21-122 Integration, Differential Equations, and Approximation
Spring 2006 - (10 units)

Instructor:

Dr. Timothy Flaherty
Office: Wean Hall 6101
e-mail: tim@andrew.cmu.edu
Course Web Page: http://www.math.cmu.edu/~tim/122s06/122s06.html
Text: Calculus: Early Transcendentals, 5th edition, by James Stewart

Introduction: First we'll learn some more techniques of integration, for which it is very important that you know integration by substitution and integration by parts. Then we'll approximate integrals using techniques such as Simpson's Rule. We'll consider improper integrals - where either the function or the domain is unbounded.

Differential equations are equations involving a function and its derivative. We wish to solve for the function that satisfies such an equation. Integration will be required to solve these equations. We'll see some of the many ways that differential equations are used in applications.

Then, the course changes to a study of sequences and series. We will really be doing analysis, and the role of Calculus will be reduced. You must adjust to a more advanced process - we will be analyzing sequences and series for convergence, using a variety of methods. Mathematical maturity is required, and you'll need to be able to write arguments (proofs). Once we understand sequences and series, we'll represent functions by power series, and using Taylor series we will be able to approximate functions by polynomials, and determine the accuracy of these approximations on specified intervals.

Lectures: Tardiness and absence from class is strongly discouraged. Students are encouraged to ask questions and participate in class. You are responsible for all of the material and announcements presented during lecture. A lesson schedule plan which will include section(s) to be covered and homework assigned on each lecture date is posted on the course web page. This schedule may be modified at any time, but we will try to follow it closely. You are encouraged to read the text material in advance to prepare for each lecture. Students will also have two periods a week of recitation supervised by a teaching assistant. The purpose of the recitation is to solve problems and ask questions related to the text or lecture.

Text Homework: Homework problems from the text will be announced in class and posted on the course web page. You are expected to do every problem assigned. Your homework will not be collected. You goal should be a complete and thorough understanding of the material as demonstrated by your ability to handle the homework problems with ease. To accomplish this, you may expect to spend a considerable amount of time working many problems, and seeking help for those problems which you can not do. Often it will be necessary to work problems that are not assigned to gain a thorough understanding. These problems will be discussed in lecture and recitation, and you are expected to contribute.

Web Homework: Homework problems will be assigned for you to do over the Web. These problems must be completed by the posted deadline for each assignment to receive full credit. Late HW will be penalized. Follow the instructions on the course web page to register and take the assignments.

Quizzes: We will have a short quiz given during most recitations. You must take your quiz during your assigned recitation. See the posted schedule for the exact dates. Your quiz will typically be one problem from the most recent homework. Each quiz will be worth $2$ points. To earn $2$ points you must solve the problem correctly, clearly presenting your work. You will recieve a $0$ if you do not take the quiz, or your work does not establish that you understand the problem and the method of solution. Anything else will earn a $1$. Your final quiz score will be determined using the curve $c(x)=x(2-x)$. If an emergency prevents you from taking a quiz you must contact your instructor immediately.

Exams: There will be four exams, scheduled as follows: Exam I: Friday, February 10th, Exam II: Wednesday, March 8th, Exam III: Monday, April 17th, Final Exam : To be announced.

Please refer to the seperate sheet posted on the couse web page for the exam policies.

Make-up Exams: Will not be provided unless the student documents an illness or emergency at the earliest possible time. Any conflict with a university sponsored event must be brought to the instructor before the exam date for a make-up to be considered. You may notify the instructor in person, by e-mail, by phone, or by leaving a message at the Mathematics Department office at 412-268-2545. Any student requiring extra time shall notify the instructor at least one week prior to an exam.

Academic Honesty: We will strictly apply the university guidelines as stated in the student handbook to ensure academic honesty.

Calculators and Computers: Calculators will not be permitted during exams or quizzes.

Pre-requisites: You are also expected to be able to apply the fundamental concepts covered in 21-120. Specifically, you are expected to understand the concepts of differentiation and integration, how to compute derivatives and integrals, and how these concepts are applied.

Grades: Your grade will be determined by the quizzes and exams using the following weights. Web HW: 15 % Quiz average: 15 %. Low Exam Score: 10 % Middle Exam Score: 15 %. High Exam Score: 20 %. Final Exam: 25 %.