SYLLABUS – MATH-08 -- Linear Algebra --Spring 07: Sec. No. 1494
Office: Communications Bldg, Room C-21. Phone 384-6291. Office hours MWF 2-3, Th10-12
Web site: http://www.mccd.edu/faculty/powerd e-mail: power.d@mccd.edu
Home phone: Refer to Atwater Phone Directory.
My Class Schedule: 7:00 MTWF I-120; 9:00 Daily I-143; 12:00 MWF I-120; 1:00 MWF AG-11
Math Lab: To be announced
Textbook: Anton, Elementary Linear Algebra, 9th edition.
Calculator: You will need a graphing calculator with a vector menu, such as TI-85, 86, 89, or 92
Lecture/Test Schedule (Approximate):
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1. |
Jan 16-19 (Monday holiday) |
1.1, 1.2 |
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*ESO
A, B, C |
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2. |
Jan 22-26 |
1.3, 1.4, 1.5 |
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D, E |
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3. |
Jan 29-Feb 2 |
1.6, 1.7, 2.1, |
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E |
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4. |
Feb 5-9 (Friday
holiday) |
2,2, 2.3, |
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E |
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5. |
Feb 12-16 |
2.4, 3.1, 3.2, |
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E, F |
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6. |
Feb 19-23
(Monday holiday) |
3.3, |
Test on
Ch 1-2 |
F |
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7. |
Feb 26 - Mar 2 |
3.4, 3.5, 4.1, |
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F, G |
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8. |
Mar 5-9 |
4.2, 4.3, 4.4, |
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G, K |
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9. |
Mar 12-16 |
5.1, 5.2, |
Test on Ch 3-4 |
G, K |
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10. |
Mar 19-23 |
5.3, 5.4,
5.5, |
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B, G, K |
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Mar 26 - 30 |
5.6,
6.1,
6.2, |
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G, H, K |
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11. |
Apr 2-6
(Friday holiday) |
6.3, 6.4, 6.5, |
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H, I |
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12. |
Apr 9-13
(Spring break) |
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13. |
Apr 16-20 |
7.1, 7.2, |
Test on Ch 5-6 |
L |
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14. |
Apr 23-27 |
7.3, 8.1, 8.2, |
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J, K |
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15. |
Apr 30 - May 4 |
8.3, 8.4, 8.5, |
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K |
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16. |
May 7-11 |
8.6, 9.1, |
Test on Ch 7-8 |
G, L |
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17. |
May 14-18 |
9.2; 9.3 or 9.4 |
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E, F, H,
I |
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18. |
Mon, May 21, 10:00 |
Final Exam
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*Expected Student Outcomes (ESO’s)
A, C, M, and N will be covered throughout the course. |
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Grading System |
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Grading Scale* |
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-- Homework (top 15 of 16), 7 each |
100 points |
90% 675-750 |
A |
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-- 4 Chapter Tests -- 100 points each |
400 points |
80% 600-674 |
B |
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-- Final Exam |
250 points |
70% 525-599 |
C |
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Total |
750 points* |
60% 450-524 |
D |
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Below 60% 0-449 |
F |
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*Plus Quizzes (2 points each) |
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Homework: Assignments will be handed out in class, and will be posted on the web site as an attachment to the syllabus.
An integral part of the homework will be a selection of technology exercises, to be done on a computer. You may use the computers in the math lab, which have Maple installed; or you may use another computer algebra system at home if you have one installed on your own computer.
Due dates: The homework for each week's lessons is due
in class on Tuesday of the following week.
I will accept late homework up to Friday afternoon (2 points off). I will not collect homework during finals
week.
Format:
Use standard notebook paper. Do not use spiral notebook paper unless you trim the ragged edge.
Start a new page for each lesson.
Put your name in the upper right corner of the page; do not write in the upper left corner.
Write clearly and organize your work neatly in one or two columns.
Leave at least one space between problems.
Staple your pages together in order in the upper left corner of the page.
Each question: Include:
Chapter Tests
Preparation: Review
the Study Guide on the web site. In the
textbook, review the Chapter Summary, Chapter Review, Chapter Test, and
Cumulative Review.
Notes: You may use one 3x5 card of notes.
Work: You must clearly show your work to explain/justify your answers.
Calculator: You may use a calculator
for most routine calculations, but you must clearly show your calculator input
and your calculator answer, and you must properly interpret your answers.
Make-ups: You may make up one chapter test without penalty. For each additional make-up, your score will be reduced by 10% (unless you make prior arrangements).
Deadline for Make-ups: within one week of the original test. No make-ups after May 18.
Location/Time of Make-ups: Developmental Ed Office in
Lowest test: Your lowest test percentage will be replaced
by your final exam percentage, if it helps your grade.
Quizzes Expect daily
quizzes, scored at 2 points each. These normally add to the 800 points
available for the class. There will be no make-ups for missed quizzes.
Comprehensive Final Exam
If you get a C (70%) or better on both the final exam and the homework,
you will receive a C or better in the course.
If you do not take the final exam, you will receive a D or F in the
course.
Attendance for the full class period is mandatory. I may count you absent if you arrive late or leave early. If you wish to drop the class, that is your responsibility. However, I may drop you if (1) you are absent for a full week of consecutive classes, (2) you miss a test and do not arrange for a make-up, or (3) you are failing the course and have missed three or more class periods total.
Academic Honesty. It is your responsibility to refrain from cheating in any form, and to refuse to aid or abet any form of academic dishonesty. See the Merced College Academic Honesty Procedure (under "Civil Assurances" in the Schedule of Classes) for definitions and a partial list of possible disciplinary actions. For a first offense, expect to receive a zero score for the particular assignment or exam; for a repeated offense, expect a failing grade for the course and referral to the Office of Instruction (since serious or repeated offenses may result in suspension from the college).
Course Description:
MATH-08 LINEAR ALGEBRA. 3 units; 3 hours
lecture.
Prerequisite: Currently, Precalculus (MATH-2, or both MATH-25 and -26).
Effective spring 2008, the prerequisite will become MATH-04B. Advisories: ENGL-A, ENGL-41.
This course is suggested for computer science, engineering, math, and science
majors. It is an introduction to systems
of linear equations, matrix and determinant operations, vector spaces, linear
transformations, eigenvalues, and eigenvectors with a strong emphasis on
applications.
Expected Student Outcomes. Upon completion of this course, the student is expected to be able to:
A. Solve linear systems by Gaussian or Gauss-Jordan elimination.
B. Determine whether a linear system is consistent or inconsistent
C. Determine whether a consistent linear system has a unique solution or an infinite number of solutions.
D. Simplify matrix expressions using matrix algebra.
E. For a given matrix, compute the transpose, determinant, and inverse, if defined.
F. Set up and solve applied problems using 2 and 3 dimensional vectors.
G. Define, discuss and apply the various elements and concepts concerning vector spaces, including subspace, linear independence, spanning set, and basis.
H. Define an inner product; discuss and apply the various elements and concepts concerning inner product spaces.
I. Construct orthogonal and orthonormal bases using the Gram-Schmidt process.
J. Construct the orthogonal diagonalization of a symmetric matrix.
K. Define matrix transformations, linear transformations, one-to-one, onto , kernel, range or image, rank, nullity, and isomorphism.
L. Compute the characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces for matrices and linear transformations.
M. Determine what constitutes an acceptable proof, and prove basic results in linear algebra.
N. Make appropriate use of available technology in solving a variety of problems in these areas.
Specific Homework Assignments
1.1 1adf, 2, 3ac, 4ac, 5b, 6, 7, 8, 12, T1 (0n page 79). For T1, I suggest the 10-minute tour of Maple-10, as well as the introductory section on Maple in the web site.
1.2 Hwk: 1acegi, 2ade, 3acd, 4abcd, 5b, 6a, 8b, 9c,
10c, 12, 13b, 16a, 17, 18, 20, 22, 24, 25, 32, T1
#24: Let 1/x = u etc. #25:
for each point, substitute x and y into the given form. Maple sample:
with(linalg); a:=matrix( [[2,1,3],[1,-5,4]] ), rref(a);
1.3 Hwk 1beg, 2, 3ej, 4dh, 5gi, 6a, 7b, 8a, 9a, 13a, 14a, 15a, 20, 21abd, 25, 31ab, T4.
1.4 Hwk part b for 1-7; 9b, 14, 15a, 17, 21, 23 graphing calculator , 29ab, 34
1.5 Hwk 1, 2, 3b, 5b, 6b, 7a, 8b, 10, 18, 21, 23
1.6 Hwk 2, 5, 11, 14, 17, 20, 25, 30, 31, T1
1.7 Hwk 1, 2, 3, 4, 5, 6, 7, 8, 10b, 11a, 12 (calculators OK from now on), 15 (Note A2 = ATA for symmetric matrices, 22a (you will need Thm 1.4.8c)
2.1 Hwk:
1, 3ad, 4, 7, 16,
21, 22, 25, 29, T3
2.2 Hwk 1a, 2, 3, 12, 14, 16 for #6, 14, 17 for #8, 18, 19
2.3 Hwk 1b, 2, 3, 4bd, 5abe, 6, 9, 12, 13, 14c, 15 (for 14c), 16, 18
2.4 Hwk 1ab, 2ab, 5, 9, 13b, 17, 19, 22, 23a
3.1 Hwk: 1af, 2bgh, 3def, 5b, 6d, 7, 8, 9, 11, 12, 14, 15, 16, 17, 18, T1
3.2 Hwk: 1bce, 2c, 3ce, 4, 5a, 7, 8bd(for parts e, g), 9ac, 10, 11, 12 (hint: the name of this inequality is the "triangle inequality"), 14 (for part d only; do the proof for a vector in 3 dimensions)
3.3 Hwk: 1ac, 2ac, 3abc, 4ac, 5ac, 6ac, 8ab (think of slope), 9b, 12 (find all 3 angles), 14, 16b, 20 (write two vectors that define the angle), 21ab, 25, 27, 28, 29, 31
3.4 Hwk: 1-22 (part b only, except do all of #9), 25b, 29, 36-39, T1
3.5 Hwk: 1ac, 2a, 5ab, 8, 9a, 10a, 11, 14, 17, 19, 25, 29, 34, 37, 39a, 42, 45, 47, 48
4.1 Hwk: 1c, 4, 5c, 9c, 14cd, 15, 17d, 19, 20, 22, 26 [use u=(a,b), v=(cost,sint)], 30, 34, 37
4.2 Hwk: 1bc, 3, 5b, 6bc, 7b, 9b, 10b, 11b, 12b, 13a, 14b, 16b, 18b, 19a, 20ab, 22a, 23 (x-axis), 24, 27, 29b, 34
4.3 Hwk: 1, 2, 4, 5a, 7, 8ab, 10ab, 12be, 14a, 15b, 16a, 17b, 18b, 19b, 20ab, 21, 24, 27
4.4 Hwk: 1b, 2b, 3b, 4a, 6b, 7a, 9a, 11, 15a
5.1 Hwk: 1, 5, 9, 11, 14, 18, 22, 25, 29, 31, 32
5.2 Hwk: 1, 2b, 3b, 4ce, 5ab, 6, 7b, 8b, 9b, 10a, 11b, 12ac, 13, 14c, 15, 16, 20, 23, 24a, 27
5.3 Hwk: 1, 2bd, 4bd, 5a, 7a, 7b for v1, 9, 10 for {v1,v2}, 12, 14, 15, 19, 20acd, 21bcd, 24
5.4 Hwk: 1b, 2bd, 3ab, 4c, 5, 6a, 9b, 10c, 11, 13, 16, 17, 18b, 19b, 21b, 24ab, 29, 33a, 34
5.5 Hwk: 1, 2b, 3b, 4ab, 5b, 6bc, 7b, 8bc, 9bc, 10bc, 11b, 12b, 13, 16b, 18
5.6 Hwk: 1, 2d, 3d, 4bdg, 5, 6, 7bdf, 8bdf, 9, 11, 13, 16, 17ab, 18ab, 19ad
6.1 Hwk: (1-4)b, 5a, (6-12)b, 13a, 16b, 17a, 20, 22, 24, 27b, 28abc, 31, 32, 34
6.2 Hwk: 1b, 2, 3, 4, 5b, 6b, 7, 8b, 10b, 13b, 15b, 17, 18b, 19, 21, 23, 28, 30, 34
6.3 Hwk: 1ab, 2ab, 4ab, 5a, 6b, 7b, 10b, 11b, 12, 15b, 17a, 18, 20, 21, 29 ,30
[omit QR decomposition]
6.4 Hwk: 1a, 2b, 3b, 4b, 5b, 6, 8b, 10, 13, (see 14)
Also do lesson 9.3 #2, 3, 4 (check with calculator LinReg, P2Reg, P3Reg)
6.5 Hwk: 1b, 2b, 3b, 4, 6, 8, 10
6.6 Hwk: 1ab, 2ab, 3abcd, 5, 6, 19
7.1 Hwk: (1 to14)b, 15a, 20. Also see 23, but don't do for homework
7.2 Hwk: 1, 2, 5, 11, 13, 19, 20c, 22, 25
7.3 Hwk: 1abc, 2, 7, 15
8.1 Hwk: 1, 5, 9, 14, 17ab, 19, 21, 22, 28
8.2 Hwk: 3, 4, 5a, 6a, 7bc, 8bc, 9, 10, 14ac, 16ac, 18, 19, 24, 25, 28, 29
9.6 Hwk: 1b, 5b, 6, 7abcd, 9, 11, 15ac
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Updated 05/11/07 by Don Power