SYLLABUS -- MATH 4C -- Third Semester Calculus -- Spring 09: Sec. No. 1491

MWF 7:40 – 8:50

Web site: http://www.mccd.edu/faculty/powerd e-mail: power.d@mccd.edu

Mailbox: Quickest: Downstairs Science; Slower: Administration Building, Box 20;

Home phone: Refer to Atwater Phone Directory.

Math Lab: My hours MWF 9:00 – 10:50. Lab open MTWTh 8-7, Fri 8-1.

Textbook: Anton, Calculus, Multivariable, 8th edition.

Calculator: You need a graphing calculator that handles vectors (such as TI-85, 86, 89, or 92)

Lecture/Test Schedule (Approximate):

1.	Jan 19-23 (Monday holiday)	12.1, 12.2		ESO C
2.	Jan 26-30	12.3, 12.4, 12.5		A, B
3.	Feb 2-6	12.6, 12.7, 12.8,		B, C, D
4.	Feb 9-13 (Friday holiday)	13.1,	Wed - Test on Ch 12	E
5.	Feb 16-20 (Monday holiday)	13.2, 13.3, 13.4,		E, F, H
6.	Feb 23-27	13.5, 13.6,		F, G
7.	Mar 2-6	13.7, 14.1, 14.2,		I
8.	Mar 9-13	14.3, 14.4,	Mon - Test on Ch 13	I
9.	Mar 16-20	14.5, 14.6, 14.7,		J, K
10.	Mar 23-27	14.8, 14.9, 15.1,		L, M
11.	Mar 30 – Apr 3	15.2, 15.3,	Wed - Test on Ch 14	M
12.	Apr 6-10 (Friday holiday)	15.4, 15.5,		M
	Apr 13-17 (Spring break)
13.	Apr 20-24	15.6, 15.7, 15.8,		M
14.	Apr 27 – May 1	16.1, 16.2,	Fri - Test on Ch 15	N
15.	May 4-8	16.3, 16.4, 16.5,		N
16.	May 11-15	16.6, 16.7,		N
17.	May 18-22 Finals start Friday	16.8,		N
18.	To be announced	Final Exam

Grading System		Grading Scale*
-- Homework (top 15 of 16), 7 each	100 points	90% 720-800	A
-- Labs (5), 10 each	50 points	80% 640-719	B
-- 4 Chapter Tests -- 100 points each	400 points	70% 560-639	C
-- Final Exam	250 points	60% 480-559	D
Total	800 points*	Below 60% 0-479	F
*Plus Quizzes (2 points each)

Homework

Due dates: The homework for each week's lessons (weeks 1-16) is due in class on Wednesday of the following week. I will accept late homework up to 10:50 on Friday (2 points off).

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:

A brief summary of the question. Do not copy the text of word problems--summarize them.
Your work (or a statement of why you chose your answer).
The answer.
A check for accuracy (Optional, but important if you really want to learn)

Labs: There are five 10-point labs, which are extended assignments, usually using Maple or Excel. In addition, homework assignments will usually include graphing calculator and/or computer problems.

A sixth lab (listed on the web site) may be done for 10 points extra credit.

Chapter Tests

Preparation: Understand the concepts and be able to solve the types of problems in the Quick Check Exercises in every lesson, the Study Guide on the web site, and in the Chapter Review in the textbook.

Notes: You may use one 3x5 card of notes.

Work: You must clearly show your work to explain/justify your answers.

Calculator: For most questions, you may not use a calculator except to check your work.

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.

Location/Time of Make-ups: Tutorial Office in Communications Building, 8AM to 3PM.

Lowest test: Your lowest test will be replaced by your final exam percentage, if it helps your grade.

Quizzes will be scored at 2 points each. These may add to the points available for the class. There will be no make-ups.

Comprehensive Final Exam

You must take the final exam. If you don't, you will receive a D or F in the course. If you get a C or better on both the final exam and the homework, you will receive a C or better 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 for nonattendance. Examples: (1) absence for a full week of consecutive classes, (2) missing a test and not arranging for a make-up, or (3) missing a total of three or more class periods if you are failing the course.

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, you should also expect to be referred to the Office of Student Personnel (since serious or repeated offenses may result in suspension from the college).

Cell Phones and Pagers are disruptive. Except for public safety (police, fire, paramedic), please make them silent. Communication devices may not be used or on students' desks during any test.

Disabled Students: “If you have a verified physical, medical, psychological, or learning disability or perhaps you feel you may have one of these disabilities which impacts your ability to carry out assigned course work, please contact the Disabled Student Services (DSS) office. DSS staff will review your needs and determine what accommodations are necessary and appropriate. All information and documentation is confidential. DSS is located in the Lesher Student Services Bldg. Room 234, phone 384-6155. In Los Banos, DSS is located in Building A, phone 381-6423.”

Expected Student Outcomes:

A. Perform vector math in two- and three-space, including norm, dot product, and cross product.

B. Apply vector techniques to analyze lines and planes in two- and three-space.

C. Identify and sketch cylinders and surfaces of revolution and quadratic surfaces.

D. Be able to work with cylindrical and spherical coordinate systems.

E. Define and graph vector valued functions: find limits, derivatives and integrals of vector valued functions.

F. Use the velocity, acceleration, tangent and normal vectors; Find tangential and normal components of acceleration.

G. Analyze the curvature of a curve in space.

H. Determine the arc length of a space curve.

I. Define functions of several variables; determine limits, continuity and partial derivatives involving them.

J. Calculate differentials, directional derivatives and gradients and be able to use them in applications.

K. Find tangent planes and normal lines to surfaces.

L. Analyze extrema by using the second partials test and by using Lagrange multipliers.

M. Define and evaluate double and triple integrals (in rectangular, polar, cylindrical, and spherical coordinates) and use them in finding areas, volumes, moments and center of mass and surface area.

N. Understand and work with vector fields, line integrals, independence of path of line integrals, Green's Theorem, the Divergence Theorem and Stokes' Theorem in applied problems.

Specific Homework Assignments:

For Maple help, go to the MAPLE INTRODUCTION section of the web site and see the Calculus and Linear algebra and vector math sections

Do all the quick check exercises, and:

12.1 1b, 5, 7, 9, 11b, 13b, 17, 21, 23b,, 25b, 27ac, 29, 35, 37, 39 Maple, 41, 45, 47b, 49

Maple graph: plot(expression in x, x=-3..3); or, type the expression, right-click, select plot…2D

12.2 1ace, 3ac, 5a, 7ac, 9b, 11ace, 13ad, 15ace, 17bc, 19b, 21bc, 23, 25a, 27, 31, 33b, 35a, 37ac, 39b, 41, 45, 49, 51, 55g, 57

12.3 1ac, 3ac, 5, 7a Maple, 7b, 9bd, 11c, 13, 15b, 19a, 24a, 25a, 27b, 29, 32, 35, 39, 43

For 7a Maple, start by defining the points, and let Maple calculate the vectors. Example: If a:=[1,2,3] and b:=[5,4,3] are points, then the vector from a to b is ab:=b-a; Do this problem two ways: (1) Pythagorean theorem (the lengths are the norms); (2) Show one of the angles is a right angle (find the angle for which the dot product is …)

12.4 1a, 3, 7ac, 9, 11, 13, 15, 17, 21, 23b, 25ac, 27b, 30, 37, 39e, 45 Maple

For 45 Maple, I had to manually delete extraneous absolute value expressions from some of the intermediate Maple output to get later steps to work (for example, abs(x)^2 is the same as x^2)

12.5 Before studying 12.5, review parametric equations (lesson 1.7) and do the quick check exercises from 1.7: (1) Find parametric equations for a circle with radius 2, centered at (3.5)
(2) Find parametric equations for the ellipse x²/a² + y²/b² = 1
(3) The graph of the curve described by the parametric equations x = 4t – 1, y = 3t + 2 is a straight line with slope _____ and y-intercept _____
(4) Suppose that a parametric curve C is given by the parametric equations x = f(t), y = g(t) for 0≤t≤1. Find parametric equations for C that reverse the direction the curve is traced as the parameter increases from 0 to 1.
(5) If f is a one-to-one function, then parametric equations for the curve y = f ^–1(x) are given by x = ____ and y = ____

Then do the quick checks and exercises for 12.5: 1a, 3b, 5b, 7b, 9a, 11, 13, 17, 19ac, 21 for xz-plane, 23, 25, 27, 29, 31, 33, 41, 43, 45, 49, 53, 56

12.6 1, 3, 9, 13ac, 15ac, 17a, 19, 21, 25, 29, 31, 39 Maple, 41, 43, 45, 47, 50ab

Maple: the line of intersection is what you get if you solve the set of simultaneous equations for the set of variables x, y, and z. Maple syntax: solve({eqn1,eqn2},{x,y,z}); try to get Maple to use z=t as the parameter.

12.7 1ace, 3ace, 5ace, 7ac, 9bcf, 13, 17, 21, 25, 29, 33 Maple and Excel, 35, 37ac, 39ac, 41ac, 43, 45, 50, 51
For #33 see lab 4 on the web site for instructions on how to graph the surface. Note: This technique will work as long as z is a function of x and y.

12.8 1ac, 3ac, 5ac, 7ac, 9ac, 11ac, 13a Maple (setup of conversion formulas only), 15, 16, 19, 21, 23, 25, 26, 29, 31, 33, 36, 37, 41, 43, 47, 51
Maple: to solve a set of equations for a set of variables: solve({__,___,___},{r,theta,z});

13.1 3, 7, 9, 15, 19, 21b, 23, 29, 33, 35 Maple, 37, 41, 43, 47b, 49 Maple

Maple: use with(plots); ?tubeplot Copy the first example from the tubeplot help file into your worksheet and modify it; for p, use Pi.

13.2 1, 5a, 6a, 7b, 9, 13, 15, 17 Maple, 21, 22, 25, 26, 29, 33, 37, 45, 49

13.3 3, 7, 11, 15, 17, 21a, 27, 29, 31, 33b, 35b, 37a, 39, 41abc

13.4 1b, 5, 11, 12 (Check with Maple), 13, 15, 19, 22a

13.5 1, 3, 7, 11, 15, 17, 21, 23, 29, 38 Maple, 41, 49, 51

13.6 3, 7, 9, 13, 15abc Gr Calc, 17, 21, 23, 27, 33, 37, 41, 45, 49, 53, 57, 61, 65, 69

13.7 Omit [2, 3, 4, 7, 9, 10]

14.1 1acf, 3b, 5, 7ac, 9a, 11b, 13ace, 15, 17a, 19, 23b, 27 Maple (use plot3d to get both a graph of the surface and a contour plot), 29, 35a, 37, 41, 45, 49, 55, 57, 61

14.2 1, 5, 7, 9, 15 Do by hand, but visualize with a contour plot with Maple, 17, 21, 25, 29, 31, 33, 35, 43

14.3 1adg, 3a, 5b, 7, 9a, 13, 17, 21, 25, 29ace, 31, 33, 37, 41 Maple, 45, 49, 55, 61, 65, 69, 77b, 79b, 81a, 85c, 87, 88b, 95a

14.4 1, 7, 9, 17, 19, 21, 25, 29, 35, 38, 43, 47, 49, 53, 57, 59

14.5 1, 5, 9, 11, 17, 21, 23, 27, 29, 33, 37, 41, 45, 47, 49, 53, 57, 65, 66a

14.6 1, 7, 9, 13, 17, 21, 25, 29, 31, 35, 39 Maple, 43, 45, 49, 55, 57, 61, 63, 64, 65, 69, 71, 77

For Maple, with(VectorCalculus); Gradient(f(x,y,z),[x,y,z]);

14.7 1, 5, 9, 13, 15, 17, 19, 21, 25, 26 Maple, 29

Maple: if the functions are f and g, plot3d({f,g},x = -a..a, y = -b..b, view = -c..c);

14.8 1abc, 3, 7, 11, 15, 21 Maple, 26, 29, 33, 37, 45, 47, 53 (Graphing calculator)

For #45, see the discussion before the problem. You'll need a couple facts: x-bar equals 1/n times the summation of x_i as i goes from 1 to n; and the summation of a constant c, as i goes from 1 to n, is nc. I suggest Cramer's Rule for part c.

14.9 1, 5, 9, 13, 15, 17, 19, 25

15.1 1, 5, 7, 9, 13, 15, 17, 19, 23, 25, 27, 29, 31 (Maple); Sample Maple instructions:

with(student):

Doubleint(sin(sqrt(x^3+y^3)),x=0..1,y=0..Pi/2);

value(%);

evalf(%);

15.2 1, 5, 10, 11, 13, 15b, 17, 21, 25, 27 Maple or graphing calculator, 29, 33, 37, 41, 45, 49, 51, 58 (formula 122), 61

15.3 1, 5, 7, 9, 15, 19, 21, 23, 25, 27, 31, 41, 43 Maple, 45

Maple tip: for θ, type the word theta.

15.4 1ac, 3a, 5b, 7, 13, 17, 23, 25, 29, 33, 37, 41, 45, 51, 53 Maple, 57 Check with Maple

Maple: plot3d([x(u,v), y(u,v), z(u,v)], v=a..b, v=c..d);

15.5 1, 5, 9, 11, 13 Maple, 17, 21a, 25a, 27, 33ab, 37a

Maple: the triple integral command is a logical extension of the double integral procedure; see the assignment for lesson 15.1 above.

15.6 1, 5, 9, 13, 15, 21, 25, 29, 33, 35, 37, 39, 42, 43

15.7 1, 3, 9, 13, 17, 22 Maple, 23, 25, 27, 37, 39, 43

15.8 1, 3, 5, 7, 9, 11, 17, 18, 21, 31, 47a

16.1 1, 3, 7, 9 Maple, 11, 12a, 15, 18, 21, 33, 37, 43, 44

16.2 1, 7, 9b, 10c, 13, 17, 21, 25a, 30, 31, 35, 39, 41, 43, 45

16.3 1, 3, 6, 7, 9, 11, 14, 15, 17, 19, 20, 28, 30, 31

16.4 1, 2, 5, 8, 9, 11, 15 Maple, 19, 23, 27, 29, 34

16.5 1, 5, 9, 15, 17 Maple, 23, 25, 29, 31, 34, 36a Maple

16.6 1acd, 3acd, 5, 7, 11, 14, 17a, 21, 23

16.7 1, 3, 5, 7, 8, 10, 11, 13, 20, 29, 31

16.8 1, 3, 5, 7, 11, 15a, 16a

Return to: Merced College; Don Power Updated 01/21/09 by Don Power