Michael Bowen's VC Course Pages
Math V46, Spring 2017
Introduction and Announcements
Welcome to Math V46 (Applied Calculus) at Ventura College. Michael Bowen (email) will be teaching this course during the spring 2017 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. 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: R. Barnett
 Title: Calculus for Business, Economics, Life Sciences, and Social Sciences, Thirteenth Edition
 ISBN13: 9780321869838
 Comment: Use this ISBN if you are purchasing online; this is likely to be the least expensive, provided that you do not wish to use MyMathLab for independent study.

 Author: R. Barnett
 Title: Calculus for Business, Economics, Life Sciences, and Social Sciences (Custom Edition for Ventura College), Thirteenth Edition
 ISBN13: 9781323051573
 Comment: This is one of the packages available in the VC bookstore; as we will not be using MyMathLab, you do not need the MyMathLab bundle unless you want to use it on your own for extra study.
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.
Holidays
Classes at Ventura College will meet Monday through Thursday each week of the term, excepting only the dates listed below.
 Monday 16 January 2017 (Martin Luther King Jr.'s Birthday)
 Friday 17 February–Monday 20 February 2017 (Presidents' Day)
 Monday 13 March–Friday 17 March 2017 (Spring Break)
 Thursday 20 April–Friday 21 April 2017 (Faculty Inservice Days)
Homework Club (Office Hours) During Finals Period
 Monday 8 May 2017: 4:00 to 5:00 p.m. in the Tutorial Center
 Tuesday 9 May 2017: 1:00 to 5:00 p.m. in the Tutorial Center
 Wednesday 10 May 2017: 1:00 to 3:30 p.m. in the Tutorial Center
 Friday 12 May 2017: 9:30 to 10:45 a.m. in SCI350
 Friday 12 May 2017: 1:15 to 3:00 p.m. in SCI350
 Saturday 13 May 2017: 9:30 a.m. to 12:45 p.m. in the Tutorial Center
 Monday 15 May 2015: 1:00 p.m. to 4:30 p.m. in the Tutorial Center
 You may also contact me by email; you may expect a response within 24 hours.
Final Examination
Place/date/time: Room SCI351, Monday 15 May 2017, 5:00 p.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.
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  E.C. 

—  Syllabus Worksheet (obtain a copy) (NOTE: This assignment is worth 15 points.)  
A.3 (p. 531) 
Factoring Polynomials  1–55 ODD  — 
A.4 (p. 536) 
Operations on Rational Expressions 
1–33 ODD; 43; 45 See solutions for selected problems 
— 
A.6 (p. 546) 
Rational Exponents and Radicals 
13–59 ODD; 83; 85; 87 See solutions for selected problems 
— 
A.7 (p. 546) 
Quadratic Equations  (Factor and/or use the quadratic formula) 13–37 ODD; 43; 45; 47  — 
B.3 (p. 572) 
Binomial Theorem  1–31 ODD  — 
1.1  Functions  15–20 ALL; 21–27 ODD; 29–35 ODD (graph paper is available here); 61–77 ODD; 87; 89; 91  — 
Chapter Test 1 (Sections A.3, A.4, A.6, A.7, B.3, and 1.1) 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 531: 20; 26; 32; 38; 44; 50 Page 536: 6; 12; 18; 24; 30; 44 Page 546: 18; 24; 30; 36; 42; 48; 54; 60; 84 Page 555: 18; 24; 30; 36; 48 Page 572: 6; 12; 18; 24; 30 Page 87: 4; 5; 6; 30; 32 

(For students with additional study time) The above plus some or all of the following Page 531: Remaining evennumbered problems not listed above from 22–48 Page 536: Remaining evennumbered problems not listed above from 8–34 and 46 Page 546: Remaining evennumbered problems not listed above from 14–58; 86; and 88 Page 555: Remaining evennumbered problems not listed above from 14–38 Page 572: Remaining evennumbered problems not listed above from 2–32 Section 1.1 22–28 EVEN; 30–36 EVEN; 62–78 EVEN; 86; 88; 90 

2.1  Introduction to Limits  9–45 ODD; 51–63 EOO; 81; 83; 85; 91; 95  88 
2.2  Infinite Limits and Limits and Infinity 
9 (behavior of a limit at a horizontal asymptote); 13 (behavior of a limit at a vertical asymptote); 15 (behavior of a limit at a jump discontinuity); 17–23 ODD (if (A) and (B) agree, then (C) is the same; if (A) and (B) disagree or one is DNE, then (C) is DNE); 33; 35; 43–49 ODD 
— 
2.3  Continuity  15–53 ODD  — 
2.4  The Derivative 
19–41 ODD; 71; 73; 75; 79(A)(B); 81; 83 Solutions to selected homework problems are posted on Canvas. 
— 
2.5  Basic Differentiation Properties 
(See problems 1 through 8 for hints on how to rewrite fractions and radicals; however, these are not assigned) 9–59 ODD; 95; 97 If you are not sure how to do problems 57 and 59, I have worked a similar example (problem 60). Link to solution for problem 60. 
— 
Chapter 2 Test (sections 2.1 through 2.5 only) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) Exam date is Wed. 8 March 
(For students with minimal study time) Page 175 (Review Exercises): 4–10 ALL; 25; 26 (use difference quotient); 27 (use any method); 28 (use difference quotient); 29–31 ODD (use the properties from section 2.5); 39; 40; 43–49 ODD (use the properties from section 2.5 to obtain needed derivatives); 55–67 ODD; 73–81 ODD; 91; 97 

(For students with additional study time) The above plus Page 175 (Review Exercises): 11–24 ALL; 30 (use any method); 44–48 EVEN (use the properties from section 2.5 to obtain needed derivatives); 56–68 EVEN; 72–82 EVEN Unassigned problems from the ranges of the homework assignments from sections 2.1 through 2.5 

2.6  Differentials 
9–19 ODD; 27–31 ODD; 33(A)(C); 35(A)(C); 45; 47; 51; 54 (answers to #54: 2.6 and 1.3) There are two ways to find the exact change $\Delta y$: either $\Delta y = f\left( {{x_2}} \right)  f\left( {{x_1}} \right)$ or $\Delta y = f\left( {x + \Delta x} \right)  f\left( x \right)$; use whichever form best matches the information given in the problem. The estimated change is given by $dy = f'\left(x\right)dx$; if $dx$ is not given, calculate it from $dx = x_{2}x_{1}$. 
— 
2.7  Marginal Analysis in Business and Economics 
9–25 EOO (all odds recommended if time permits); 33; 37; 49 ("breakeven" means that profit is zero, or $P\left(x\right) = 0$) These are really just more differential problems, so the formulas from section 2.6 still work; however, when "marginal" is used, the implied value of the run is $dx = 1$. So if a problem asks "what is the cost of the 26th widget", then assume that $x_{1} = 25$, $x_{2} = 26$, and $dx = x_{2}x_{1}=1$. 
— 
3.1  The Constant $e$ and Continuous Compound Interest  13–21 ODD; 25–29 ODD; 33; 35; 41; 45; 47  42 
3.2  Derivatives of Exponential and Logarithmic Functions  9–33 ODD; 41–53 EOO; 63; 65  — 
3.3  Derivatives of Products and Quotients 
9–33 ODD; 49–65 EOO; 77–89 EOO; 93 Typo warning: Problem 81 should read $\frac{{6\left( {\sqrt[3]{x}} \right)}}{{{x^2}  3}}$ not $\frac{{\left( {{6^3}} \right)\sqrt x }}{{{x^2}  3}}$ 
— 
3.4  The Chain Rule  17–65 EOO; 95(A); 98  — 
3.5  Implicit Differentiation  13–29 ODD; 35; 37; 51; 53 (for the last two problems, treat $p$ as if it were the dependent variable $y$)  48 
3.6  Related Rates  9–25 ODD  — 
3.7  Elasticity of Demand  (No assignment)  — 
4.1  First Derivative and Graphs 
33–45 ODD; 85; 87; 89; 95; 97 Notes:

— 
4.2  Second Derivative and Graphs  33; 37; 49; 53; 57; 61; 65; 69; 87; 91; 93 (graphs are optional)  — 
4.3  L'Hopital's Rule  (No assignment)  — 
4.4  CurveSketching Techniques  (No assignment)  — 
4.5  Absolute Maxima and Minima  (No assignment)  — 
4.6  Optimization  9–45 EOO  — 
Chapter 3–4 Test Download PDF copy using link at right 
Chapter 3–4 takehome exam; due Monday 17 April 2017 at 5:00 p.m. PDT  
5.1  Antiderivatives and Indefinite Integrals  9–23 ODD; 43–61 ODD; 65; 67; 69; 81; 85  93 
5.2  Integration by Substitution  9–41 EOO; 43; 59–69 ODD; 77; 79; 81(A)  88 
5.3  Differential Equations; Growth and Decay  (No assignment except for optional extra credit problems ===>)  26; 28 
5.4  The Definite Integral  31–53 ODD  — 
5.5  The Fundamental Theorem of Calculus  13–45 EOO (all ODDs recommended if time permits); 47; 49(A)–61(A) EOO (the graphs in part (B) are very optional); 71; 75; 77(A)(B)  — 
6.1  Area Between Curves  43–57 ODD; 87; 89; 97  — 
6.2  Applications in Business and Economics  25; 27; 41  — 
6.3  Integration by Parts 
9; 11; 15–27 ODD; 37–57 ODD; 63; 67 (review 6.2); 69 (review 6.1) (Warning: Some of these problems may be solved by the method of $u$substitution, as in section 5.2; you may need to experiment with both of these methods. For the problems involving integration by parts, multiple applications of the method may be necessary for #37 and some of the others) 
38; 46; 56 
6.4  Other Integration Methods  5–27 ODD; 31; 35; 37–61 EOO (all ODDs recommended if time permits)  78 (use your choice of a table or Simpson's rule) 
Final Examination (Chapters 5 and 6) Recommended studyguide problems (These are sample examlike problems for practice purposes; do not turn in with your homework) Exam date is Mon. 15 May or makeup on Wed. 17 May Bring your Chapter 5/6 homework to the final for up to 20 points credit. (Not extra credit!) Exam starts at 5:00 p.m. 
(For students with minimal study time) Page 377 (Review Exercises): 1–9 ODD; 15; 17 (use Simpson's rule with 2 rectangles instead of a right sum, and skip "calculate an error bound"; you should get close to the book's answer, but not quite the same); 18; 20; 39–57 ODD (these may require any combination of $u$substitution, integration by parts, or integration by table) Page 422 (Review Exercises): 5–15 ODD; 25; 27; 29; 33–41 ODD; 44; 46; 48; 49; 54 (hints: integrals may be evaluated using $u$substitution, integration by parts, or tables; try the methods in the order listed here) Page 329: (optional review of 5.1, if you have forgotten how to do "tricky" integrals without using $u$substitution) 44–62 EVEN (email me if you need to check a solution, although you should be able to check 44–54 yourself by differentiating your solution) 

(For students with additional study time) The above plus Page 377 (Review Exercises): 2–10 EVEN; 14; 16; 25–31 ODD; 38–56 EVEN (for #56, you can tell by inspection that the answer is zero, but why?); 64 (ignore the book's instructions and use Simpson's rule with 10 intervals; your answer may differ slightly from the back of the book) Page 422 (Review Exercises): 4–16 EVEN; 24; 26; 28; 34–42 EVEN; 47(B); 52 ("fourth hour" means from $t=3$ to $t=4$); 57 (find the probability for $t=0$ to $t=2$, then subtract this result from the total probability for all possible times, which is 1) Additional problems taken from the unassigned homework exercises 
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)
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. 