Mathematical Methods             2002 – 2003

 

                                                       Draft of August 15 , 2002

 

      3-page OVERVIEW + 5 SYLLABI FOR YEAR

 

Faculty:  Don Middendorf      donm@turbotek.net  (no e-mail through evergreen.edu)                                                       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.     First meeting: Tuesday, October 1, 2002 in room 2242 of Lab II at 1 p.m. 

 

  1. PLEASE NOTE:  TEXTS WILL COST over $500 AND MUST BE PURCHASED BY THE SECOND DAY OF CLASS.  MY PREVIOUS EXPERIENCE IS THAT THOSE WHO DO NOT PURCHASE THE TEXTS BY THE SECOND DAY OF THE QUARTER END UP DROPPING THE PROGRAM.  (We will use these texts all year, so the book costs for winter and spring will be under $200, I think.)  Do not buy texts without the student solutions manual (and Mathematica guides).  These will come “bundled” with texts purchased at our bookstore, THEY WILL NOT BE AVAILABLE FOR SEPARATE PURCHASE THROUGH OUR BOOKSTORE!  BE SURE to get the correct edition of the texts if you buy them somewhere besides our bookstore.  Don’t buy the seminar books until you get to campus and be sure to get the same edition that everyone else gets so that we all have the same page numbers to refer to in the seminar.  I’ll list the approximate prices of the texts through the bookstore, but they could be a bit less.

 

1.  Advanced Engineering Mathematics, 8th edition by Kreyszig

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                        

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                                 

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 073422996  (paper)   Wait to purchase until 1st 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 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

 

 

 

 

 

 

 

      

        FALL

                     

       WINTER

         

      SPRING

 

     

       Tuesday

     1- 6:30 p.m.

 

 

 

 

    Ordinary   

     Differential 

      Equations

 

   

     Nonlinear

       Differential

        Equations

 

    

       Partial

        Differential   

         Equations

 

 

 

 

       Thursday

    1 – 6:30 p.m.

 

 

 

 

       Computer Lab

 

  A.  Applications for 

      Differential Equations

         & Linear Algebra

 

  B.  Mathematica

 

 

 

 

       Differential   

        Geometry

          

   

 

           Projects

 

   

        Friday

    1 – 6:30 p.m.

 

 

 

  

  

    

         Linear Algebra

 

 

 

    Linear Algebra

      (1st half of quarter)   

 

    Differential

     Geometry

       (2nd 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 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

 

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 high-level 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 America has a nice deal for students - $30 for 2 journals.  These will help us become part of the community of mathematicians, follow the "hot" news, and learn some nifty mathematics.

 

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 proof-based 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 calculus-based 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 in-class 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 1 p.m       in room 2242 of Lab II

 

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

 

 

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SYLLABI FOR YEAR FOLLOW – these are all subject to revision

 

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Mathematical Methods   2002-2003            Differential Equations Syllabus                                                                                                                                                                                                

Tuesdays 1 – 7 p.m.          Room 2242, Lab II                                                               Draft of August 16, 2002

                                                                                                                                                                                               

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

1-63

 3

      15

1.5 Existence and Uniqueness Theorems

1.6 Equilibria and the Phase Line

 

1.9

 

65-117

 4

      22

App. A   First-Order Linear Equations Revisited

1.8 Linear Differential Equations, Integrating Factor

 

 

 119 – 169

 5

      29    

1.7   Bifurcations & 1st quiz (ONLY announced quiz) 

 

 

to 231

 6

Nov 5

2.1  Modeling via Systems: mass-on-spring; prey

2.2  GEOMETRY of Systems; vector fields

 

2.5

8.4

Chaos

1-31

  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  Straight-Line 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. 20th !  Bring faculty evaluation to conference.  Self-eval. 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  Second-Order Linear Equations

3.7  The Trace-Determinant 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  Tacoma Narrows Bridge

 

 

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.1-2

 7

      18

3.8  Linear Systems in 3-D

5.5  Nonlinear Systems in 3-D

5.6   Periodic Forcing of Nonlinear Systems ,Chaos

 

3.5

3.6

Chap. 3 – 4

 8

      25

6.1  - 6.3  Laplace Transforms

 

5.1 – 5.2

Chap. 5 - 6

 9

Mar 4

6.4 - 6.6 Delta Functions and Qualitative Theory of Laplace Transforms  (& Kreyszig 4.1 – 4.2)

 

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

10.6-10.11  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 Laplace’s Equation; Potential

 

 

 

 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 1 – 5 p.m. Lab II room  2211 (down the hall from our classroom)

 

 

 

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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

 

Presenter

1

Oct. 4

Friday

8.1, JRA 2.1-2.2

Vector Algebra in 2-space (the plane)

Vector Algebra in 3-space

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.           (1st 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 1st)

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

 

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

Cauchy-Riemann 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.

 

 

 

 

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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

 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 Gauss-Jordan 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 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

 

TBA FROM CMJ

 

7

 

      15

3.8  Least-Squares 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 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)

 

 

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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

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  Gauss-Bonnet 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 19TH – DON’T LEAVE BEFORE JUNE 20TH !  No conference w/o faculty evaluation

 

c:\math methods\SYLLABUS DG year