Mth 306 Matrix and Power Series Methods


Last updated: March 10, 2008
Sample problems

Term: Winter 2008
CRN: 23043
Time: MWF 1300-1350
Location: Kidder 350

Final Exam Monday Mar 17 1200-1350 With 109 (Withycombe Hall)

Recitation

Recitations for our section are

T 1000-1120 23044 STAG 211
T 1200-1320 23045 STAG 310
T 1400-1520 24861 STAG 310
You should attend the recitation section in which you are actually enrolled. The sections are not interchangeable. If you have a serious need to change your recitation section, check with the GTA to see if your need can be accomodated.

Our recitation GTA is Dave Wing. His email address is

wingda@math.oregonstate.edu.
His math dept web page is
http://www.math.oregonstate.edu/people/view/wingda

Texts and Syllabus

Lee, Matrix and Power Series Methods, Wiley 2006

A calculus text: Access to any suitable single variable calculus text may be useful.

Syllabus: We will cover all of the material in Lee's manual (I hope). You should keep up to date. In particular you should attempt most of the problems in each section even if you are not asked to turn them in.

Mth 253 Note

The content of Mth 253 overlaps the content of Mth 306 as far as the subject of series is concerned, though Mth 253 may stress theory more. At any rate you may find some of the Mth 253 notes of interest.

Grades

I may answer email queries about grades as time permits. Please read the document Grade Information before requesting grade information by email.

The following grade distribution will be used:

Recitation=TR %
Test 1=T1 %
Test 2=T2 %
Exam=TE %

Your grade will be computed as

Final grade = 0.15*TR  + 0.20*T1  + 0.20*T2  + 0.45*TE

Calculators

You may use a simple graphics calculator on tests, but not a laptop computer, palm computer, nor any device capable of extensive symbolic manipulation (other than your own brain). I will expect that you have at the very least a scientific calculator or a simple graphics calculator. Note your calculator will need to be in radians mode (not degrees). Questions about calculators will not be answered during tests. You must know how to use your own calculator.

Because many calculators are capable of solving equations and finding eigenvalues and eigenvectors you should expect that test problems may be a little bit indirect, at least in some cases, and require a modicum of thought.

Calculators may not be shared during tests nor may you use a calculator capable of communicating with other calculators.

Programming

Mth 306 does not require any programming nor any mathematical software, but you may find Maple, Matlab, Octave, Euler, Mathematica, MathCad or even a Spreadsheet helpful in investigating some topics in the course, or just to check your work. Maple is my favorite tool but the Engineering School seems to prefer Matlab. If you are planning to study engineering you should probably learn Matlab as soon as possible. Check with your advisor.

Maple:  Maple is a symbolic mathematics tool. Maple tries to find an exact symbolic answer to any problem. For some problems this feature is not very useful or is extremely time consumming, but Maple is also capable of doing very high precision approximate calculations (thousands of decimal digits if required). See Maple.

Matlab:  Matlab, matrix laboratory, is used to obtain numerical solutions to mathematical problems. Its primary (really only) data type is the array and it is its ability to manipulate arrays directly that gives it most of its power. You may find the brief description of a small part of Matlab in Mth 355 Matlab Introduction useful.

Octave:  GNU Octave is a high-level interactive numerical computation language which to a large extent is compatible with Matlab. The command line switch "--traditional" improves the compatibilty. Octave runs on Unix-like systems (in particular, on Linux). You can download Octave from

http://www.octave.org

Test Information

You may use a single 8.5 by 11 inch (21.6 by 27.9 cm) notesheet, or smaller, prepared in advance, to bolster your memory on the tests. You may write on both sides of your notesheet. Notesheets may not be shared. If you don't prepare a notesheet in advance you will have to do without a notesheet.

In view of the size of the class, the tests will consists mostly, or entirely, of multiple-choice problems. Be sure you work very carefully. Do not be misled by answers which appear to be correct.

If you do fairly well on the midterms and then miss the final exam, your grade will be I (incomplete). If you do poorly on the midterms and then miss the final exam, your grade will be F. In order to obtain a W you must formally withdraw from the course in accord with institutional rules.

If you make arrangements before a test, or on the same day, and if you have a very good reason, it may be possible to schedule a make-up test. At most one make-up test may be taken during the quarter. Note, it is not possible to make-up the final exam. The make-up test is normally similar, but not identical, to the in-class test.

Winter Calendar

More calendar information will be added (and some corrected) during the quarter.

    January 2008
Su Mo Tu We Th Fr Sa
       1  2  3  4  5
 6  7  8  9 10 11 12 week 01
13 14 15 16 17 18 19 week 02
20 21 22 23 24 25 26 week 03 MLK Day 21
27 28 29 30 31       week 04

    February 2008
Su Mo Tu We Th Fr Sa
                1  2 week 04
 3  4  5  6  7  8  9 week 05 TEST 1 Wed Jan 6
10 11 12 13 14 15 16 week 06
17 18 19 20 21 22 23 week 07
24 25 26 27 28 29    week 08

     March 2008
Su Mo Tu We Th Fr Sa
                   1 week 08
 2  3  4  5  6  7  8 week 09 TEST 2 Wed Mar 5
 9 10 11 12 13 14 15 week 10
16 17 18 19 20 21 22 exam week
23 24 25 26 27 28 29 spring break
30 31                spring classes begin

Class Record

This record is a bit sketchy, but you may find it useful, especially if you miss a few classes. Each entry below is a record of what we actually did in class, or occasionally, what I plan to do in class.

Mon week 1 Jan 07
Section 1. Discusion of course - tests, homework, etc. Complex numbers functions of a complex variable.
Wed week 1 Jan 09
Section 1. More on complex numbers. A bit on power series (more to come later). Polar representation of complex numbers.
Fri week 1 Jan 11
Section 2/3/4. I briefly discussed section 2: vectors, lines and planes and then assigned it for self-study. Next we discussed linear equations, matrices, row reduction of the augmented matrix and parametrization of the solution space using the free vaiables. We will continue sections 3 and 4 on Monday.
Mon week 2 Jan 14
Section 3/4. Row reduction of augmented matrix of a linear system and parametrization of solutions (using free variables as parameters). Note the specific parametrization of solutions by the free variables we discussed is frequently known as the canonical parametrization of the solutions. It is not the only way to parametrize the solutions. Examples.
Wed week 2 Jan 16
Section 4. Row echelon form (Gauss-Jordan). Note Maple uses rref() which is an abbreviation for row reduced echelon form (in linalg module). The command gaussjord() is an alias. structure of solutions of systems of linear equations.
Fri week 2 Jan 18
Section 4. Matrix multiplication. Permutations and parity. Determinants and inverses of square matrices. Calculation of inverse by row reduction.
Mon week 3 Jan 21
No class - Martin Luther King, Jr. Day
Wed week 3 Jan 23
Adjunct matrix and inverse. Solution of Ax=b by Kramer's rule when A is square and nonsingular.
Fri week 3 Jan 25
Section 4 and 5. Review of invertible matrices and calculation of inverse.
Mon week 4 Jan 28
Section 5 and 6. Abstract vector spaces and subspaces. Linear dependence and independence. Span of a set of vectors. Basis and dimension.
Wed week 4 Jan 30
Section 6. Matrices and linear transformations
Fri week 4 Feb 1
Section 6. Matrices and linear transformations. Projections.
Mon week 5 Feb 4
REVIEW
Wed week 5 Feb 6
TEST 1
Fri week 5 Feb 8
Section 7. Eigenvalues and eigenvectors. Diagonizable matrices and diagonalizing matrices. Unlinking systems of first order ordinary differential equations.
Mon week 6 Feb 11
Section 7. Symmetric matrices and diagonalization. Orthogonal matrices. Moment of inertia, ellipsoid of inertia and principal axes of inertia. (Check a good classical mechanics text for more information.)
Wed week 6 Feb 13
Example. Explicit diagonalization of a 3 × 3 symmetric matrix. Throw away your notes and try the calculations on your own
A = matrix(3,3,[1,0,3, 0,1,0, 3,0,1]).
Section 9. Introductory remarks on series.
Fri week 6 Feb 15
Section 8. Taylor polynomials
Mon week 7 Feb 18
Section 10: Infinite series. Convergence, divergence, sum. Geometric series. Estimating the exponential - computing Euler's number to 6 decimal places.
Wed week 7 Feb 20
Section 10: Infinite series - additional discussion. Section 11: Taylor series - discussion of sin(x), cos(x), tan(x), exp(x), arctan(x).
Fri week 7 Feb 22
Section 12: Series with nonnegative terms - the integral test.
Mon week 8 Feb 25
Lesson 12: Series with nonnegative terms - the integral test. A better estimator for the sum.
Wed week 8 Feb 27
Lesson 13: Comparison tests and limit comparison tests.
Fri week 8 Feb 29
(Plan: Lesson 13, 14, 15)
Mon week 9 Mar 3
REVIEW Mon March 3
Wed week 9 Mar 5
TEST 2 Wed March 5
Fri week 9 Mar 7
Sun Mar 9
Daylight savings time begins?
Mon week 10 Mar 10
Wed week 10 Mar 12
Fri week 10 Mar 14
Mon exam week Mar 17
Final exam: Location TBA

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