Mathematical Methods 2002 - 2003
Differential Equations
Linear Algebra
Differential Geometry
Physical Systems

Draft of August 15 , 2002

3-page OVERVIEW + 5 SYLLABI FOR YEAR Faculty: Don Middendorf (no e-mail through 867-6618

Prerequisites: 2 quarters of calculus

Part-time options? No. (Register for 16 credits)

Schedule: Tuesday, Thursday, Friday 1 – 6:30 p.m.

1.  Advanced Engineering Mathematics, 8th edition by Kreyszig, pub. WILEY  0-471-42331-9       $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, pub. Brooks/Cole 0-534-67428-3
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 0-12-640730-4

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 1st day of class. Purchase by 2nd day of class $30

TOTAL $528 + tax

Remember, this is approximate!

useful for work in mathematics: Schaum’s Mathematical Handbook

1- 6:30 p.m.











1 – 6:30 p.m.

  Computer Lab 

A. Applications for 

Differential Equations

& Linear Algebra

B. Mathematica





1 – 6:30 p.m.

  Linear Algebra 


Linear Algebra

(1st half of quarter) 



(2nd half of quarter)




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 1 p.m. to 6:30 p.m. Tuesday, Thursday, and Friday. Tutors will probably be available on Monday afternoon and on Wednesday afternoon, so keep those times free, too.

Frequently Asked Questions

C:/math methods/OVERVIEW 1st day handout.doc


SYLLABI FOR YEAR FOLLOW – these are all subject to revision


Mathematical Methods 2002-2003 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


Link to DiffEq SYLLABUS

Tutor day and time: Monday 1 – 5 p.m. Lab II room 2211 (down the hall from our classroom)

Mathematical Methods 2002-2003 Student Presentations Syllabus

Draft of August 11, 2002

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 co-presenters is absent, the two (or one) remaining should be prepared to cover all of the material for that day. For your 1st presentation: Use the blackboard only; have 1-page handout with big TITLE at top, plus name & date.

For your 2nd presentation: Use the overhead projector; have 1-page 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

1 Oct. 4 Friday 8.1, JRA 2.1-2.2 Vector Algebra in 2-space (the plane) 

Vector Algebra in 3-space



2 10 Thursday 8.2


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


Vector and Scalar Functions and Fields.

Partial Derivatives

Vector Calculus

3 17 Thursday 8.5



Curves. Tangents. (1st Introduction to Differential Geometry)

Arc Length. Parameterization 

Curves in Mechanics. Velocity and Acceleration

3 18 Friday JRA 2.4



Lines and Planes in Space

Chain Rule for multivariable (also cover single variable 1st)

Mean Value Theorem (use old calc. text to go over single variable, 1st)

4 24 Thursday 8.9



Gradient of a Scalar Field. Directional Derivative

Divergence of a Vector Field


4 25 Friday 8.11


A74 - 76



Kronecker Delta and Curl proofs EVERYONE STUDY pp. 461 - 463

5 31 Thursday 9.1




Line Integrals Independent of Path

Double Integrals

6 Nov. 7 Thursday 9.4



Green’s Theorem

Surfaces: Parameterization, Tangents, Normals

Surface Integrals

7 14 Thursday 9.7



Divergence Theorem

Applications of Divergence Theorem

Stokes’s Theorem EVERYONE STUDY p. 523

8 21 Thursday 12.1



Complex Numbers. Complex Plane

Polar Form of Complex Numbers. Powers and Roots.

Derivative. Analytic Function

9 Dec. 5 Thursday 12.4



Cauchy-Riemann Equations. Laplace’s Equation. (Challenging)

Geometry of Analytic Functions: Conformal Mapping (Challenging)

Exponential Functions (Challenging)

10 12 Thursday 13.1



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



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 2002-2003 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 3rd. (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


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 Gauss-Jordan Elimination

1.3 Consistent Systems of Linear Equations

Order MAA journals ( BEFORE class today

2 11 1.4 Applications

1.5 Matrix Operations

1.6 Algebraic Properties of Matrix Operations

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


4 25 3.1 Vector Space in Rn

3.2 Vector Space Properties of Rn

3.3 Examples of Subspaces

5 Nov 1  3.3 Examples of Subspaces

3.4 Bases of Subspaces

3.5 Dimension

  CMJ 385-400
6 8 3.5 Dimension

3.6 Orthogonal Bases for Subspaces

3.7 Linear Transformations from Rn to Rm

7 15 3.8 Least-Squares Solutions to Inconsistent System

3.9 Theory and Practice of Least Squares


8 22 4.2 Determinants and the Eigenvalue Problem

4.3 Elementary Operations and Determinants

4.4 Eigenvalues and the Characteristic Polynomial


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 20th    
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 Least-Squares Sol’ns

7.7 Matrix Polynomials & the Cayley-Hamilton 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 2002-2003 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 1st 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 Gauss-Bonnet Theorem      
10 14 Fri 7 Complex Variables; Enneper Representations   12 & 13  
1 Apr 3 Th 7 Bjorling’s Problem & Minimal Surfaces      
2 10 Th Rest of Thursdays reserved for spring projects No class, but be available to meet    
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 19TH – DON’T LEAVE BEFORE JUNE 20TH ! No conference w/o faculty evaluation

c:\math methods\SYLLABUS DG year