

