Michael Bowen's VC Course Pages
Math V21B, Fall 2016
Introduction and Announcements
Welcome to Math V21B (Calculus/Analytic Geometry II) at Ventura College. Michael Bowen (email) will be teaching this course during the fall 2016 term.
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 inclass 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, which is only available from the bookstore, not online. 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.
Select any one of the following required texts.

 Author: J. Stewart
 Title: Calculus: Early Transcendentals, Eighth Edition
 ISBN13: 9781285741550
 Comment: This version is available online and may be less expensive than the college bookstore, but with shortcomings:
 Purchase this package if you are willing to use Maple software in the BEACH computer lab only during the hours they are open.

 Author: J. Stewart
 Title: Calculus: Single Variable Calculus Early Transcendentals, Eighth Edition
 ISBN13: 9781305270336

Comment: Probably the least expensive BOUND option (especially if you get the Kindle version), but with more shortcomings:
 Purchase this package if you are willing to use Maple software in the BEACH computer lab only during the hours they are open.
 This version does not include any Math V21C material (which is OK if you are not planning to take Math V21C).
 Even if you do not take Math V21C, you may need to photocopy portions of Chapter 12 from one of the other textbooks listed here.

 Author: J. Stewart
 Title: Calculus: Early Transcendentals, Loose Leaf Eighth Edition
 ISBN13: 9781305272354 (less expensive UNBOUND (loose pages) version; binderready)
 Comment: Probably the least expensive option, but with the same shortcomings as choice #1 above, plus you must provide your own threering binder.

 Author: J. Stewart
 Title: Calculus: Early Transcendentals, Eighth Edition, plus Maple
 ISBN13: 9781305782198 (this is the ISBN stocked at the VC bookstore)
 Comment (applicable to all versions of the text): If you purchased a satisfactory version of Stewart for V21A within the last two semesters, you do not need to purchase a new text.
If you use the Kindle or other digital version, you will want to be able to refer to the information during class, so be sure you own a compatible device (laptop, mobile phone, or ereader) that you are willing and able to bring to class with you every day.
These additional texts are optional; select none, any, or all. (Note that when there is a conflict between the solution given in the textbook and the solution given in the student solutions manuals, the textbook is usually correct.)

 Author: J. Stewart, R. St. Andre
 Title: Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, Eighth Edition
 ISBN13: 9781305279148

 Author: J. Stewart, J.A. Cole, D. Drucker, D. Anderson
 Title: Student Solutions Manual for Stewart's Single Variable Calculus: Early Transcendentals (Chapters 1–11), Eighth Edition
 ISBN13: 9781305272422

 Author: J. Stewart
 Title: Student Solutions Manual for Stewart's Multivariable Calculus (Chapters 10–17), Eighth Edition
 ISBN13: 9781305271821
Holidays
Classes at Ventura College will meet Monday through Thursday each week of the term, excepting only the dates listed below.
 Monday 5 September 2016 (Labor Day)
 Friday 11 November 2016 (Veterans' Day)
 Thursday 24 November–Friday 25 November 2016 (Thanksgiving Holidays)
Please note that Columbus Day and Halloween are not Ventura College holidays.
Homework Club (Office Hours) During Finals Period
 Monday 5 December 2016: 1:00 to 2:00 p.m. in the Tutorial Center
 Tuesday 6 December 2016: 1:00 to 2:00 p.m. in the Tutorial Center
 Wednesday 7 December 2016: 1:00 to 2:00 p.m. in the Tutorial Center
 Wednesday 7 December 2016: 4:30 to 5:30 p.m. in SCI223
 Monday 12 December 2016: 10:15 a.m. to 12:15 p.m. in SCI352 (may move to MCE227 if there is a conflicting final)
 You may also contact me by email; you may expect a response within 24 hours.
Final Examination
Place/date/time: Room SCI352, Tuesday 13 December 2016, 10:15 a.m.
Important Note: This is 45 minutes earlier than our usual class meeting time!
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.
Homework Assignments
 These are listed in 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. These are due at the next exam.
 These are tentative; the instructor may make changes to this list from time to time. Due dates will be announced in class.
 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 should not expect to earn extra credit for completing tentatively assigned exercises that are later modified or removed from this list.
§  Title  Problems and Supplements  E.C. 

—  Syllabus Worksheet (obtain a copy) (NOTE: This assignment is worth 15 points.)  
4.9  Antiderivatives 
(Optional review; do not turn in with homework at the first exam) 1–45 EOO; 5963 ODD; 71 
— 
5.5  The Substitution Rule 
(Optional review; do not turn in with homework at the first exam) 1–45 EOO; 53–73 ODD; 81; 83 
— 
7.1  Integration by Parts  1–41 ODD; 51; 53 (see solution to #21 and solution to #53; for #53, rewrite ${\tan ^n}x$ as $\frac{{{{\sin }^n}x}}{{{{\cos }^n}x}}$, then set $u = {\sin ^{n  1}}x$, figure out what $dv$ has to be, and follow through with the integration by parts)  66 
Optional video supplement: MIT Open Courseware Lecture "Integration by Parts"  
7.2  Trigonometric Integrals  1–49 ODD  65 (see page 461 for the average value formula); 66 (you will see problems similar to 66 in Physics V05); 70 (hint: multiply both sides of the first equation given by $\sin{mx}$, then integrate both sides of the equation from $\pi$ to $\pi$, and finally show that all the terms go to zero except for the one term in which the coefficients of both sine functions are equal) 
7.3  Trigonometric Substitution  5–31 ODD  42 (this is another Physics V05 problem) 
Optional video supplement: MIT Open Courseware Lecture "Inverse Substitution" (note that the lecturer spends the first halfhour or so of the lecture justifying the formulas in the table above Example 1 on page 486 of the textbook so you may wish to start viewing around 33:00, particularly if you would like to review completing the square)  
7.4  Integration of Rational Functions by Partial Fractions 
7–37 ODD; 65 (see solution to #37) 
— 
7.5  Strategy for Integration 
1–81 EOO (all ODDs recommended if time permits) (see solution to #29; solution to #49; solution to #69) 
— 
7.6  Integration Using Tables and Computer Algebra Systems  1–29 EOO (all ODDs through #31 recommended if time permits)  — 
7.7  Approximate Integration 
7–17 ODD You may download the student version of MS Office or OpenOffice if you wish to use a spreadsheet to help you with numerical integration 
— 
7.8  Improper Integrals 
5–41 EOO (see solution to #37) 
62; 68 
Chapter Test 1 (Chapter 7) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) 
(For students with minimal study time) Page 537 (Exercises): 1–11 ODD; 13–25 EOO; 27; 29–49 EOO; 55; 57; 59; 63; 66; 71; 78a 

(For students with additional study time) The above plus some or all of Page 537 (Exercises): 4; 6; 10; 15; 16; 19; 20; 22; 23; 24; 26; 31–47 EOO; 56; 58; 64; 79 Page 537 (Concept check): 1; 2 Page 537 (TrueFalse Quiz): 1–14 ALL Additional problems taken from the unassigned homework exercises from chapter 7 

6.1  Areas Between Curves  1–29 EOO (all odds recommended); 57; 59; also 7.2 #57  56 
6.2  Volumes  1–29 EOO (all odds recommended); 39; 41; 47; 49; 65  70 
6.3  Volumes by Cylindrical Shells  3–19 ODD; 37–47 ODD  — 
Videos (offsite): construction of shells; finding a volume  
6.4  Work  1–25 ODD; 29; 33  22; 24; 30 
6.5  Average Value of a Function  1–9 ODD; 13; 15; 17; 21; also section 7.2 #55 and section 7.3 #33  — 
8.1  Arc Length  1; 9–19 ODD; 25; 27; 33 (the curve is not a function; find a way to integrate a subset of the curve that is a function); 41  — 
8.2  Area of a Surface of Revolution  7–17 ODD; 27; 31(a)  — 
8.3  Applications to Physics and Engineering  5; 9; 13; 21–35 ODD  — 
8.4  Applications to Economics and Biology  (Extra credit only)  19; 21 
8.5  Probability  (No assignment)  — 
Chapter Test 2 (Chapters 6 and 8) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) 
(For students with minimal study time) Page 466 (Exercises): 1–17 ODD; 27; 28; 29(a); 31 Page 537 (Exercises): 73; 75 Page 581 (Exercises): 1; 3; 6; 7–17 ODD 

(For students with additional study time) The above plus some or all of Page 466 (Exercises): 2–16 EVEN; 32(a)(b) Page 466 (Concept check): 2; 4(a); 5; 6 Page 581 (Exercises): 2; 4; 8–16 EVEN Additional problems taken from the unassigned homework exercises from chapter 6 Additional problems taken from the unassigned homework exercises from chapter 8 

9.1  Modeling with Differential Equations  (Extra credit only)  2; 4 
10.1  Curves Defined by Parametric Equations  1–21 ODD  44 
10.2  Calculus with Parametric Curves 
1–7 ODD; 11–19 ODD; 25–35 ODD; 41; 43; 51; 61; 63; 65 (see the Animation of cycloid generation) (see solution to #40) 
73 
10.3  Polar Coordinates  1–11 ODD; 15–45 ODD; 61; 63 (you may use Maple to create the polar plots; see "Polar Plot (No Animation)" in the "Classic Maple" Scripts section below for an example)  68; 70; 72 
10.4  Areas and Lengths in Polar Coordinates  1–33 ODD; 45; 47  — 
10.5  Conic Sections  1–47 ODD  62; 64 
10.6  Conic Sections in Polar Coordinates 
1–15 ODD; 21; 25; 29 In problems 25 and 29, obtain the semimajor axis of each planet's orbit, then predict the period of its orbit (in years) via Kepler's third law. When comparing two planets, if $T_1$ and $T_2$ are the periods, and $a_1$ and $a_2$ are the semimajor axes, then Kepler's law may be written $\frac{{{T_1}^2}}{{{a_1}^3}} = \frac{{{T_2}^2}}{{{a_2}^3}}$. Earth's orbital parameters: period is 1 year, semimajor axis is 149.6 × 10^{6} km or 1.000 AU 
— 
Chapter Test 3 (Chapter 10) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) 
(For students with minimal study time) Page 690 (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 some or all of Page 690 (Exercises): 2–18 EVEN; 28–42 EVEN; 46–52 EVEN Additional problems taken from the unassigned homework exercises from chapter 10 

11.1  Sequences  3–17 ODD; 25–53 EOO; 71–77 ODD  68 
11.2  Series  5–63 ODD (graphs are optional in 9–13)  73 or 74 (choose only one) 
11.3  The Integral Test and Estimates of Sums  3–31 ODD; 35; 37; 39  34abc (all three parts must be completed to earn credit) 
11.4  The Comparison Tests  3–31 ODD  38 
11.5  Alternating Series  3–19 ODD; 23–29 ODD  — 
11.6  Absolute Convergence and the Ratio and Root Tests  3–39 ODD  — 
11.7  Strategy for Testing Series 
1–37 EOO (all odds recommended if time permits for extra practice; many of the final examination questions will be based on this section) (See the Series Convergence/Divergence Flow Chart) 
— 
11.8  Power Series  3–27 ODD  — 
11.9  Representations of Functions as Power Series  3–19 ODD; 25–33 ODD  22; 24 
11.10  Taylor and Maclaurin Series  5–43 ODD; 53–65 ODD  — 
11.11  Applications of Taylor Polynomials  (In this section, all graphs are optional) 3–9 ODD; 13–25 ODD  33; 35ab 
Final Examination (Chapter 11) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) Bring your Chapter 11 homework to the final for up to 20 points credit! (Not extra credit!) Exam starts at 10:30 a.m. on Tuesday 13 December 
(For students with minimal study time) Page 785 (Exercises): 1–37 ODD; 41–55 ODD; 59; 61 You may wish to print the handout Series Convergence/Divergence Flow Chart to help with your review. 

(For students with additional study time) The above plus some or all of Page 785 (Exercises): 2–8 EVEN; 12–34 EVEN; 38–56 EVEN Page 784 (Concept Check): 1; 2; 3; 4; 5; 8; 9; 11; 12 Page 784 (TrueFalse Quiz): 1–22 ALL Additional problems taken from the unassigned homework exercises from chapter 11 
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, printerfriendly; this is the best format for onscreen reading, and if you can read these words, you already have the software!
 DOC and DOCX 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)
Course Information (PDF) 
Course Requirements and Grading, Side 1 (HTML)
Course Requirements and Grading, Side 1 (PDF) 
Course Requirements and Grading, Side 2 (HTML)
Course Requirements and Grading, Side 2 (PDF) 
Tips for Success (HTML)
Tips for Success (PDF) 
Standards of Student Conduct and Classroom Rules (HTML)
Standards of Student Conduct and Classroom Rules (PDF) 
Syllabus Worksheet (DOC)
Syllabus Worksheet (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)
Multiplication Tables (PDF) 
Divisibility Rules (DOC)
Divisibility Rules (PDF)  Sieve of Eratosthenes (PDF) with directions (HTML) (finds prime numbers)
 Powers of Ten Tutorial (HTML) (offsite; requires Java™ Runtime Environment [free download] to be installed and enabled on your computer)

Translating English Phrases into Algebraic Expressions (DOCX)
Translating English Phrases into Algebraic Expressions (PDF)  Multilingual Vocabulary for Mathematics (possibly helpful for students whose first language is not English) (HTML)

Basic Algebra Review (DOC)
Basic Algebra Review (PDF) 
Basic Geometry Review (PPT)
Basic Geometry Review (PDF)  Rectangular Graph Paper:

Quadratic Functions: Questions and Answers (DOC)
Quadratic Functions: Questions and Answers (PDF)  Transformations of Functions (HTML) (may require downloading and installation of free software to view all portions; see the page itself for details)

Essential Trigonometric Identities for Physics & Calculus (DOC)
Essential Trigonometric Identities for Physics & Calculus (PDF)  Polar Graph Paper:
 Math V21B Maple Scripts for 3D Visualization and Plotting Polar Functions (HTML)
 Series Convergence/Divergence Flow Chart (PDF)
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 inclass 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. 