Math 1102: Calculus II

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Session: Fall 2009		Instructor: Barry McQuarrie		Office Hours:
Location: Sci 3510		Office: Science 1380		MWF 9:15-10:30am
MWF 11:45-12:50pm		Phone: 589-6302 (I do not use voicemail)		Th 10:30-11:30am
Th 12:00-1:40pm		mcquarrb@morris.umn.edu		drop in (if my door is open we can talk, if it is closed I am not available)
		http://cda.morris.umn.edu/~mcquarrb/		other times via email appointment

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Course Prerequisites

To succeed in this course you will need to have mastered the basic concepts of differentiation and integration studied in Calculus I. You should also be comfortable working both graphically and algebraically when solving problems.

Goals

The primary goals of a student taking this course are to

• be able to create integral representations for volumes by revolution,
• understand and apply various advanced integration techniques, including:
• integration by parts, trigonometric substitution, partial fractions,
• approximate integration
• identify and evaluate improper integrals,
• understand some of the basic theory behind differential equations, and solve certain classes of differential equations,
• understand sequences and how sequences are related to series,
• work with series, and know how to test if a given series is convergent or divergent,
• continue to gain fluency in a powerful computer algebra system, Mathematica (this entails learning some of the syntax of Mathematica).

Beyond the curriculum, you should also expect to

• develop skill at presenting solutions to problems,
• think beyond technique, and understand the problems studied in some depth,
• develop confidence in your problem solving skills,
• see the benefit of computers to aid calculation, but also see the absolute necessity of understanding the theory completely before using a computer.

Textbook

James Stewart Single Variable Calculus, early transcendentals 6th or 5th Ed--the bookstore will have the latest edition, and the course calendar below is based on the 6th Edition. The differences between the editions is minimal, but if you use an earlier edition be aware that some of the sections may be numbered differently, content may be slightly different, and problems listed as practice below may not line up with your older edition. We will be covering Chapters 6--11 from this book.

We will be using the computer algebra system (CAS) Mathematica. This program is not described in our text. Rather you will be learning it as you go in class, using resources I will provide.

Time Commitment

University policy says ''one credit is defined as equivalent to an average of three hours of learning effort per week (over a full semester) necessary for an average student to achieve an average grade in the course''. Our course is a five-credit course, meeting approximately five hours per week: 5 credits times 3 hours/week/credit - 5 hours/week in lecture = 10 hours/week outside class. Thus, you are expected to spend 10 hours per week working outside of class, reading the textbook and working problems.

Please make the most of my office hours! The content of the course can be difficult at times and I expect to see you all in my office at some time or other. To get the most out of the course you should

• do homework every day (more on this later),
• allot time to think about what it is we are doing,
• discuss the techniques we are studying and their implementation with your classmates,
• discuss any difficulties with me during office hours.

Course components

I am demanding that solutions be written up well. This means solutions should be a self-contained document. They should be written legibly, contain diagrams or tables where appropriate, and should state the problem and explain the solution. Interspersing English sentences which explain what you are doing can help in this regard. With its worked-out examples, the book provides many examples of a good solution. There are also examples in the homework in the course calendar below. To say it in a more concrete way, solutions with totally correct computations lacking in necessary good explanations will tend to receive a B, not an A. We will be discussing the importance of communicating your results in more detail at various times in the course.

Textbook. The book presents the material we will be learning in an organized and comprehensive way. You should try to understand the main point of a given section before coming to the corresponding class.

Class periods. We meet four times a week in Sci 3510. Class periods will be a mixture of activities. I will lecture on some of the high points of the section. I will work out solutions to problems like your homework problems. Generally we will do a fair amount of work using Mathematica. I will be asking the class questions and you should always feel free to ask questions throughout the class period. It is important that you attend lectures because announcements regarding the class (upcoming tests, possible take-home assignments or homework, etc.) will be made in class. If you miss a lecture it is your responsibility to find out what you have missed.

Practice. Practice questions will not be collected. Mastery of the topics we study will only come with practice, making homework a crucial component of our course. Every day when we cover a new section there are four homework problems. You should faithfully write out solutions to all these homework problems, before the next class begins! If you're wondering where to put in those ten weekly out-of-class hours, this is the main place! Although only four practice questions are suggested for each lecture, you should do as many problems as needed to understand the day's lecture.

WeBWorK. You will be completing some assignments using the online homework utility WeBWorK, which you can learn more about here. The WeBWorK problems are provided to give you practice implementing the computational techniques we will be studying, although occasionally a problem will be more theoretical in nature. I have provided links to the WeBWorK problem sets in the course calender below.

Tests. There will be five in-class tests and then a cumulative final. Test 1 and 5 is labeled hand, no aids on the syllabus, meaning on these tests you will work without Mathematica or even calculators. Tests 2 and 4 are take home. For take home tests you will be able to use resources like your text book and Mathematica, however you will be required to work on the test alone. Test 3 is labeled hand, aids allowed, and for this tests you will not use Mathematica, but you will be able to use your textbook and other aids during the test.

Journals. Each week you will submit a short journal entry, usually based on your experiences with calculus in the past week. I will require that all journal entries be emailed to me by Friday--include your journal in the body of the email, not as a Word or other attachment. You should spend about ten minutes composing your journal entry each week, and ensure that your submission uses correct spelling, punctuation, and grammar.

I am having you write journal entries for the following reasons:

• I want to encourage conversations between you and I, and give you the opportunity to tell me how the class is going for you as often as possible,
• I want you to have the chance to reflect on your learning, and try to determine what works well for you and what does not work as well,
• I also want to provide an opportunity for you to think about calculus outside the bounds of solving specific problems.

I have provided journal topics for each week on the course web page. However, you should feel free to write about other aspects of the class than the one I suggest.

For the journal entry to be useful to you and me, it should include some explanation of your thoughts. Saying ``I find related rates difficult." doesn't tell me much, or help you at all. Contrast the above with the following, which definitely will help both you and me!

``I find related rates difficult. I think it might be because they can require a long written solution. Seeing the entire solution at the beginning is impossible! I am going to try to spend time breaking the complete solution into smaller ones I can handle, and then putting those bits together to get the complete solution."

When no journal topic is provided, you might want to complete one or a few statements that begin like the following:

In class, I felt... In class, I learned... The most positive result of class this week was... The least positive result of class this week was... Some additional comments related to class are...

While doing homework, I felt... While doing homework, I learned... The most positive result of doing homework was... The least positive result of doing homework was... Some additional comments related to homework are...

You may decide not to use these guiding phrases at all. You may want to talk about how you see calculus used in other courses, or ask questions that you hope to be able to answer when the section we are studying is over. Journals are very useful for me to look back on when I write letters of reference for students later in life, and allow me to write good, detailed letters of reference for future employers--so if you think you may one day be asking me for a letter of reference, take the time now to reflect deeply in the journals.

Applied Projects. There will be a few applied projects you will work on during the semester. These are meant to give you a chance to see calculus in action, outside of the bounds of specific questions. The applied projects will be handed out in class, and are due on the dates shown on the syllabus. You may work in groups of up to four people on the applied projects, and each group turns in one solution. Each group member will receive the same grade. Your groups can change for each applied project you do. The solutions for the applied projects must be well explained, written legibly and use correct mathematics.

Mathematica. We will be learning Mathematica as the semester progresses. Mathematica is a powerful computer algebra system that can do far more than a calculator. The skills you acquire when you learn Mathematica will translate to other technologies, and other areas of your life. If you are a math major, Mathematica is used throughout UMM's math major in virtually all of our courses to some extent, so this introduction will prepare you to do very interesting things with it later on in your academic career. If you are not a math major, studying Mathematica is an important aspect of understanding mathematics in a liberal arts setting--computation and using tools like Mathematica, maple, fortran, C, C++, Java, MuPad, SAS, Origin, etc, are increasingly an important part of Mathematics.

Mathematica will never do our thinking for us. It will help us understand concepts and answer questions that would be difficult to answer if we were working the solution out solely by hand. Our goal in Calculus II is to become fluent in basic Mathematica syntax and get an introduction to some of Mathematica's power.

Grading

Here is the University-wide uniform grading policy.

• A: Represents achievement that is outstanding relative to the level necessary to meet course requirements.
• B: Represents achievement that is significantly above the level necessary to meet course requirements.
• C: Represents achievement that meets the course requirements in every respect.
• D: Represents achievement that is worthy of credit even though it fails to fully meet the course requirements.
• F: Represents failure and indicates that the coursework was completed but at a level unworthy of credit, or was not completed and there was no agreement between the instructor and student that the student would be temporarily given an incomplete.
• I: See the catalog.

A few of you may be taking the course S-N. In this case, you need to earn a C- to receive an S.

The grade for the course will be calculated by the following formula:

Five chapter tests worth 10% each	50%
WeBWorK	18%
Three applied projects worth 3% each	9%
Final exam	20%
Nine Journals worth 1/3% each	3%

Your numerical grades will be converted to letter grades and finally Grade Points via the following cutoffs (see the UMM Catalog for more on Grades and Grading Policy):

Numerical	95%	90%	87%	83%	80%	77%	73%	70%	65%	60%	Below 60%
Letter	A	A-	B+	B	B-	C+	C	C-	D+	D	F
Grade Point	4.00	3.67	3.33	3.00	2.67	2.33	2.00	1.67	1.33	1.00	0.00

Please note that you are not competing against your fellow students. I will adjust the difficulty of the questions and the severity of the grading so that say a B+ score corresponds to what I consider B+ achievement. Please note that your performance will likely fluctuate substantially. However my experience says that with so many components to your final grade, the final grade always adequately reflects your achievement.

Respectful Classroom

• Be in class on time. I nor you fellow classmates enjoy the disruption late arrival causes. I know that situations crop up that will entail late arrival (please come even if you are late!) but try to ensure it is the exception and not the rule. Buy an alarm clock with a battery backup, as the power often goes out for a moment in Morris.
• If you need to leave class early, let me know before class and slip out as unobtrusively as possible.
• During class, cell phones and music devices should be turned off, and headphones removed from ears. If I find you are surfing the internet during class I will ask you to leave.

• As a student you may experience a range of issues that can cause barriers to learning, such as strained relationships, increased anxiety, alcohol/drug problems, feeling down, difficulty concentrating, and/or lack of motivation. These mental health concerns or stressful events may lead to diminished academic performance or reduce a student`s ability to participate in daily activities. If you have any special needs or requirements to help you succeed in the class, come and talk to me as soon as possible, or visit the appropriate University service yourself. You can learn more about the range of services available on campus by visiting the websites:

  The Academic Assistance Center www.morris.umn.edu/services/dsoaac/aac/

  Student Counseling www.morris.umn.edu/services/counseling/

  Disability Services www.morris.umn.edu/services/dsoaac/dso

  Multi-Ethnic Student Program www.morris.umn.edu/services/msp/
  

• Cooperation is vital to your future success, which ever path you take. I encourage cooperation amongst students where ever possible, but the act of copying or other forms of cheating will not be tolerated. Academic dishonesty in any portion of the academic work for a course is grounds for awarding a grade of F or N for the entire course. Any act of plagiarism that is detected will result in a mark of zero on the entire assignment or test for both parties. I will make it clear during class what is appropriate collaboration for each activity, but if you still have questions about what constitutes academic dishonesty, please come and talk to me. UMM's Academic Integrity policy and procedures can be found at www.morris.umn.edu/Scholastic/AcademicIntegrity/.
• Since the assignments are handed out days in advance, only under exceptional circumstances (which can be officially documented) will I accept late work. You will receive a mark of zero if an assignment is submitted late. However, please talk with me asap (do not wait until the next class) if you missed turning something in, even if it is after the deadline. If an assignment is partially complete but you are not granted an extension, still submit the work you have completed so you can earn some partial credit. This is far preferable to earning zero on the assignment by not submitting anything.
• Putting take home portions of tests in my mailbox or under my office door while I am teaching another course is severely frowned upon unless we have agreed that you will be doing this.
• If you are going to miss a quiz or exam (for a documented reason), let me know in advance so we can work out alternate plans. If you unexpectedly miss an exam/quiz/etc for a documentable reason, get in touch with me asap so we can work out alternate arrangements, or schedule a make-up.
• Since I want the journal reflections to occur throughout the semester, journals for a given week submitted after Friday at 6pm will not count towards your journal total.

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Course Calendar

#	Date	Lecture Topic	Assignments	Resources/FYI
	Mon Aug 24
1	Wed Aug 26	Course Introduction Prerequisite Quiz Solutions	journal 1	Review Mathematica Basics
2	Thu Aug 27	Review Trig, Exponentials, and Logarithms	ww: Review	Making Sense of Trig
3	Fri Aug 28	Review Derivatives	ww: Review
4	Mon Aug 31	Review Integration	journal 2 ww: Review	Making Sense of Basic Integrals
5	Wed Sep 2	6.1 Areas Between Curves	ww: 6.1	6.1.50 (MMA file)
6	Thu Sep 3	6.2 Volumes	ww: 6.2	examples Surface of Revolution (MMA) Demo of the Washer Method
7	Fri Sep 4	6.3 Volume by Cylindrical Shells	ww: 6.3	examples
8	Mon Sep 7	Labour Day--no class
9	Wed Sep 9	6.5 Average Value of a Function	journal 3 ww: 6.5
10	Thu Sep 10	7.1 Integration by Parts	ww: 7.1	examples
11	Fri Sep 11	7.2 Trigonometric Integrals	ww: 7.2	examples
12	Mon Sep 14	7.3 Trigonometric Substitution	journal 4 ww: 7.3	examples | 7.3.5
13	Wed Sep 16	7.3 Trigonometric Substitution		examples Solutions to Quiz
14	Thu Sep 17	7.4 Partial Fractions	ww: 7.4	examples
15	Fri Sep 18	7.5 Strategy for Integration	ww: 7.5	examples
16	Mon Sep 21	7.8 Improper Integrals	ww: 7.8	examples
17	Wed Sep 23	7.8 Improper Integrals
18	Thu Sep 24	Test 1: 6.1-6.3, 6.5, 7.1-7.5, 7.8 (hand, no aids)	journal 5	Practice Problems
19	Fri Sep 25	7.6 Integration Using Tables and CAS
20	Mon Sep 28	7.7 Approximate Integration	ww: 7.7	examples (MMA file) 7.7.7 (MMA file)
21	Wed Sep 30	8.3 Applications to Physics and Engineering		Moments and Center of Mass
22	Thu Oct 1	8.3 Applications to Physics and Engineering	Applied Project 1 Due	Example from Lecture (MMA file)
23	Fri Oct 2	8.4 Applications to Economics and Biology	journal 6	lecture notes and examples from Economics
24	Mon Oct 5	8.4 Applications to Economics and Biology	journal 7	AUC for blood plasma
25	Wed Oct 7	8.5 Probability Test 2 Handed Out
26	Thu Oct 8	No class. Work on Test 2: 7.6, 7.7, 8.3, 8.4, 8.5 (take home)
27	Fri Oct 9	11.1 Sequences Test 2 Turned In	ww: 11.1	examples Integer Sequences Database Limit of a Sequence Closer look at Monotonic Sequence Theorem
28	Mon Oct 12	11.2 Series	journal 8 ww: 11.2	examples Geometry Gives Rise to Sequences and Series Fractal Application of Series
29	Wed Oct 14	11.2 Series		Limit of Sequence and Summing Series (MMA)
30	Thu Oct 15	11.3 The Integral Test and Estimates of Sums	ww: 11.3	examples
31	Fri Oct 16	11.4 The Comparison Tests	ww: 11.4	examples
32	Mon Oct 19	Fall Break--no class
33	Wed Oct 21	11.5 Alternating Series	journal 9 ww: 11.5	examples
34	Thu Oct 22	11.6 Absolute Convergence: The Ratio and Root Tests	ww: 11.6	examples
35	Fri Oct 23	11.6 Absolute Convergence: The Ratio and Root Tests
36	Mon Oct 26	11.7 Strategy For Testing Series for Convergence	journal 10	examples Choosing a Test
37	Wed Oct 28	11.7 Strategy For Testing Series for Convergence	ww: 11.7
38	Thu Oct 29	Test 3: 11.1-11.7 (hand, aids allowed)		Practice Problems Concept Map for Sequences & Series
39	Fri Oct 30	11.8 Power Series		Geometry Gives Rise to Sequences and Series
40	Mon Nov 2	11.8 Power Series	journal 11 ww: 11.8	examples
41	Wed Nov 4	11.9 Representations of Functions as Power Series	ww: 11.9	examples
42	Thu Nov 5	11.10 Taylor and Maclaurin Series	Applied Project 2 Due	examples What is "0!"?
43	Fri Nov 6	11.10 Taylor and Maclaurin Series	ww: 11.10
44	Mon Nov 9	11.11 Applications of Taylor Series	journal 12
45	Wed Nov 11	11.11 Applications of Taylor Series		Questions
46	Thu Nov 12	Test 4: 11.8-11.11 (hand, no aids)		Practice Problems Concept Map for Taylor Series
47	Fri Nov 13	9.1 Modeling with Differential Equations	ww: 9.1	examples (MMA file)
48	Mon Nov 16	9.2 Direction Fields and Euler's Method	journal 13 ww: 9.2	examples (MMA file) Direction Field and Euler's Method (MMA file)
49	Wed Nov 18	9.3 Separable Equations	ww: 9.3	examples (MMA file)
50	Thu Nov 19	9.3 Separable Equations		examples
51	Fri Nov 20	9.4 Models for Population Growth
52	Mon Nov 23	9.5 Linear Equations	journal 14
53	Wed Nov 25	9.6 Predator-Prey Systems
54	Thu Nov 26	Thanksgiving Holiday--No Class
55	Fri Nov 27	Thanksgiving Holiday--No Class
56	Mon Nov 30	9.6 Predator-Prey Systems	journal 15
57	Wed Dec 2	10.1 Curves Defined by Parametric Equations	ww: 10.1
58	Thu Dec 3	Test 5: 9.1-9.6 (hand, no aids)		Practice Problems
59	Fri Dec 4	10.2 Calculus with Parametric Curves	ww: 10.2	Arc Length Thoughts
56	Mon Dec 7	10.2 Calculus with Parametric Curves	journal 16	Examples from Lecture
57	Wed Dec 9	10.3 Polar Coordinates	ww: 10.3	examples
58	Thu Dec 10	10.4 Areas and Lengths in Polar Coordinates	Applied Project 3 Due ww: 10.4	examples
59	Fri Dec 11	Review: Integral Types, Volume of Revolution, Integration Techniques, Separable DE, Arc Length, Probability Density Function, Orthogonal Trajectories, Sequences and Series.
	Mon Dec 14	11:00am-1:00pm in Sci 3510	Final Exam