Offered: Fall 2015 Instructor: Kevin J. Mitchell Office: Lansing 305 Phone: (315) 781-3619 Fax: (315) 781-3860 E-mail: mitchell@hws.edu Office Hrs: M & W 2:30-4:00, Tu 2:00-3:30, F 1:30-2:30. Available at other times by appointment. Class: Section 131-01: M-W-F 8:00 to 8:55 in Napier 201 Lab: Thursday 10:20 to 11:45 in Gulick 206A Final Exam: Thursday, December 17, 2015 8:30-11:30 AM (NOTE: Exam time is for our lab period.) Text:Calculus: Early Transcendentals, second edition by Briggs, Cochran, & Gillett Math Intern: Ms Tasha Williams. Office Hours in Lansing 310 Sun: 2:00-5:00, 7:00-10:00pm; Mon through Thurs: 3:00-5:30pm, 7:00-10:30pm Website: http://math.hws.edu/~mitchell/Math131F15/index.html where I will post (all) course documents. Please bookmark and use this site. WeBWorK: WeBWorK Home Page for Math 131 WeBWorK Instructions and FAQs WeBWorK Syntax and List of Functions

To prove the Fundamental Theorem of Calculus requires us to connect the process of
antidifferentiation to the notion of area under a curve.
You know how to find the areas of some regions: squares, rectangles,
triangles,
and circles.
While you might be able to justify the area formula for a rectangle, it is unlikely
that you could give a satisfactory proof for the area formula of a circle. In fact,
there is a more fundamental problem here: **What is area?**

In differential calculus, the motivating problem was the paradoxical notion of an
"instantaneous" rate of change. What do we mean by speed "at an instant?" Average rates or
speeds are familiar ideas: divide distance by time. But in an instant, no time passes and
no distance is
travelled. So there is no (rate of) change! We resolved the paradox by using average
rates of change over smaller and smaller time intervals. In the end, the instantaneous
rate of change (or derivative) was **defined** to be the limit of average
rates of change. But note, the concept of an "instantaneous" rate had to be defined
through a fairly long process and was not "obvious."

In the same way, area, though familiar, is not an obvious notion. Some area formulas are familiar, but what is area? What are its defining characteristics? We will start with this problem and see that its solution has a wide variety of applications. In learning how to find area, we will also learn how to find or define the length of a curve, the volume of a solid, the work done by a force applied over a distance, and so on.

As with derivatives, limits will be crucial to the solution of the "integral" or area
problem. This time the "paradox" will be that we add up lots (i.e., an infinite
number in the limit) of small areas (0-sized in the limit) to obtain the area of a
figure. There are lots of questions to resolve: How do you add an infinite number of
things? How do you divide a region under a curve into smaller pieces whose areas you know? Answers
to such questions will motivate our "definition" of area.

I also intend to put some notes on line that are based on my class lectures. These will
have additional examples and problems to try. Look for them at our course website,
http://math.hws.edu/~mitchell/Math131F15/index.html .

About twice a week there will be an assignment consisting of selected problems to hand in for grading.
In the past, I have insisted that graded assignments are to be your own work without collaboration.
But this term, I will try something different. You may discuss graded homework assignments with others.
Verbalizing your questions, explaining your mathematical
ideas, and listening to others will increase your understanding. BUT **you are not free to simply copy
others' work or to make your work available in this way to others**. You will be heavily penalized for
such instances. Make sure you write up your answers on your own.
Plagiarism acts against my obligation as an instructor to insist that students do work that
will benefit them and help them think and learn independently. You may wish to review the
Handbook of Community Standards.
I reserve the
right to change this policy if it is abused. (Note: Other faculty will have
different policies about homework.)
Your work will be due at the beginning of the next class. It should be **neat and done in pencil**.
If more than one page is required, please **staple** them.
No late assignments, please.

There will be (almost) daily graded
**WebWork** computer
exercises that review the material and concepts we are currently covering.
You will get immediate feedback from these exercises that will allow
you to assess your progress. Further, if you submit an incorrect answer, you
may return to the problem and work on it again until you get it right. Students typically earn 90-100% on
this part of the course. Though every student's problems will be similar, they will not be identical
to each other.
You may find these problems frustrating at first because you will have to be quite careful in
entering your answers. Stick with it! Using WeBWorK will mean that there are fewer or shorter
written assignments.

I may also use a few **announced 10-minute quizzes** to check your progress.

There will be **three in-class tests** and a
**final exam**. The dates are listed in the outline below. Tests will be cumulative but
will concentrate on more recent material. It is impossible to construct fair makeup exams
in mathematics. For your own protection, my policy is that there are **no makeup examinations**.
If for some extraordinary reason you find you are unable to take an exam,
let me know as soon as possible, certainly well before the exam is administered.

Your **course grade** will be calculated as follows. First I will
make a list of your grades:

**Extra Credit:** You may earn extra credit
by attending a Mathematics and Computer Science Department seminar.
You may recieve a maximum of three such credits.

- Each of the fourth, fifth, and sixth absences will result in a deduction of 3, 4, and 5 points, respectively, from your final grade.
- Beyond six absences will likely result in your expulsion from the course.

Finally, common courtesy demands that you be on time for class, that
you **do not leave the room during class** (unless you are ill), and that **cell phones
are turned off**. This will help you, your
classmates, and me to give our full attention to the course.

I expect that you will put in at least **two to three hours of work outside of class for each hour
in class**, including lab. This includes reading the text, reviewing class notes,
finishing lab problems, doing
practice problems, and then doing assigned homework problems. This effort will be rewarded by making the
exams seem easy.

- Come to all classes.
**Take complete and careful notes.** - Do the readings and practice problems carefully.
- Keep the answers to problems and notes on the readings in a journal.
- Review/recopy the notes from the last class before coming to class again. This makes studying for a test easy.
- Start homework and WeBWorK assignments early.
- Come in for help whenever you need it, preferably before you get too far behind.
- Visit the
**Math Intern**for help in the evenings. - Review the notes I place online at the course website.
- Review some of the lab questions once a week.
- Ask questions in class. Ask questions about the homework and readings.

- Week 1: The Area Problem, Summation Notation. Riemann Sums. Chapter 5.1-5.2. On you own: Review Chapter 4.7 and 4.9 (L'Hopital's Rule, Antiderivatives) and the Mean Value Theorem (page 292; make sure you understand Figure 4.70).
- Week 2: Riemann Sums and the Definite Integral. The Fundamental Theorem of Calculus. Chapters 5.2-5.3.
- Week 3: Properties of Integrals. Integrals via Substitution. Chapter 5.4-5.5.
- Week 4: Substitution. (Net Change?) Area Between Curves Chapters 5.5. (6.1?) 6.2.
- Week 5. Application: Volume by Slicing and by Shells. 6.3-6.4.
- Thursday Week 5, October 1:
**First Hour Test (in Lab)**. - Week 6: Applications: Arc Length. Work? Chapter 6.5 and 6.7 (pp 462-464).
- Week 7: Log and Exponential Functions, again. Integration by Parts. Chapters 6.8 and 7.2 and Handout. Review on your own: Chapter 7.1.
- Week 8: Trig Integrals (briefly). Trig (Triangle) Substitution. Chapter 7.3-7.4 and Handout.
- Thursday Week 9, October 29:
**Second Hour Test (in Lab)**. - Week 9: Partial Fractions (briefly). Improper Integrals. Chapter 7.5, 7.8.
- Week 10: Sequences and Series. Chapter 8.1-8.3.
- Week 11: The Divergence Test and Convergence Tests. Chapter 8.4-8.5.
- Week 12: Convergence Tests, continued. Alternating Series. Chapter 8.5-8.6.
- Monday, November 23:
**Third Hour Test (@7:40am)**. - Week 13: Thanksgiving Break Wednesday through Friday.
- Week 14: Alternating Series. Taylor Polynomials. Power Series. Chapters 8.6 and 9.1-9.2.
- Week 15: Power series and Taylor (McLaurin) series. Chapter 9.2-9.3.
**Final Exam**: Thursday, December 17, 2013 8:30-11:30 AM (NOTE: This exam time is for our lab period.)

Disability Accommodations: If you are a student with a disability for which you may need accommodations, you should self-identify and register for services with the Coordinator of Disability Services at the Center for Teaching and Learning (CTL), and provide documentation of your disability. Disability related accommodations and services generally will not be provided until the registration and documentation process is complete. The guidelines for documenting disabilities can be found at the following website: http://www.hws.edu/academics/ctl/disability_services.aspx.

Please direct questions about this process or Disability Services at HWS to Administrative Coordinator, Jamie Slusser, (slusser@hws.edu, 781-3351) or Coordinator of Disability Services, David Silver at silver@hws.edu.

Hobart and William Smith Colleges

Department of Mathematics and Computer Science

Copyright © 2015

Author: Kevin Mitchell (mitchell@hws.edu)

Department of Mathematics and Computer Science

Copyright © 2015

Author: Kevin Mitchell (mitchell@hws.edu)