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COURSE SYLLABUSMath 422.01 -- LINEAR ALGEBRA II

Fall 2012

CRN: 9744CREDIT HOURS: 3HOUR/DAY: 1:00 2:15 p.m. T RMEETING ROOM: Wickersham Hall, Room 200

INSTRUCTOR: Dr. Ron UmbleOFFICE: Wickersham Hall, Room 203OFFICE HOURS: 10:00 -- 11:00 M T W R F and by appointmentOFFICE PHONE: 872-3708E-MAIL: ron.umble@millersville.eduURL: http://www.millersville.edu/~rumble

DEPT. PHONE: 872-3531DEPT. FAX: 871-2320

REQUIRED TEXTS: H. Anton and C. Rorres. Elementary Linear Algebra, Applications Version, 10th

Ed., JohnWiley & Sons, Inc., New York, 2010. ISBN 9-780470-432051.

L. Johnson, R. Riess and J. Arnold, Introduction toLinear Algebra, 5thEd., Addison

Wesley/Pearson Education, Inc. 2002. ISBN 0-201-65859-3.

CALCULATOR: TI-86 or higher (TI-83/84 cant handle some necessary calculations)

FORMAT: Lecture

RATIONALE: Linear algebra is an essential cornerstones of mathematics. Its powerful tools are appliedin virtually every area of pure and applied mathematics. A strong foundation in linearalgebra is essential for success in every mathematical endeavor.

Throughout this course you will encounter many new theoretical ideas and a wide range ofpractical applications. Working with applications helps to solidify your theoreticalunderstanding, strengthen your computational skill, and build your self-confidence.

OBJECTIVES: Upon completion of this course, the student will be able to:

1. Apply concepts of Linear Algebra to solve a variety of practical problems2. Find the matrix of a linear map relative to given bases3. Find the transition matrix for a change of basis4. Compare square matrices for similarity5. Compute eigenvalues and identify the eigenspaces of a linear operator6. Diagonalize matrices whenever possible7. Find the matrix representation of a quadratic form8. Diagonalize a quadratic form9. Compute the Jordan form of a square matrix

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COMMENTS: This course begins with a review of Linear Algebra I. After the fundamentals are well inhand, well move on to the new topics in the course. Lectures during the review periodinclude a brief discussion of the Review Topic (RT) followed by an application (APP).Your two texts provide somewhat different expositions of each topic. Its important to readboth expositions carefully, take notes, flag points that seem difficult to understand, and

bring your questions from the reading to class for discussion. You will find that oneexposition often makes more sense to you than the other. Thats good! Play one offagainst the other

UNDERSTANDINGS: 1. You are expected to attend all classes and complete all assigned work on time.

2. You may work together on problem sets, however you must write up your solutionsindependently.

3. Exams missed for the following reasons may be made up:a. Illness documented by campus infirmary or family physicianb. Death of a family memberc. Out-of-classroom educational experiences*d. University athletic contests*e. Religious holidays*

*Requires advance notification

EVALUATION: Course Component Weight

Problem sets (6 @ 3%) 24%Hour exams (2 @ 21%) 50%Final examination 26%

Grading Scale:

93% - 100% A*90% - 92% A-87% - 89% B+83% - 86% B

80% - 82% B-77% - 79% C+

73% - 76% C70% - 72% C-67% - 69% D+63% - 66% D

60% - 62% D-Below 60% F

*Course Honors will be awarded at my discretion for exceptional scholarship.

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COURSE SCHEDULEMath 422.01 -- LINEAR ALGEBRA II

Fall 2012

Date Topic Text Reading Homework (A=Anton;A-R J-R-A J=Johnson)

Aug 28T RT: Systems of linear equations with real coefficients 1 22 1 34 J59:43,49,61,69Systems of linear equations with complex coefficients 320 321 J324:1-17(x2),25,27

APP: Network analysis: traffic and current flow 73 78 A84:1,3,5,7PROBLEM SET #1:A84:8; A524:9; J79:49; J60:58,67; J324:26

30R RT: Computing the inverse of a matrix 51 57 92 102 A58:19; J102:11,29,48RT: Determinants 83 109 447 453 J453:1,9,15,21

APP: Curves and surfaces through specified points 520 524 A524:1a,2a,3,4a,6a

Sept 4T RT: Real vector spaces 171 207 71 78 A199:7,9,19; J78:9,13Complex vector spaces 315 317 316 317 A326:1-13(x2)

APP: Polynomial interpolation, systems of linear 80 88 A207:9,15; J90:5,9,11,13differential equations, numerical integration

6R RT: Real inner product spaces 335 364 392 400 A344:22; J401:1,13,14Complex inner product spaces 317 318 A326:27

APP: Least squares and data fitting 366 372 243 254 A351:7; J254:1,7,11PROBLEM SET #1 DUEPROBLEM SET #2:A444:34; A281:20; A452:18; A458:18; J401:21,23

11T General linear transformations 433 442 225 239 J239:3,5,8,11,19-29(x2)

APP: Geometry of matrix operators on R2 273 280 A280:1-4,5-19(2),22-24

13R Isomorphisms 445 451 A451:1,3,5,7,11Compositions and inverse transformations 452 456 A457:1,11,13,15,21

APP: Computer graphics 597 602 A603:1-8

18T Matrices for general linear transformations 458 465 419 429 A466:1,5,9,13Homogeneous coordinates

APP: Rotating the 4D cube Handout

20R RT: Change of basis 217 222 431 438 A222:2a,3a,4,5,7,11APP: Reflections in R2; rotations in R3 Lecture notes

PROBLEM SET #2 DUEPROBLEM SET #3:rotating 4D cube; an original fractal; J305:18,21,24; J314:18;

25T RT: Real eigenvalues and eigenspaces 295 302 298 315 A303:1,3a,5a,13,15Complex eigenvalues and eigenspaces 319 325 319 324 A326:21,23; J324:19

APP: Fractal geometry 626 639 A639:1-7

27R RT: Diagonalization 306 313 327 330 A313:1,3,5-25(x4)

Oct 2T Orthogonal matrices 389 395 330 333 A395:3,5,11,13,16,21Orthogonal diagonalization 397 400 333 336 A404:1,2,7,9,10

APP: The Fibonacci sequence and the golden ratio Lecture notes J336:15,17

4R HOUR TEST I

6 9 FALL RECESS

11R APP: Systems of linear differential equations 327 331 A331:1,3,6,10Spectral decomposition 400 402 A404:16,18

16T Quadratic forms and the Principle Axis Theorem 405 415 484 492 A415:1,3,9,11-21(x2)PROBLEM SET #3 DUE J492:7,19PROBLEM SET #4:A396:14,15; A474:15,16; A404:17,20

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Date Topic Text Reading Homework (A=Anton;A-R J-R-A J=Johnson)

Oct 18R Optimizing with quadratic forms 417 422 A423:3,5,7,9,11,19

23T Hermitian, unitary, and normal matrices 424 429 A430:1,3,7,13,25, 27,Similarity invariants 468 473 325 327 37-39,T/Fa,b

A473:1,3,11,13

25R Row-reduction to Hesenberg form (Algorithm 1) 502 509 J509:1-9(x2)PROBLEM SET #4 DUEPROBLEM SET #5:A431: 35,45; J519:19,20; J530:22,23

30T Krylovs Method Computing the characteristic polynomial 510 518 J518:1-13(x4)

Nov 1R Householder transformations and reduction to 519 529 J529:1-15(x2)Hessenberg form (Algorithm 2)

6T APP: Least-squares and the QR Algorithm 531 539 J539:1-17(x4)

8R Matrix polynomials and the Cayley-Hamilton Theorem 540 545 J545:1-4(all)PROBLEM SET #5 DUEPROBLEM SET #6:J546:6; J553:2,6,Conceptual 4a; Lecture notes exercises 120,125

13T Generalized eigenvectors. 546 553 J553:1-5APP:Systems of differential equations

15R Schurs Triangularization Theorem Lecture notes Exercise 121Another proof of the Cayley-Hamilton Theorem Lecture notes Exercises 124,128

PROBLEM SET #6 DUE

20T HOUR TEST II

21 25 THANKSGIVING BREAK

27T Range-Nullspace decomposition of Cn

Lecture notes Exercises 131,145,146PROJECT DUE

29R Core-Nilpotent decomposition of a singular matrix Lecture notes Exercise 151,161

Dec 4T Jordan form of a nilpotent matrix Lecture notes Exercise 165-169TAKE-HOME FINAL EXAM DISTRIBUTED

6R Jordan form of a general nxn matrix Lecture notes Exercises 179-182,184APP: Powers of a general nxn matrix Lecture notes Exercises 188,189

11T Project presentations (2:45 4:45 p.m.)TAKE-HOME FINAL EXAM DUE AT 2:45 p.m.