Michael Bowen's VC Course Pages

# Math V23, Spring 2018

## Introduction and Announcements

Welcome to Math V23 (Introduction to Differential Equations) at Ventura College. Michael Bowen (email) will be teaching this course during the spring 2018 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, 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: D.G. Zill
• Title: A First Course in Differential Equations with Modeling Applications, Eleventh Edition plus WebAssign Access
• ISBN-13: 978-1337761000 (this is the ISBN stocked at the VC bookstore; it is also available online)
• Author: D.G. Zill
• Title: A First Course in Differential Equations with Modeling Applications, Eleventh Edition
• ISBN-13: 978-1305965720 (hardcover; does not come with WebAssign, but may be available used online for a lower price)
• Author: D.G. Zill
• Title: A First Course in Differential Equations with Modeling Applications, Loose Leaf Eleventh Edition plus WebAssign Access
• ISBN-13: 978-1337604994 (less expensive UNBOUND (loose pages) version; binder-ready)
• Author: D.G. Zill
• Title: A First Course in Differential Equations with Modeling Applications, Eleventh Edition (Kindle)
• ASIN: B01MRYFB8T (less expensive ELECTRONIC version; does not come with WebAssign)

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.

This additional text is optional. (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: D.G. Zill
• Title: Student Solutions Manual for Zill's A First Course in Differential Equations with Modeling Applications, Eleventh Edition
• ISBN-13: 978-1305965737

## Holidays

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

• Monday 15 January 2018 (Martin Luther King, Jr., Day)
• Friday 16 February–Monday 19 February 2018 (Presidents' Days)
• Monday 26 March–Friday 30 March 2018 (Spring Break)
• Thursday 26 April–Friday 27 April 2018 (Faculty Training)

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

## Final Examination

Place/date/time:  Room SCI-352, Wednesday 16 May 2018, 2:45 p.m.

Important Note: This is 75 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.
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.)
(WebAssign) For students who wish to use WebAssign for OPTIONAL extra practice and have purchased an access code (possibly with your textbook), you will need to enroll yourself. The Class Key is "ventura 4884 0921" (without the quotes). The suggested extra homework problems start in Week 3. Don't worry about the "due dates," as I am not collecting or grading these assignments. They are only for your own study.
1.1 Definitions and Terminology 1–27 ODD
Instructor's lecture notes (DOC) for this section
1.2 Initial-Value Problems 1–27 ODD; 39–43 ODD
Instructor's lecture notes (DOC) for this section
1.3 Differential Equations as Mathematical Models (For this section, you are asked to derive, but not solve, a differential equation that appropriately models the situation described in each problem.)

1; 6 (hint: determine an equation for $T_m\left(t\right)$ from the given curve, using your knowledge of amplitude, period, bias, and phase for trig functions); 9; 15; 16; 17
28
Instructor's lecture notes (DOC) for this section
2.1 Solution Curves Without a Solution 1–27 ODD
Instructor's lecture notes (DOC) for this section
Download wxMaxima software for Windows, Mac OS X, or Linux if you need a free computer algebra system to construct direction-field plots for the homework assignment.
Documentation: Reference for the wxMaxima "plotdf" function, which produces direction plots (this includes information on how to superimpose graphs of functions on top of a direction-field plot for problems like #17), and a tutorial that describes how to deal with possible error messages.
(Note that the syntax used in the tutorial is for differential equations that are specified parametrically; use the simpler version in the reference instead if you wish.)
2.2 Separable Equations 1–33 ODD; 45–49 ODD
Instructor's lecture notes (DOC) for this section
2.3 Linear Equations 1–35 ODD; 45; 46
Instructor's lecture notes (DOC) for this section
(Review) Review of Multivariable Calculus Concepts Supplemental problems 1–4 at the end of Review of Multivariable Calculus Concepts
Review of Multivariable Calculus Concepts (DOC)
2.4 Exact Equations 1–25 ODD; 31–35 ODD
Instructor's lecture notes (DOC) for this section
2.5 Solutions by Substitutions (No assignment)
2.6 A Numerical Method (No assignment)
Chapter Test 1

Sections 1.1–1.3 and 2.1–2.4

Mon. 12 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 34 (Review Exercises): 7–13 ALL; 15; 17; 19; 21(b); 23; 25; 27; 31–37 ODD
Page 81 (Review Exercises): 17; 19 (separable); 22 (exact); 23 (linear equation with integrating factor); 24 (nonexact equation with integrating factor; note that a constant is still a function of $x$ or $y$); 25 (separable); 27; 29; 33; 39
(For students with additional study time) The above plus some or all of
Page 34 (Review Exercises): 16; 18; 21(c); 22; 24; 28–30 ALL; 32–38 EVEN
Page 81 (Review Exercises): 26 (exact); 28; 30; 34; 40; and
Even-numbered homework problems from the textbook sections covered
3.1 Linear Models 1–19 ODD; 29–39 ODD
(this is the updated assignment announced in class)
Instructor's lecture notes (DOC) for this section
3.2 Nonlinear Models (No assignment)
3.3 Modeling with Systems of First-Order DEs (No assignment)
4.1 Preliminary Theory—Linear Equations 1–35 ODD
Instructor's lecture notes (DOC) for this section
4.2 Reduction of Order 1–21 ODD
Instructor's lecture notes (DOC) for this section
4.3 Homogeneous Linear Equations with Constant Coefficients 1–41 ODD
Instructor's lecture notes (DOC) for this section
4.4 Undetermined Coefficients—Superposition Approach 1–39 ODD
Instructor's lecture notes (DOC) for this section
4.5 Undetermined Coefficients—Annihilator Approach (No assignment)
4.6 Variation of Parameters 1–21 ODD; 29; 31
Instructor's lecture notes (DOC) for this section
4.7 Cauchy-Euler Equations (No assignment)
4.8 Green's Functions (No assignment)
4.9 Solving Systems of Linear DEs by Elimination (No assignment)
4.10 Nonlinear Differential Equations (No assignment)
Chapter Test 2

Sections 3.1, 4.1–4.4, and 4.6

Wed. 21 Mar.

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 91 (Section 3.1 Exercises): 2; 6; 10; 14; 30; 32
Page 114 (Review Exercises): 5; 6
Page 193 (Review Exercises): 17; 19; 23; 27; 41; 44
(For students with additional study time) The above plus some or all of
Page 114 (Review Exercises): 7; 8
Page 193 (Review Exercises): 13(a); 14(abcdef); 18; 24; 38; 40; 42; 44
5.1 Linear Models: Initial-Value Problems 1–37 ODD
5.2 Linear Models: Boundary-Value Problems (No assignment)
5.3 Nonlinear Models (No assignment)
6.1 Review of Power Series 1–33 ODD
6.2 Solutions About Ordinary Points 1–21 ODD
Instructor's lecture notes (DOC) for this section
6.3 Solutions About Singular Points 1–23 ODD
Instructor's lecture notes (DOC) for this section
6.4 Special Functions (No assignment)
Chapter Test 3

Sections 5.1 and 6.1–6.3

Wed. 25 Apr.

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 209 (Section 5.1 Exercises): 2; 6; 10
Page 276 (Review Exercises): 9; 11; 13; 19; 20 (read the instructions carefully; only the solve the equation when it says to!)
(For students with additional study time) The above plus some or all of
Page 232 (Review Exercises): 12(abdef); 13; 15
Page 276 (Review Exercises): 10; 12; 14
7.1 Definition of the Laplace Transform 11–17 ODD (compute using the integral on page 279 of the textbook); 19–35 ODD (compute using the table on page 282 of the textbook)
Instructor's lecture notes (DOC) for this section
7.2 Inverse Transforms and Transforms of Derivatives 35–44 ALL
Instructor's lecture notes (DOC) for this section
7.3 Operational Properties I 1–33 ODD; 37–75 ODD
Instructor's lecture notes (DOC) for this section
7.4 Operational Properties II (No assignment)
7.5 The Dirac Delta Function (No assignment)
7.6 Systems of Linear Differential Equations (No assignment)
8.1 Preliminary Theory—Linear Systems 1–25 ODD
8.2 Homogeneous Linear Systems 1–13 ODD
Instructor's lecture notes (DOC) for this section

## Course Handouts and Study Aids

• 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 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.

## 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.

Michael Bowen's VC Course Pages: Math V23, Spring 2018