MATH 102: Calculus 2

Mathematics Department, Bryn Mawr College, Spring 2009

Professor Victor Donnay

Professor: Victor Donnay	Class Meeting: Mon, Wed, Friday 10 – 11am
Office: Park Science Building #330	Office Hours: Mon, Wed*, Frid 2:30-4pm * on a few Wed the time will need to be changed to accommodate Dept Meetings
Phone: 526-5352, E-mail: vdonnay	and by appointment at other times.

All information about the course can be found at the Math 102 website located on Prof. Donnay’s homepage:

http://www.brynmawr.edu/math/people/donnay

Required Textbook: Calculus, 6th Edition, by James Stewart.

Recommended Supplement: The student solutions manual contains worked out solutions for all even problems in the textbook. The solutions manual for our textbook has ISBN 0495012343. Stewart has written several different calculus textbooks, each of which appears in several different editions, so please check the ISBN before making a purchase. Copies of the solution manual will be available at the Reserve Readings collection in Collier Science Library (not there quite yet)

Help Sessions: There will be several help sessions per week with our undergraduate TA Bethany Azuma. Time/Place tba.

Content Goals of the Course: In this course, you will:

• Learn that mathematics can be used to study real world situations. This process is called mathematical modeling. In our course it will involve using functions and their derivatives and integrals .
• Learn how to work with various representations of functions (graphical, tables, formulas) and become proficient in using certain types of functions (linear, quadratic, polynomial, trigonometric, exponential and logarithmic).
• Understand how the area under a curve can be approximated by adding up boxes and that the limit of this procedure leads to the integral.
• Understand how derivatives and integrals are related via the Fundamental Theorem of Calculus.
• Learn how to compute integrals both for simple functions and for more complicated functions.
• Learn the meaning of an integral in a variety of applications.
• Learn how to add up infinitely many numbers (a series) and then add up infinitely many functions.
• How to use simple functions to approximate complicated functions (Taylor approximations, Taylor Series).
• Use the computer system Mathematica to do computations related to the above topics and to plot curves.

Process Goals of the Course: In this course, you will

• Find connections between the mathematics we are studying and real world situations.
• Communicate your mathematical reasoning in writing and verbally.
• Develop your ability to work as an independent and self-sufficient learner by facing the challenge of “What to do when you do not know what to do”.
• How to take what you have learned in one situation and apply it to a new and different situation (transfer of knowledge)
• Get comfortable with not knowing the answer immediately
• Learn material we have not covered in class by reading the book and applying this newly learned information to solve problems.
• Become part of a community of learners who support, encourage and learn from one another.

We will cover the following material from Stewart. Sections in () indicate material that will be covered briefly or might be omitted.

• Ch.5: Section 5
• Ch. 6: Section 1, 2, (3), 4, 5
• Ch. 7: Section 1, 2, 3, 4, 5, 6, 8.
• Ch. 8: Section 1, 2, 3, (4), 5, 6, 7, 8
• Ch. 9: Section 1, 2, 3, 4,
• Ch. 12: Section 1, 2, 3, 4, 5, 6, 8, 9, 10, 11

Other material might be included as time permits.

Learning Theory:

A common misconception in the United States is that only a gifted few people can do mathematics successfully; “you either have it (the ability to mathematics) or you don’t”. The reality, as demonstrated by educational studies of student learning, is that the majority of learners can reach a reasonable level of mathematical competency providing they work hard at it. Another misconception is that one’s intellectual ability is fixed from a young age onward. Research in neuroscience shows that people’s brains continue to develop throughout life; the brain makes 20,000 new neural connections per day. Thus, by appropriate training, one can actually “get smarter”.

My goal is to have all students in this course be successful in mathematics and to help you become smarter at the end of the course than you were at the beginning. This will require hard work and facing new challenges that will stretch your thinking. Learning new ideas and becoming fluent in applying them takes time and can involves periods of frustration. If you have this experience, do not worry; it is normal.

Course Components:

Classroom:

During class, there will be a mixture of lecturing by the professor and time spent by the students working out problems and discussing their results in groups. Research has shown that this type of active participation, in which one explains one’s reasoning as well as thinks about others’ explanations, leads to improved learning. Explaining your reasoning requires a different and higher level of thinking skill than does simply doing the problem.

The group work does not go well when members of the group are absent. Therefore it is important that you attend class. Please be respectful of your fellow students.

If you decide to take this course, you must commit to attending class regularly.

Homework:

a. There will be homework related to each class session coming from the textbook: practice problems and assigned exercises. The assigned problems will be collected once a week on Mondays. Even though the homework will only be collected weekly, you should do part of the homework after each class. Out of respect for the time and effort of the graders, late work will not be accepted unless there is a special situation (ex. serious medical problem) and you get my permission ahead of time.

b. To make the time we spend working in groups most effective, you will have some short assignments that will need to be completed by the following class period so that you can share your work with your group.

The best way to learn mathematics is by doing lots of problems. Do not limit yourself to just doing the assigned problems that you are required to hand in. You should do some problems after each class. This way, the next lecture will make a lot more sense. Do not wait till the last minute and do all the problems at once. You will have much more trouble understanding the lectures and will therefore be using your time inefficiently.

To help you be aware of the time you are spending on the homework and how your are distributing the time over the course of the week, you will turn in a time log with each homework assignment which states the number of hours you spent studying Calculus and working on the homework that week.

I encourage you to work together with other students to solve the homework. However, the work you hand in must be your own (i.e. you may not simply copy the answer from someone else).

Connections:

A major goal of the course is for you to see how mathematics is related to things you are interested in. To this end, we will have a “Connections” component to the course:

• Over the course of the semester, you will choose from the homework you are assigned, two problems and for each one, write a short description (one – two paragraphs), describing how the mathematics in the problem could link to a real world situation. We will set up a forum on Blackboard in which you will post these responses.
• You will look at other students’ “connections” write ups, choose one that you find interesting and write a short “reaction” to their post.
• Final Connections Project. You and a partner will chose one problem, from a list I will give you, to explore independently. You will solve the mathematics involved and write up your work clearly, demonstrating the mathematical communication skills you have developed over the term. As part of your write up, you will include a discussion of the problem. This project will be due at the last class of the term.

Computer Component: Technology plays an increasingly important role in our world. To prepare you to make use of the basic technology tools related to mathematics and the sciences, you will learn the basics of the computer system Mathematica. Many of you have used graphing calculators in high school. Mathematica is a step up the technology ladder from graphing calculators.

To help you learn how to use Mathematica, there will be regular computer-based assignments. Math majors will be available in the Mathematics Computer Lab (Park Sciences 354) at a variety of times to assist you in completing these assignments.

At times, I will be using Mathematica during our classes to illustrate material we are covering.

Tests: There will be two self-scheduled mid-term exams and a final exam. Tentative dates:

- 1^st Mid-term: week of Feb 23 – 27th

- 2^nd Mid-term: week of April 6^th – 10th

Final grades will be determined using the following percentages:

Homework and Computer Assignments	20%
Midterm Exam 1	20%
Midterm Exam 2	20%
Connections Project	15%
Final Exam	25%
Total	100%