Math V21B Start Page, Fall 2009

Introduction and Announcements

Welcome to the start page for Math V21B (Calculus/Analytic Geometry II) at Ventura College. Michael Bowen (email) will be teaching this course during the fall 2009 semester.

Important note: This web page is not a substitute for attending class; regular attendance is an expectation of this course. Modifications to homework assignments, and other important news announced in class, may not appear on this page for several days. You are still responsible for all assignments and in-class announcements even if they do not appear here! If you wish to verify information on this page, please contact the instructor.

Textbook Information

The ISBN number is provided as a convenience if you wish to purchase this item online. The VC bookstore may stock a different ISBN number; either may be used for the course. If you buy from the bookstore, obtain the least expensive version you can find; do not pay extra for MyMathLab, WebAssign, or other software. Exception: You may wish to purchase the textbook bundled with the student edition of Maple; although we will not use it this semester, your V21C instructor may use it later. If you obtain the book from another source, please be sure to obtain the correct edition, as noted below. Older editions are, of course, much less expensive, but the homework problems are different. This will place you at a disadvantage relative to your classmates on quizzes, which are taken directly out of the homework problems in the current edition.

This text is required:

• Author: J. Stewart
• Title: Calculus: Early Transcendentals, Sixth Edition
• ISBN-10: 0-495-01166-5
• ISBN-13: 978-0-495-01166-8

This additional text is optional:

• Author: J. Stewart
• Title: Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, Sixth Edition
• ISBN-10: 0-495-01239-4
• ISBN-13: 978-0-495-01239-9

Holidays

Classes at Ventura College will meet Monday through Friday each week of the semester, excepting only the dates listed below.

• Monday 7 Sep 2009 (Labor Day)
• Monday 9 Nov 2009 (Veterans Day)
• Thursday 26 Nov through Friday 27 Nov 2009 (Thanksgiving)

Final Examination

Date/time:  Monday 14 December 2009 at 10:00 a.m.

Be sure that your big party to celebrate the end of finals occurs after the appropriate date. Requests for administration of early or late finals that require the instructor to reschedule his work or make a special trip to campus are subject to a deduction of points, regardless of the reason for the request.

Current Assignments

• These are listed in reverse chronological order.
• Note: "EOO" (every other odd) means to do problems
  1, 5, 9, 13, 17, 21, 25, 29, 33, 37, 41, 45, 49, 53, 57, 61, etc.
• Note: Please do "E.C." (extra credit) problems on a separate sheet of paper from the regular assignment.

Due Date	§	Title	Problems	E.C.
23 Nov 2009	12.3	The Dot Product	1–47 ODD	—
	12.4	The Cross Product	1–35 ODD; 37; 41; 45; 46; 47	50
16 Nov 2009	12.1	Three-Dimensional Coordinate Systems	1; 2; 3; 5; 10; 11; 13; 15; 17; 20; 23–31 ODD	—
	12.2	Vectors	1–37 ODD	—
10 Nov 2009	Chapter 10 Exam, Take-Home		PDF download
5 Nov 2009	Chapter 10 Test Optional study problems suggested at right		(For students with minimal study time) Page 670 (Exercises): 1–17 ODD; 21; 23; 25 (first derivative only); 29–41 ODD; 45–51 ODD; 55
			(For students with additional study time) The above plus Page 670 (Exercises): 2–18 EVEN; 28–42 EVEN; 46–52 EVEN Remaining odd-numbered problems from the EOO homework assignments from chapter 10
4 Nov 2009	10.6	Conic Sections in Polar Coordinates	1–15 ODD; 21; 25; 29	—
2 Nov 2009	10.5	Conic Sections	1–47 ODD	—
26 Oct 2009	10.3	Polar Coordinates	7–47 ODD; 57–69 ODD (you may use Maple to create the polar plots; see "Polar Plot (No Animation)" in the "Classic Maple" Scripts section below for an example)	72; 74; 76
	10.4	Areas and Lengths in Polar Coordinates	1–33 ODD; 45; 47	—
19 Oct 2009	9.1	Modeling with Differential Equations	1–6 ALL	—
	10.1	Curves Defined by Parametric Equations	1–21 ODD	—
	10.2	Calculus with Parametric Curves	1–7 ODD; 25–35 ODD; 41; 43; 51; 59; 61	—
8 Oct 2009	Chapter 8 Test Optional study problems suggested at right		(For students with minimal study time) Page 562 (Exercises): 1–13 ODD
			(For students with additional study time) The above plus Page 562 (Exercises): 2–14 EVEN Remaining odd-numbered problems from the EOO homework assignments from chapter 8
7 Oct 2009	8.3	Applications to Physics and Engineering	21–35 ODD; 36	—
5 Oct 2009	8.1	Arc Length	1; 7–17 ODD; 23; 25; 31 (the curve is not a function; find a way to integrate a subset of the curve that is a function); 37	—
	8.2	Area of a Surface of Revolution	5–11 ODD	25
	8.3	Applications to Physics and Engineering	5; 9; 13	—
	8.4	Applications to Economics and Biology	(Extra credit only)	15; 17
25 Sep 2009	Chapter 7 Test Optional study problems suggested at right		(For students with minimal study time) Page 518 (Exercises): 1–49 EOO; 55; 57; 59; 63; 66; 71; 73; 75; 78a
			(For students with additional study time) The above plus Page 518 (Exercises): Remaining problems from 1–49; 56; 58; 64; 79 Page 518 (True-False Quiz): 1–14 ALL Remaining odd-numbered problems from the EOO homework assignments from chapter 7
24 Sep 2009	7.7	Approximate Integration	7–17 ODD	—
	7.8	Improper Integrals	5–39 EOO	62; 68
21 Sep 2009	7.5	Strategy for Integration	1–77 EOO (all ODDs recommended if time permits)	—
	7.6	Integration Using Tables and Computer Algebra Systems	5–29 EOO (all ODDs recommended if time permits)	—
14 Sep 2009	7.4	Integration of Rational Functions by Partial Fractions	9–49 EOO; 63	—
8 Sep 2009	7.1	Integration by Parts	3–37 ODD; 45; 49	—
	7.2	Trigonometric Integrals	1–49 EOO (all ODDs recommended if time permits); 55; 57	64
	7.3	Trigonometric Substitution	5–29 EOO (all ODDs recommended if time permits)	40
2 Sep 2009	Chapter 6 Test Optional study problems suggested at right		(For students with minimal study time) Page 446 (Exercises): 1–17 ODD; 23–27 ODD; 29(a); 30
			(For students with additional study time) The above plus Page 446 (Exercises): 2–16 EVEN; 24; 26; 28 Page 445 (Concept check): 2; 4(a); 5; 6 Even-numbered problems from the ranges of the homework assignments from chapter 6
31 Aug 2009	6.4	Work	1–19 ODD; 27; 29	22; 24; 28
	6.5	Average Value of a Function	1–13 ODD; 19	—
24 Aug 2009	—	Syllabus Worksheet (obtain a copy) (NOTE: This assignment is worth 15 points.)
	6.1	Areas Between Curves	1–29 EOO (all odds recommended); 45; 49; 51	50
	6.2	Volumes	1–29 EOO (all odds recommended); 41; 43; 49; 51; 65	70
	6.3	Volumes by Cylindrical Shells	3–19 ODD; 37–43 ODD	—

Future Assignments

• These are tentative; the instructor may make changes to this list from time to time.
• Students must not rely on printed versions of this list; instead, they should check the live online version periodically for possible updates.
• Students who work ahead and complete one or more assignments in advance are taking a risk that the assignment(s) may change before the due date, in which case the advice in the preceding sentence is particularly applicable.
• Students are responsible for completing the assignments as finalized in the Current Assignments section above, and should not expect to earn extra credit for completing tentatively assigned exercises that are later modified or removed from this list.
• (Assignments to be determined)

Course Handouts and Study Aids

The documents listed below are available for viewing or download. The list below provides links to download free software to read the file formats of the various documents.

• PDF (Adobe® Acrobat Reader™) is the best format to use if you want to print on paper (for example, to replace a lost copy).
• HTML files are not, for the most part, printer-friendly; this is the best format for on-screen reading, and if you can read these words, you already have the software!
• DOC files are in the native Microsoft® Word format; if you do not have Word, use this Word Viewer from the Microsoft web site (this software can display Word files, but cannot modify them).
• PPT files are PowerPoint® presentations; if you do not have PowerPoint, use this PowerPoint Viewer, again from the Microsoft web site.

Course Handouts

• Course Information:  (HTML)  |  (PDF)
• Course Requirements and Grading, Side 1:  (HTML)  |  (PDF)
• Course Requirements and Grading, Side 2:  (HTML)  |  (PDF)
• Tips for Success:  (HTML)  |  (PDF)
• Standards of Student Conduct and Classroom Rules  (HTML)  |  (PDF)
• Syllabus Worksheet:  (DOC)  |  (PDF)
• Instructor's Schedule (PDF; not really a handout; this is a copy of the printed schedule that appears on the instructor's office door)

Study Aids

• Multiplication Tables:  (DOC)  |  (PDF)
• Divisibility Rules:  (DOC)  |  (PDF)
• Sieve of Eratosthenes (PDF) with directions (finds prime numbers) (HTML)
• Powers of Ten Tutorial (off-site; requires Java™ Runtime Environment [free download] to be installed and enabled on your computer):  (HTML)
• Translating English Phrases Into Algebraic Expressions:  (DOC)  |  (PDF)
• Multilingual Vocabulary for Mathematics (possibly helpful for students whose first language is not English):  (HTML)
• Basic Algebra Review:  (DOC)  |  (PDF)
• Basic Geometry Review:  (PPT)  |  (PDF)
• Rectangular Graph Paper (PDF):  5 squares to the inch  |  2.5 squares to the inch
• Transformations of Functions (may require downloading and installation of free software to view all portions; see the page itself for details):  (HTML)
• Essential Trigonometric Identities for Physics & Calculus:  (DOC)  |  (PDF)
• Polar Graph Paper (PDF):  15-degree markings  |  10-degree markings

"Classic Maple" Scripts

• Animation of Surface of Revolution About x-axis, One Function f; right-click the image to control the animation via menu.

  User-adjustable parameters:
   f := function to revolve;
   a := lower limit;
   b := upper limit;
   fracrev := fraction of a complete revolution to display at the end of the animation 
              (try 0.5 for a cross-section, or 0.75 for a cut-away view)
   frames := number of animation frames
          

  with(plots): with(plottools):
  f := t -> t^3/2-2*t^2+2*t+1:
  a := -0.75:
  b := 3:
  fracrev := 1:
  frames := 40:
  start := spacecurve([0,t,f(t)],t=a..b,thickness=3):
  pic := n -> cylinderplot(f(z),theta=0..-n*2*Pi*fracrev/frames,z=a..b):
  display(start,seq(rotate(pic(n),Pi/2,Pi/2,0),n=1..frames),insequence=true,axes=normal,tickmarks=[0,0,0]);
          

• Animation of Surface of Revolution About x-axis, Two Functions f and g.

  User-adjustable parameters:
   f := first function to revolve;
   g := second function to revolve;
   a := lower limit;
   b := upper limit;
   fracrev := fraction of a complete revolution to display at the end of the animation
              (try 0.5 for a cross-section, or 0.75 for a cut-away view)
   frames := number of animation frames
          

  with(plots): with(plottools): 
  f := t -> t^3/2-2*t^2+2*t+1:
  g := t -> 0.15*t^2:
  a := -0.75:
  b := 3:
  fracrev := 0.75:
  frames := 40:
  start := spacecurve({[0,t,f(t)],[0,t,g(t)]},t=a..b,thickness=3):
  pic := n -> cylinderplot({f(z),g(z)},theta=0..-n*2*Pi*fracrev/frames,z=a..b):
  display(start,seq(rotate(pic(n),Pi/2,Pi/2,0),n=1..frames),insequence=true,axes=normal,tickmarks=[0,0,0]);
          

• Parametric Curve and Animation of Parametric Curve Construction.

  User-adjustable parameters:
   x := x(t);
   y := y(t);
   a := lower limit of t;
   b := upper limit of t
          

  with(plots): 
  x := t -> sin(3*t):
  y := t -> sin(2*t):
  a := 0:
  b := 2*Pi:
  plot([x(t),y(t),t=a..b]);
  
  animate([x(c*u),y(c*u),u=a/25..b/25], c=0..25, numpoints=600);
          

• Polar Plot (No Animation).

  User-adjustable parameters:
   r := function of theta to be plotted;
   theta := theta;
   a := lower limit of theta;
   b := upper limit of theta;
   "scaling=constrained" guarantees that the scale is the same on both axes (without this, some graphs will be distorted; try removing it)
          

  with(plots):
  r := theta -> sin(4*theta):
  a := 0:
  b := 1*Pi:
  plot([r(theta),theta,theta=a..b],coords=polar,scaling=constrained);
          

  Code for graphing two functions simultaneously:
   r1 := first function of theta to be plotted;
   r2 := second function of theta to be plotted;
   (other variables as described in the previous example)
          

  with(plots):
  r1 := theta -> 1+cos(theta):
  r2 := theta -> 1-cos(theta):
  a := 0:
  b := 2*Pi:
  plot([r1(theta),r2(theta)],theta=a..b,coords=polar,scaling=constrained);
          

Will You Succeed or Fail in Mathematics?

This checklist is adapted from a handout prepared by math and philosophy instructor Steve Thomassin. It will allow you to compare your approach to a mathematics course to the approaches taken by successful … and unsuccessful … students.

Attribute Type	Predictor of Success	Predictor of Failure
Attitude	Focus on things that are under your control.	Blame things that are out of your control (the text, the instructor, or "the system") for your difficulties.
	Be optimistic. Believe that you can do it.	Be pessimistic. Convince yourself that you will fail.
	Be positive. Find ways to make math interesting and fun.	Be negative. Find ways to make math dull and painful.
	Be open. See the uses, power, patterns, and magic of mathematics.	Be closed. Blind yourself to math's uses and its practical and esthetic value.
	Be practical. Make yourself aware of the doors that passing each math class opens to you.	Be impractical. Ignore the doors that open when you pass a math class.
Class Work	Attend every class. Aim for perfect attendance, even if you already know it all.	Be absent often. Dig a hole so deep that you cannot climb out except by dropping the course.
	Be focused. Concentrate on the math topic at hand.	Be mentally elsewhere. Daydream. Talk. Distract and annoy neighboring students.
	Take good notes. Solve problems along with the instructor.	Avoid participating in the discussion. Just watch the instructor.
	Be inquisitive. Ask questions so that the instructor knows what you would like to learn more about.	Be uninterested. Make the instructor guess what it is that you might be confused about.
Homework	Be regular. Always do at least some homework before the next class, and finish by the due date.	Be sporadic. Do homework only when it easily fits your schedule.
	Invest time. Spend double to triple the amount of in-class time.	Invest little time. Spend less time doing homework than you spend in class.
	Review notes; read text; do all assigned problems (maybe even more), and check the answers.	Ignore notes and text explanations; try a few problems, and don't bother checking to see if they are right.
Getting Help	When needed, take advantage of all opportunities: study groups, tutors, instructor office hours.	Even when lost, never seek assistance.