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Michael Bowen's VC Course Pages

Michael Bowen's VC Course Pages

Math V46, Spring 2019

Introduction and Announcements

Welcome to Math V46 (Applied Calculus) at Ventura College. Michael Bowen (email) will be teaching this course during the spring 2019 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 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. 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
    • ISBN-13: 978-0321869838
    • 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
    • ISBN-13: 978-1323051573 or 978-1323051634
    • 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 e-reader) 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.

Please note that Valentine's Day and St. Patrick's Day are not Ventura College holidays.

Homework Club (Office Hours) During Finals Period

Final Examination

Place/date/time:  Room SCI-352, Monday 13 May 2018, 2:45 p.m.

Important Note: This is 15 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.

Students with Disabilities

Students with disabilities who may need accommodations in this class are encouraged to contact the Educational Assistance Center (EAC) as soon as possible to ensure that such accommodations are implemented in a timely manner. Authorization, based on verification of disability, is required before any accommodation can be provided. You may contact the EAC by telephone at (805) 289‑6300, or visit the EAC office in the Administration (ADM) Building on campus.

Basic Needs

Any student who faces challenges securing food, housing, health care (including mental health), child care, or transportation, and believes this may affect his/her performance in this or other classes is urged to contact the Basic Needs Specialist for support. If you are comfortable in doing so, please also notify the professors of your courses. This may enable them to provide additional resources and/or make accommodations to help you succeed. The Basic Needs Department may be reached at (805) 289‑6583 or via email; more information is available online. Among the services provided are assistance in applying for CalFresh (food stamps) and access to an on-campus food pantry, assistance for foster and homeless youth, referrals to community resources, counseling, and tutoring.

Topics: Top of Page | Homework Assignments | Final Exam Info | Students with Disabilities | Course Handouts and Study Aids

Homework Assignments

Overview: This table lists homework assignments and announces examinations. It contains four columns. First row: Column headers. Second and subsequent rows: The homework due for each section covered in the course. Details: The first row is the table header, with column headings describing the data listed in the main body of the table. The second and subsequent rows contain section numbers and titles, assigned problem numbers, and extra credit problems, if any. Column one of these rows contains a section number. Column two of these rows contains the corresponding section title. Column three lists the problem numbers for each section. Column four lists extra credit problems, if any.
§ Title Problems and Supplements E.C.
Handout (required) Obtain a PDF or DOC (Word) version of the Syllabus Worksheet, answer all 15 questions, and return it to the instructor by the second week of class.
(NOTE: This assignment is worth 15 points toward your final score in the class.)
A.3, p. 531
(optional)		 Factoring Polynomials 1–55 ODD —
A.4, p. 536
(optional)		 Operations on Rational Expressions 1–33 ODD; 43; 45
See solutions for selected problems 		—
A.6, p. 546
(optional)		 Rational Exponents and Radicals 13–59 ODD; 83; 85; 87
See solutions for selected problems 		—
A.7, p. 546
(optional)		 Quadratic Equations (Factor and/or use the quadratic formula) 13–37 ODD; 43; 45; 47 —
B.3, p. 572
(required)		 Binomial Theorem 1–31 ODD —
1.1 (required) 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)

Mon. 4 Feb.

Recommended study-guide problems

(These are sample exam-like 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 even-numbered problems not listed above from 22–48
Page 536: Remaining even-numbered problems not listed above from 8–34 and 46
Page 546: Remaining even-numbered problems not listed above from 14–58; 86; and 88
Page 555: Remaining even-numbered problems not listed above from 14–38
Page 572: Remaining even-numbered 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
For #91 and #95, create $x$-$y$ tables, and select $x$ values from 1 to 30 for #91 and from 100 to 6000 for #95; graph the $x$-$y$ tables, but note that the resulting graphs will be piecewise, consisting of several separate line segments that may or may not connect with each other; be sure to select $x$ values just below and just above where the price or discount change 		88
2.2 Infinite Limits and Limits at 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
(If you get stuck, email me and I'll post a link to the solution here) 		—
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. 		—
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 ("break-even" 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 $dx = x_{2}-x_{1}=1$. 		—
Chapter Test 2

(Sections 2.1 through 2.7)

Date TBA

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework) 		(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; 87; 91; 95; 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; 88; 90
Additional problems taken from the unassigned homework exercises from chapter 2
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 Optional: 1–8 ALL
Required: 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; 97

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 Optional: 9–15 ODD
Required: 17–65 EOO; 91; 95(A); 97; 98 ("Rate of change" means the derivative of $T$; answers are $-9.7$ degrees per hour and $-1.7$ degrees per hour)		 —
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; 56
3.6 Related Rates Optional: 1; 3; 4
Required: 9–25 ODD; 33		 —
3.7 Elasticity of Demand (Optional extra credit only; see next column) 52; 82
Chapter Test 3

(Sections 3.1 through 3.6)

(Postponed to include Ch. 4)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework) 		(For students with minimal study time)
Page 235 (Review Exercises): 5; 7; 9; 10; 12; 15–23 ODD; 29; 35; 37; 41; 45; 48; 50
(For students with additional study time)
The above plus
Page 235 (Review Exercises): 6; 8; 14–24 EVEN; 34; 36; 40; 42; 43; 44; 51
Additional problems taken from the unassigned homework exercises from chapter 3
4.1 First Derivative and Graphs 33–45 ODD; 85; 87; 89; 95; 97

Notes:
  1. A "partition number" is a value of $x$ for which either $f'\left( x \right) = 0$ or $f'\left( x \right)$ does not exist. A "critical number" is any partition number which is also in the domain of $f\left( x \right)$. So every critical number is a partition number, but not every partition number is a critical number. For example, consider $f\left( x \right) = x - 2\ln{x}$. The domain is $\left( {0,\;\infty } \right)$ because the natural logarithm is not defined for $x \leq 0$. The derivative is $f'\left( x \right) = \frac{x-2}{x}$, so the partition numbers are $x=0$ (because $f'\left( x \right)$ is undefined there) and $x=2$ (because $f'\left( x \right) = 0$ there). But only $x=2$ is a critical number, because $x=0$ is not an element of the domain of $f\left( x \right)$.
  2. Every extremum (local minimum or maximum) of a function occurs at a critical number, but not every critical number is an extremum. There must be a sign change in $f'\left( x \right)$ at the critical number for that location to be an extremum. For example, $f\left( x \right) = x^3$ has a critical number at $x=0$, but it is not an extremum because $f'\left( x \right) = 3x^2$ is positive on both the left and right sides of $x=0$.
  3. For the word problems, note that the increasing/decreasing intervals do not extend to infinity. Only evaluate increasing/decreasing behavior on the given domains. In #95, for example, only evaluate increasing/decreasing behavior on $\left( {0,\;150 } \right)$.
 —
4.2 Second Derivative and Graphs 9; 13; 15; 33; 37; 49; 53; 57; 61; 65; 69; 87; 91; 93 (for problems 91 and 93 ONLY, graphs are optional) —
4.3 L'Hôpital's Rule 25–53 EOO 58
4.4 Curve-Sketching Techniques (No assignment) —
4.5 Absolute Maxima and Minima (No assignment) —
4.6 Optimization 9–49 EOO (in problem 49, note that you are trying to maximize $N'\left( t \right)$, not $N\left( t \right)$) —
Chapter Test 4

(Ch. 3 and sections 4.1, 4.2, 4.3, and 4.6)

Mon. 29 Apr.

 (For students with minimal study time)
(No recommendation)
(For students with additional study time)
The above plus
(No recommendation)
Additional problems taken from the unassigned homework exercises from chapter 4
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); 87 —
6.1 Area Between Curves 43–57 ODD; 87; 89; 97 —
6.2 Applications in Business and Economics (Optional; will not be on the final examination) 25; 27; 41 (see Example 2 on page 394 of the textbook) —
6.3 Integration by Parts 9; 11; 15–27 ODD; 37–57 ODD; 63; 67 (review section 6.2)
(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)
(For income-stream problems, use the income-stream integration formula from section 6.2, even though we didn't cover that section) 		38; 46; 56
6.4 Other Integration Methods 5–27 ODD; 31; 35; 37–61 EOO (all ODDs recommended if time permits); 75; 87; 89 78 (use your choice of a table or Simpson's rule)
Final Examination

(Chapters  5 and 6)

Recommended study-guide problems

(These are sample exam-like problems for practice purposes; do not turn in with your homework)

Bring your Chapter 5/6 homework to the final for up to 20 points credit! (Not extra credit!)

Exam starts at 2:45 p.m. on Monday 13 May 		(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; the textbook authors messed up and placed one or two Chapter 6 questions in the Chapter 5 review!)

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

Topics: Top of Page | Homework Assignments | Final Exam Info | Students with Disabilities | Course Handouts and Study Aids

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.

Course Handouts

Study Aids

Topics: Top of Page | Homework Assignments | Final Exam Info | Students with Disabilities | Course Handouts and Study Aids

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.

Overview: This table lists typical attributes of successful and unsuccessful mathematics students. It contains three columns. First row: Column headers. Second and subsequent rows: Student attributes. Details: The first row is the table header, with column headings describing the data listed in the main body of the table. The second and subsequent rows describe specific attributes that contribute to success or failure. Column one of these rows specifies whether the attribute is related to attitude, class work, homework, or getting help. Column two of these rows contains attributes of successful students. Column three of these rows contains attributes of 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.
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Michael Bowen's VC Course Pages: Math V46, Spring 2019

Last modified: Sunday 12 May 2019 19:48:13
Created by Michael Bowen (Professor of Mathematics)
Department of Mathematics, Ventura College, California, USA
Ventura College is an independent college within the Ventura County Community College District.
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