











Draft of August 15 , 2002
Prerequisites: 2 quarters of calculus
Parttime options? No. (Register for 16 credits)
Schedule: Tuesday, Thursday, Friday 1 – 6:30 p.m.
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, pub. 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 , pub. 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 0743422996 (paper)
8. Chaos by Gleick, Penguin 0140092501 $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, pub. Addison Wesley (included with the bundled ISBN above)
11. Subscriptions and Membership in
the Mathematical Association of America
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
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.
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SYLLABI FOR YEAR FOLLOW – these are all subject to revision
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Mathematical Methods 20022003 Differential Equations Syllabus
Tuesdays 1 – 6:30 p.m. Room 2242, Lab II Draft of August 14, 2002
Texts: Differential Equations, SECOND edition by Blanchard, Devaney, Hall  bring to every class; get correct edition!
AEM = Advanced Engineering Mathematics by
Kreyszig
Tutor day and time: Monday 1 – 5 p.m. Lab II room 2211 (down the hall from our classroom)
Mathematical Methods 20022003 Student Presentations Syllabus
Draft of August 11, 2002
GOALS: 1. Practice communicating mathematical ideas using words, blackboard, and overhead projector.
Algebra, Differential Equations, and Differential Geometry. (NOTE: "introduce" is not same as "learn".)
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. Laplace’s Equation. (Challenging)
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. 
Mathematical Methods 20022003 LINEAR ALGEBRA Syllabus
Fridays 1 – 6:30 p.m. Room 2242, Lab II
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 
Intros  
2  11  1.4 Applications
1.5 Matrix Operations 1.6 Algebraic Properties of Matrix Operations 
Intros  
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 1 – 5 p.m. Lab II room 2211 (just down the hall from our classroom)
Mathematical Methods 20022003 Differential Geometry Syllabus
Draft of August 11, 2002
Winter: Thursdays 1 – 6:30 p.m. plus Fridays during winter quarter weeks 7 through 10
Spring: Fridays 1 – 6:30 p.m. plus Thursday of 1^{st} week of spring quarter
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 
AEM  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