Mathematical
Methods 2002 – 2003
Draft
of
3page
OVERVIEW + 5 SYLLABI FOR YEAR
Faculty: Don Middendorf donm@turbotek.net (no
email through evergreen.edu) 8676618
Prerequisites: 2
quarters of calculus
Parttime options? No.
(Register for 16 credits)
Schedule: Tuesday,
Thursday, Friday
1. First meeting:
1. Advanced Engineering Mathematics, 8th edition by Kreyszig
WILEY 0471423319
$166
at bookstore (approx.)
2. Mathematica Computer Guide for Kreyszig's AEM (bundled with
above text using the ISBN above)
3. Student Solutions Manual for Kreszig's
AEM (bundled with above text
using the ISBN above)
4. Differential Equations, 2nd edition by Blanchard, Devaney, Hall
Brooks/Cole 0534674283
This is a “bundled” ISBN including the student man. below. $126 at bookstore (approx.)
5. Student Solutions Manual for
Differential Equations by Blanchard
Brooks/Cole (bundled with ISBN above)
6. The Joy of Mathematica, 2nd
edition by Shuchat and Shultz $60 retail
(bookstore?)
Harcourt Academic Press 0126407304
7. The Mystery of the Aleph by Aczel $15 (approx.)
Pocket Books 073422996 (paper) Wait to purchase until 1^{st}
day of class to see the ISBN in bookstore.
Get correct ISBN
8. Chaos by Gleick
Penguin 0140092501
Do NOT buy until
after 1st day of class to see which ISBN is correct $13
9. Introduction to Linear Algebra, FIFTH edition by Johnson, Riess, Arnold $118
(approx.)
Addison Wesley 032114340x)
This is a “bundled” ISBN including the student solutions manual below.
10. Student Solutions Manual for Linear Algebra text above by
Camp
Addison Wesley (included with the bundled ISBN above)
11. Subscriptions and Membership
in the Mathematical Association of
Information on 1^{st} day of class. Purchase by 2^{nd} day of class $30
TOTAL $528
+ tax
Remember,
this is approximate!
useful for work in mathematics: Schaum’s Mathematical Handbook


FALL 
WINTER 
SPRING 
Tuesday 1 

Ordinary Differential Equations 
Nonlinear Differential Equations 
Partial Differential Equations 
Thursday 

Computer
Lab A.
Applications for Differential Equations & Linear Algebra B. Mathematica 
Differential Geometry 
Projects 
Friday 

Linear
Algebra 
Linear
Algebra (1^{st}
half of quarter) Differential Geometry (2^{nd} half of quarter) 
Differential Geometry includes Calculus of Variations 
Changes from the catalog: I wrote the catalog copy well over a year ago and since
that time, I have had discussions with colleagues at Evergreen and other
colleges about the content of the program.
After these discussions, I have decided that we should replace
Functional Analysis and Number Theory with Differential Geometry. Differential Geometry is an upper division
class at all universities and it will be more theoretical than other portions
of the program, but I’ve chosen a text that stresses applications. The program is primarily designed as an
adventure in applied mathematics and many examples will be drawn from physics
or engineering, but we will definitely examine both the historical and
philosophical foundations of mathematics as well as using mathematically
rigorous proofs in some portions of the program. The catalog states that credit will be awarded
in number theory and functional analysis, but that is not correct. Upper division credits for the program are
dependent on performance at an upper division level. (Upper division performance includes being present
at virtually all classes, turning in all homework on time with substantial
writing, doing well on exams, giving good presentations, etc. NO UPPER DIVISION CREDIT WILL BE AWARDED TO
ANYONE LEAVING THE PROGRAM BEFORE THE END OF SPRING QUARTER. Differential Equations, Linear Algebra, and
an Introduction to Mathematica are lower division at
all colleges, but I can justify upper division credit for fall and winter
quarters based on the advanced level of understanding of such topics that occur
for those who continue to study them throughout the year.
What can I do to prepare?
1. Prerequisites: two quarters
of calculus. Three quarters would be
better.
2. Most important: Come ready to start! Have your living situation settled before classes start, so you're ready to start learning seriously
in the first week. Have a functional
study area, reliable transportation, and money for books. The books will costs over $500 and must be
purchased by the second day of class. Be
prepared to work about 50 hours per week (including class time) starting the
first day of class. Students working at
a job more than 12 hours per week outside of class tend to have difficulty with
the workload. We are scheduled to meet
from
Frequently Asked Questions
1. Which books do I need for
the first class? Just the differential
equations books by Blanchard. Read
Section 1.1 before the first class.
However, all the books need to be purchased by the second class,
so come with the money to buy books. DO
NOT COUNT ON YOUR FINANCIAL AID TO BE READY FOR YOU! Experience has shown that students who are
unable to buy books during the first week have a very difficult time catching
up and usually end up dropping out of advanced mathematics and science
programs. Come with the money ($570) to
buy your texts immediately after the first class!
1. Can I drop the seminar portion
of the program? No. Seminar is a tool for learning not a separate
portion of the class. We will use two
hours each week for class discussions of philosophical, historical, and
scientific issues.
1. Can I take portions of the
program? Not in fall quarter unless you
already have credits in an identical mathematics class (differential equations
or linear algebra).
1. What proportion of the
credits are upper division? It is possible to earn 48 upper
division credits in this program depending on performance. At any other college, linear algebra and
differential equations are not considered upper division work, so upper
division credit depends on exceptionally highlevel performance in these areas
and the depth which comes from continuing your study of these topics through
spring quarter.
1. Are we required to subscribe
to journals? Yes. You'll get more information on the first day
of class. The Mathematical Association
of
2. Will I have the equivalent
of a mathematics degree at the end of this year? No, but you'll have a
excellent start on one! You will also
have most of the prerequisites for further work in physics and
engineering. More information on first
day of class. See the next two
questions.
3. Will I fulfill the
requirements for an endorsement for teaching high school mathematics by taking
this program? You will fulfill some but
not all of the requirements for your endorsement. Bring the checklist to go over it with me.
4. What other mathematics
beyond the first year level is available at Evergreen? This is the main mathematics program beyond
the calculus level that is offered this year.
There will be a bit of discrete mathematics in the Data to Information
program this year. Next year, the
Mathematical Systems program will offer additional upper division
mathematics. The Mathematical Methods
program is designed to be a more applied approach than the more proofbased
approach of Mathematical Systems.
However, the Mathematical Methods program will involve proofs as well,
but the emphasis is on learning to use the mathematics of differential
equations, linear algebra, etc.
5. Is Mathematical Methods the
right program for me or should I be in Matter and Motion? Matter and Motion covers first year calculus
and calculusbased physics. Mathematical
Methods requires calculus as prerequisite.
1. Will it be fun? You bet!
Will it be a lot of work? Yes,
about 50 hours per week including inclass time.
2. Are the syllabi for the year
ready? Yes. through the
Evergreen web site under fall quarter programs.
I will also post them on my office door (room 2002, Lab I), and the door
of our classroom – room 2242, Lab II. If
you are new to the campus, you might want to find the classroom before the
first day since we’ll cover important information about the year in the first
hour of the first class.
3. First meeting: Tuesday, October 1 at
C:/math methods/OVERVIEW 1st day handout.doc
**************************************************************************
SYLLABI
FOR YEAR FOLLOW – these are all subject to revision
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Mathematical Methods 20022003 Differential Equations Syllabus
Tuesdays
Texts: Differential Equations, SECOND
edition by Blanchard, Devaney,
Hall  bring to every class; get correct edition!
AEM = Advanced Engineering Mathematics by Kreyszig
Wk 
Date 
Read Before Class 
Homework Due the following week 
A E M 
SEM 
1 
Oct. 1 
1.1 Intro to program, Intro. to DE’s, modeling 
1, 2,3, Make plane reserv’ns 
1.1 
None 
2 
8 
1.2 Separation of Variables (Analytic
Technique) 1.3 Slope Fields
(Geometrical/Qualitative Tech.) 1.4 Euler’s Method (Numerical
Technique) 

1.3 1.7 1.2 
Aleph 163 
3 
15 
1.5 Existence and Uniqueness Theorems 1.6 Equilibria
and the Phase Line 

1.9 
65117 
4 
22 
App. A
FirstOrder Linear Equations Revisited 1.8 Linear Differential Equations,
Integrating Factor 


119 – 169 
5 
29 
1.7
Bifurcations & 1^{st} quiz (ONLY announced quiz) 


to 231 
6 
Nov 5 
2.1
Modeling via Systems: massonspring; prey 2.2
GEOMETRY of Systems; vector fields 

2.5 8.4 
Chaos 131 
7 
12 
2.2
More on Geometry of Systems & vector fields 2.3
Analytic Methods for Special Systems 


35 – 56 
8 
19 
2.4
Euler’s Method for Systems 2.5
Lorenz Equations 


57 – 80 
9 
Dec 3 
LINEAR
SYSTEMS 3.1 Linear Systems: Properties and
Linearity Princip. 3.2
StraightLine Solutions 3.3.
Phase Planes for Lin Sys with Real Eiengvalues 

3.0 3.1 3.2 3.3 
81 – 118 
10 
10 
EXAM – HW, Lectures thru 3.3;
presentations 
Bring: portfolio; book; notebook;
journal 

None 

20 
Evaluation conferences: stay through
Dec. 20^{th} ! Bring faculty evaluation to
conference. Selfeval.
due Dec. 17 

1 
Jan
7 
Appendix B: Complex Numbers 3.4
Complex Eigenvalues 3.5
Special Cases: Repeated and Zero Eigenvalues 

12.1 12.2 
119 – 181 
2 
14 
3.6
SecondOrder Linear Equations 3.7
The TraceDeterminant Plane 


189 – 211 
3 
21 
4.1
Forced Harmonic Oscillators 4.2
Sinusoidal Forcing 

2.9 
213 – 240 
4 
28 
4.3
Undamped Forcing and Resonance 4.4
Amplitude and Phase of the Steady State 4.5

Labs 4.2 & 4.3 as homework. Typed! 
2.11 2.12 
241  270 
5 
Feb 4 
NONLINEAR
SYSTEMS 5.1
Equilibrium Point Analysis 5.2
QUALITATIVE ANALYSIS 

3.4 
273 – 317 
6 
11 
5.3
Hamiltonian Systems 5.4
Dissipative Systems 


Math&Humor Ch.12 
7 
18 
3.8
Linear Systems in 3D 5.5
Nonlinear Systems in 3D 5.6
Periodic Forcing of Nonlinear Systems ,Chaos 

3.5 3.6 
Chap. 3 – 4 
8 
25 
6.1
 6.3 

5.1 – 5.2 
Chap. 5  6 
9 
Mar 4 
6.4  6.6 Delta Functions and
Qualitative Theory of 

5.3 – 5.9 
? no sem? 
10 
11 
EXAM 



1 
Apr
1 
Kreyszig 10.1 –
10.5 Fourier Analysis ( ~ review ) 
Kreyszig is our only
text for spring 


2 
8 
10.610.11 Forced Oscillations; Fourier Transforms 

B6.1 

3 
15 
11.1 – 11.4 PARTIAL
DIFFERENTIAL EQUATIONS 



4 
22 
11.5 – 11.7 Heat & Wave Equations 



5 
29 
1.8, 11.8 – 11.12 



6 
May 6 
19.1 – 19.7 Numerical Methods for PDE’s 



7 
13 
EXAM 



C:\math methods\SYLLABUS DEs year.doc
Tutor day and
time: Monday
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Mathematical Methods 20022003 Student Presentations Syllabus
Draft of
GOALS:
1. Practice
communicating mathematical ideas using words, blackboard, and overhead
projector.
2.
Introduce everyone to Multivariable Calculus and Complex Analysis as
background material for Linear
Algebra, Differential
Equations, and Differential Geometry.
(NOTE: “introduce” is not
same as “learn”.)
Texts:
Kreyszig’s Advanced Engineering Mathematics
except for “JRA” is the Linear Algebra text (Johnson, Reiss, Arnold)
Do at least 2
examples in your presentation. You might
want to read the material in an introductory calculus book, too.
You’ll have 20 minutes for your
presentation + 5 minutes for questions.
We’ll use 5 more minutes for feedback.
All 3 presenters
for a given day should practice their presentations with each other at least one day before your
presentation to the class. If one of
your copresenters is absent, the two (or one) remaining should be prepared to
cover all of the material for that day.
For your 1^{st} presentation:
Use the blackboard only; have 1page handout with big TITLE at top, plus
name & date.
For your 2^{nd} presentation: Use
the overhead projector; have 1page handout with big TITLE at top, plus your
name & the date.
Wk 
Date 
Day 
Section 
Topics: Multivariable (Vector) Calculus – Chapters 8 & 9
Complex Analysis – Chapters 12 – 14 
Presenter 
1 
Oct. 4 
Friday 
8.1, JRA 2.12.2 
Vector Algebra in 2space (the plane) Vector Algebra in 3space 
Tutor Tutor 
2 
10 
Thursday 
8.2 8.3 JRA 2.3 
Inner (Dot) Product Vector (Cross) Product Geometric Properties of Cross Product
and Triple Products 

2 
11 
Friday 
8.4 App. 3.2 8.4 
Vector and Scalar Functions and Fields. Partial Derivatives Vector Calculus 

3 
17 
Thursday 
8.5 8.5 8.6 
Curves. Tangents. (1^{st} Introduction to
Differential Geometry) Arc Length. Parameterization Curves in Mechanics. Velocity and
Acceleration 

3 
18 
Friday 
JRA 2.4 8.8 8.8 
Lines and Planes in Space Chain Rule for multivariable (also
cover single variable 1^{st}) Mean Value Theorem (use old calc. text
to go over single variable, 1^{st}) 

4 
24 
Thursday 
8.9 8.10 8.10 
Gradient of a Scalar Field. Directional Derivative Divergence of a Vector Field Divergence 

4 
25 
Friday 
8.11 8.11 A74  76 
Curl Curl Kronecker Delta and Curl
proofs EVERYONE STUDY pp. 461  463 

5 
31 
Thursday 
9.1 9.2 9.3 
Line INTEGRALS Line Integrals Independent of Path Double Integrals 

6 
Nov. 7 
Thursday 
9.4 9.5 9.6 
Green’s Theorem Surfaces: Parameterization, Tangents, Normals Surface Integrals 

7 
14 
Thursday 
9.7 9.8 9.9 
Divergence Theorem Applications of Divergence Theorem Stokes’s Theorem EVERYONE STUDY p.
523 

8 
21 
Thursday 
12.1 12.2 12.3 
Complex Numbers. Complex Plane Polar Form of Complex Numbers. Powers
and Roots. Derivative. Analytic Function 

9 
Dec. 5 
Thursday 
12.4 12.5 12.6 
CauchyRiemann Equations. Geometry of Analytic Functions:
Conformal Mapping (Challenging) Exponential Functions
(Challenging) 

10 
12 
Thursday 
13.1 13.2 13.3 
Line Integral in the Complex Plane
(Challenging) Cauchy’s Integral Theorem (Challenging) Cauchy’s integral Formula
(Challenging) 







1 
Jan. 9 
ALL on Thursday 
13.4 14.1 14.2 
Derivatives of Analytic Functions (Challenging) Sequences, Series, Convergence Tests Power Series 

2 
16 

14.3 
Depends on number of students. .. 

3 
23 
YOUR CHOICE OF
TOPICS for winter and spring! Three
additional presentations plus your final presentation on your spring
project. I urge you to consider
Chapter 5 – 7 in our Linear Algebra text (Applications of Eigenvalues
or Vector Spaces) and Chapter 8 (Discrete Dynamical Systems) in our
Differential Eq. text. 
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Mathematical Methods 20022003 LINEAR ALGEBRA Syllabus
Fridays
Draft
of August 11, 2002
Texts: Introduction to Linear Algebra,
FIFTH edition by Johnson, Riess, Arnold  bring to
every class
Bring the current MAA journals to every
class. Order those required before
October 3^{rd}. (See notes at
first day of class.)
Kreyszig’s Advanced
Engineering Mathematics might be useful during fall quarter (Chapters 6 &
7), it’s required winter quarter
Wk 
Friday Date 
Read Before Class 
Homework Due the following week at start
of class 
MAA journal 
1 
Oct. 4 
1.1
Introduction to Matrices; Systems of Linear Eqns 1.2
Echelon Form and GaussJordan Elimination 1.3
Consistent Systems of Linear Equations Order MAA journals (maa.org) BEFORE
class today 

Intro’s 
2 
11 
1.4
Applications 1.5
Matrix Operations 1.6
Algebraic Properties of Matrix Operations 

Intro’s 
3 
18 
1.7
Linear Independence and Nonsingular Matrices 1.8
Data Fitting, Numerical Integration & Different’n 1.9
Matrix Inverses and Their Properties 

Lib or 1059 
4 
25 
3.1
Vector Space in R^{n} 3.2
Vector Space Properties of R^{n} 3.3
Examples of Subspaces 


5 
Nov 1

3.3
Examples of Subspaces 3.4
Bases of Subspaces 3.5
Dimension 

CMJ 385400 
6 
8 
3.5
Dimension 3.6
Orthogonal Bases for Subspaces 3.7
Linear Transformations from R^{n} to
R^{m} 

TBA FROM CMJ 
7 
15 
3.8
LeastSquares Solutions to Inconsistent System 3.9
Theory and Practice of Least Squares 4.1
EIGENVALUE PROBLEMS 


8 
22 
4.2
Determinants and the Eigenvalue Problem 4.3
Elementary Operations and Determinants 4.4
Eigenvalues and the Characteristic
Polynomial 


9 
Dec 6 
4.5
EIGENVECTORS AND EIGENSPACES 4.6
Complex Eigenvalues and Eigenvectors 4.7
Similarity Transformations and Diagonalization 


10 
13 
4.7
Diagonalization 4.8 Difference Equations:
Systems of Diff. Eqn’s. 



20 
Evaluation Conferences: stay through
December 20^{th} 


1 
Jan 10 
4.8 7.1
Quadratic Forms 7.2 Systems of
Differential Equations (review!?) 


2 
17 
7.3
Transformations to Hessenberg Form 7.4
Eigenvalues of Hessenberg
Matrices 7.5
Householder Transformations 


3 
24 
7.6
The QR Factorization and LeastSquares Sol’ns 7.7
Matrix Polynomials & the CayleyHamilton
Thm 7.8 EV’s and
Solutions of Systems of Diff. Eq’ns 


4 
31 
Numerical Linear Analysis Kreyszig 18.6 – 18.9; 


5 
Feb 7 
Exam part 1; class will meet 


6 
14 
EXAM & Review. ( faculty retreat,
but class will meet) 


7 
21 
See Differential Geometry Syllabus for
rest of quarter 


8 
28 
DG 


9 
Mar 7 
DG 


10 
14 
DG 


1 
Apr 4 
CALCULUS OF VARIATIONS (see DG
syllabus) 


c:\math
methods\SYLLABUS Lin Alg YEAR
Tutor: Wednesday
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Mathematical Methods 20022003 Differential Geometry Syllabus
Draft
of August 11, 2002
Winter: Thursdays
Spring: Fridays
Text:
Differential Geometry and Its Applications by John Oprea
Recommended or required: Schaum’s Outline  Differential Geometry; Grya’s
Modern Diff’l Surfaces
Wk 
Date 
Read Before Class (from Oprea’s
text) 
Homework Due the following week 
A E M 
Pres’n or
journal 

1 
Jan
9 Th 
1
The Geometry of Curves 

8.5 
CMJ 

2 
16 Th 
1 

8.7 
AMM 

3 
23 Th 
2
Surfaces 

9.5 


4 
30 Th 
2 

9.6 


5 
Feb 6
Th 
3
Curvature 

8.7 


6 
13 Th 
Class will meet. Don at Faculty Retreat? 




7 
20 Th 
3
Curvatures 




7 
21 Fri 
4
Minimal Surfaces 




8 
27 Th 
4
Constant Mean Curvature Surfaces; Harmonic functions 




8 
28 Th 
5
Geodesics, METRICS 




9 
Mar 6
Th 
5
Isometries and Conformal Maps 

12.5 


9 
7 Fri 
6
Covariant Derivative & Parallel Vector Fields (and see Chapter 9
in May) 




10 
13 Th 
6
GaussBonnet Theorem 




10 
14 Fri 
7
Complex Variables; Enneper Representations 

12 & 13 









1 
Apr 3
Th 
7
Bjorling’s Problem & Minimal Surfaces 




1 
4 Fri 
8
CALCULUS OF VARIATIONS 




2 
10 Th 
Rest of Thursdays reserved for spring
projects 
No class, but be available to meet 



2 
11 Fri 
8
CALCULUS OF VARIATIONS 




3 
18 Fri 
8
CALCULUS OF VARIATIONS 




4 
25 Fri 
8
Calculus of Variations 9
Manifolds 




5 
May 2 Fri 
9
Covariant Derivative 




6 
9 Fri 
9
Christoffel Symbols (if time: Dual, wedge products, Killing vectors,
Schwarzschild sol’n in GR) 




7 
16 Fri 
Exam – plus take home due 




8 
23 Fri 
No class – prepare for your final
project presentation 




9 
30 Fri 
Project Presentations – attendance
required even if you’re not usually in class on Fridays 



10 
Jun
6 Fri 
Project Presentations 




EVALUATIONS START JUNE 19^{TH}
– DON’T LEAVE BEFORE JUNE 20^{TH }! No conference w/o faculty evaluation 

c:\math methods\SYLLABUS DG year