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Michael Bowen's VC Course Pages

Michael Bowen's VC Course Pages

Math V21A, Fall 2017

Introduction and Announcements

Welcome to Math V21A (Calculus/Analytic Geometry I) at Ventura College. Michael Bowen (email) will be teaching this course during the fall 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 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 V21B or V21C instructors 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.

Select any one of the following required texts.

    • Author: J. Stewart
    • Title: Calculus: Early Transcendentals, Eighth Edition
    • ISBN-13: 978-1285741550
    • 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, or if you are not taking calculus beyond MATH V21A.
    • Author: J. Stewart
    • Title: Calculus: Single Variable Calculus Early Transcendentals, Eighth Edition
    • ISBN-13: 978-1305270336
    • 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, or if you are not taking calculus beyond MATH V21A.
      • This version does not include any Math V21C material (which is OK if you are not planning to take Math V21C).
    • Author: J. Stewart
    • Title: Calculus: Early Transcendentals, Loose Leaf Eighth Edition
    • ISBN-13: 978-1305272354 (less expensive UNBOUND (loose pages) version; binder-ready)
    • Comment: Probably the least expensive option, but with the same shortcomings as choice #1 above, plus you must provide your own three-ring binder.
    • Author: J. Stewart
    • Title: Calculus: Early Transcendentals, Eighth Edition, plus Maple
    • ISBN-13: 978-1305782198 (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 e-reader) 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
    • ISBN-13: 978-1305279148
    • 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
    • ISBN-13: 978-1305272422
    • Author: J. Stewart
    • Title: Student Solutions Manual for Stewart's Multivariable Calculus (Chapters 10–17), Eighth Edition
    • ISBN-13: 978-1305271821

Holidays

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

Please note that Columbus Day and Halloween are not Ventura College holidays.

Final Examination

Place/date/time:  Room SCI-107, Wednesday 13 December 2017, 12:30 p.m.

Important Note: This is 30 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

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) 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.)
Appendix A (page A9; the Appendices begin immediately following page 1182) Numbers, Inequalities, and Absolute Values 1–12 ALL; 13–37 ODD; 43–55 ODD
Appendix C (page A23) Graphs of Second-Degree Equations 1–9 ODD (for problems 5, 7, and 9, you will need to complete the square in both $x$ and $y$)
Appendix D (page A32) Trigonometry 13; 15; 29; 31; 33; 65–71 ODD
Appendix E (page A38) Sigma Notation 1–33 EOO
(Handout) Factoring and the Binomial Theorem (obtain a copy) Problems 1–9 ALL on reverse side of handout Problem 10 on reverse side of handout
1.1 Four Ways to Represent a Function 1–4 ALL; 25; 27–30 ALL; 51; 52; 73; 75; 77
1.2 Mathematical Models: A Catalog of Essential Functions 3; 4; 5; 9; 11; 15; 17; 19 22
1.3 New Functions from Old Functions 3 [$f(x)$ is in blue]; 5; 7; 9–21 EOO (do all odds if time permits); 31–45 ODD; 51 58
1.4 Exponential Functions 1–4 ALL; 11; 13; 15; 31abc 31d
1.5 Inverse Functions and Logarithms 3–25 ODD; 35–38 ALL (parts (a) and (b)); 39; 40; 41; 51–54 ALL (parts (a) and (b)); 63–68 ALL (parts (a) and (b))
Chapter Test 1

(Chapter 1, appendices, and binomial theorem handout)

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 69 (Exercises): 1–3 ALL; 5–19 ALL; 22–27 ALL
Find the first three terms of the binomial expansion of ${(a + b)^{ - 5/2}}$.
Use the first three terms of the binomial expansion of ${(6.0 - 0.3)^5}$ to estimate the value of ${5.7^5}$, and compare with the exact answer obtained using your calculator.
(For students with additional study time) The above plus some or all of
Page 68 (Concept check): 1; 3; 4; 6; 10–13 ALL
Page 69 (True-false quiz): 1–14 ALL
Additional problems taken from the unassigned homework exercises from chapter 1
2.1 The Tangent and Velocity Problems 5, 6, 8
Note: "Average velocity" is really just "average rate of change of $f(t)$," where $s$ or $y$ is the function $f(t)$, and $t$ is the independent variable
2.2 The Limit of a Function 3–11 ODD; 19–27; ODD (for #23 through #27, ignore the textbook's instructions and use the technique from #19 and #21 instead, except you will have select your own sample values of $x$); 31–43 ODD; 49 54
2.3 Calculating Limits Using the Limit Laws 1–31 ODD; 37–49 ODD (use Squeeze Theorem for #37 and #39) 54
2.4 The Precise Definition of a Limit 15–31 ODD; 41; 42 (the last two problems are infinite limits; use the appropriate method of proof)
2.5 Continuity 13–31 ODD; 51; 53; 55 (use Intermediate Value Theorem for the last three problems)
2.6 Limits at Infinity; Horizontal Asymptotes 15–39 ODD; 75; 77 Write down how Hotel Infinity accommodated all the passengers from Infinity Bus Lines; specifically, how the room assignments were rearranged
2.7 Derivatives and Rates of Change 13–39 ODD (for the last two problems, consider both variations of the difference quotient; a different variation works for each problem)
2.8 The Derivative as a Function 21–31 ODD; 41–44 ALL 60
Chapter Test 2

(Sections 2.1–2.8)

Recommended study-guide problems

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

(Last day to turn in Hotel Infinity for extra credit)
(For students with minimal study time)
Page 166 (Exercises): 1–19 ODD; 25–29 ALL; 33–37 ALL; 39ab; 45ab
(For students with additional study time) The above plus some or all of
Page 166 (Exercises): 4–20 EVEN; 26; 28
Page 165 (Concept check): 2; 4; 5–16 ALL
Page 166 (True-false quiz): 1–22 ALL
Additional problems taken from the unassigned homework exercises from chapter 2
3.1 Derivatives of Polynomials and Exponential Functions 3–35 ODD; 45; 46; 49–59 ODD; 63; 65
3.2 The Product and Quotient Rules 1–33 ODD; 41; 45; 47; 51
3.3 Derivatives of Trigonometric Functions 1–23 ODD; 33; 35; 39–49 ODD
3.4 The Chain Rule 7; 9–45 EOO; 47–53 ODD; 59; 75; 79 78; 94
3.5 Implicit Differentiation 5–19 ODD; 25–31 ODD; 49–59 ODD

Check out this online graphing calculator if you would like to see what the graphs of any of the equations look like; just type in the equations exactly as they appear in the textbook (except change $f(x)$ to $y$)
3.6 Derivatives of Logarithmic Functions 3–25 ODD; 31; 33; 39–51 ODD
Chapter Test 3

(Sections 3.1–3.6)

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 267 (Exercises): 1–41 ODD; 49; 51; 53; 57–61 ALL; 63ab; 65; 67; 83
(For students with additional study time) The above plus some or all of
Page 267 (Exercises): 2–46 EVEN; 52; 54; 68; 87; 88
Page 266 (Concept check): 2(a) through 2(n)
Page 266 (True-false quiz): 1–15 ALL
Additional problems taken from the unassigned homework exercises from sections 3.1–3.6
3.7 Rates of Change in the Natural and Social Sciences 1; 3; 7–15 ODD; 25; 31; 37
3.8 Exponential Growth and Decay (No assignment) 22
3.9 Related Rates 1–45 EOO (for #45, try the law of cosines as your operating formula)
3.10 Linear Approximations and Differentials 1; 3; 11ab; 13ab; 15–27 ODD; 33; 35
(#33: for a cube, the volume is $V = s^3$ and the surface area is $A = 6s^2$)
(#35: for a sphere, the volume is $V = \frac{4}{3}\pi r^3$ and the surface area is $A = 4\pi r^2$)
3.11 Hyperbolic Functions 7–21 ODD; 29–51 ODD
Chapter Test 4

(Sections 3.7–3.11)

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 267 (Exercises): 43; 45; 47; 89abc; 92–94 ALL; 96; 97; 99; 101; 102a; 103a; if you need more practice with chain rule, then also try 1–37 EOO
(For students with additional study time) The above plus some or all of
Page 267 (Exercises): 48; 50; 84; 90; 96; 98; 102ac; 104
Page 264 (Concept check): 2(o) through 2(t); 5
Additional problems taken from the unassigned homework exercises from sections 3.7–3.11
4.1 Maximum and Minimum Values 17–41 EOO; 49–61 EOO
4.2 Mean Value Theorem (No assignment) 34
4.3 How Derivatives Affect the Shape of a Graph 9–21 ODD; 34; 37–53 ODD
4.4 Indeterminate Forms and L'Hospital's Rule 9–65 EOO
4.5 Summary of Curve Sketching 1–49 EOO
4.6 Graphing with Calculus and Calculators (No assignment)
4.7 Optimization Problems 3; 5; 7; 9–37 EOO; 61; 65 71; 72
4.9 Antiderivatives 1–45 EOO; 59–63 ODD; 71
5.1 Areas and Distances 1; 3; 5; 17
5.2 The Definite Integral 1; 3; 5; 17; 18; 19; 20; 27; 33; 35; 37; 39
To complete the last 3 problems, sketch the graph of each function, then use geometry (triangles, circles, and/or rectangles) to find the areas. Geometrical formulas, if needed, are found on the inside front cover of the textbook. Don't forget that, in the context of integration, any areas lying below the $x$-axis provide a negative contribution to the integral.
5.3 The Fundamental Theorem of Calculus 7; 9; 11; 19–43 ODD
5.4 Indefinite Integrals and the Net Change Theorem 5–45 EOO (all odds in this range are recommended for finals prep if time permits); 59; 61; 67; 71
5.5 The Substitution Rule 1–45 EOO; 53–73 ODD; 81; 83
4.8 Newton's Method 11–21 ODD 20
Final Examination

(Chapters 4 & 5)

Recommended study-guide problems

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

Bring your Chapter 4/5 homework for up to 20 points credit! (Not extra credit!)

Exam starts at 12:30 p.m. on Wednesday 13 December
(For students with minimal study time)
Page 359 (Exercises): 1–13 ODD; 18; 19–33 ODD; 45; 47; 53–73 ODD; 79a; 79c
Page 422 (Exercises): 1–37 ODD; 43 (graphing calculator helpful but not necessary); 45; 47; 57; 59; 69 (use the Substitution Rule and set u = f(x))
(For students with additional study time) The above plus some or all of
Page 359 (Exercises): 2–14 EVEN; 20–34 EVEN; 46–58 EVEN; 62–74 EVEN;
Page 358 (Concept check): 1–7 ALL; 10;
Page 358 (True-false quiz): 1–21 ALL;
Page 422 (Exercises): 10–38 EVEN; 44; 46; 48;
Page 421 (Concept check): 5b; 6;
Page 421 (True-false quiz): 1–18 ALL; and
Additional problems taken from the unassigned homework exercises from chapters 4 & 5

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

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.

http://academic.venturacollege.edu/mbowen/courses/2017aki/m21a.shtml

Michael Bowen's VC Course Pages: Math V21A, Fall 2017

Last modified: Wednesday 15 November 2017 16:06:45
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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