J. E. Helmreich
Spring 2008
Calculus II 
MATH 242L-111

Syllabus 

Overview: The two major concepts of Calculus are differentiation and integration. The former involves slopes, rates of change, acceleration etc., while the latter concerns areas, volumes, mass. What makes both processes work is the idea of a limit, an infinite (and yet finite) process. Many of these ideas were known geometrically to the ancient Greeks. They were developed analytically (using algebra) by mathematicians such as Leibnitz and Newton, and finally put on a solid theoretical foundation by the mathematicians of the nineteenth century. It is not an overstatement to say that Calculus represents one of the greatest creations of the rational human mind. In this course we continue the study of Calculus begun in Math 241, while concentrating on integration and tests of convergence of sequences and series.

Class: Monday 11:00 - 12:15, Wednesday and Friday 9:30 - 10:45 in Lowell Thomas 208.

Office Location: Lowell Thomas 107
845-575-3000 x2615
James.Helmreich@Marist.edu

Office Hours:  I am available at hours other than those listed below; if you would like to meet outside these posted hours please email or call to set up an appointment.  During the hours given below you do not need an appointment, I will be in my office and available on a first come basis.  I am actually in my office many more hours than the list indicates.  Generally if I am in my office I will be happy to meet with you, so feel free to stop by to see if I am in at times other than those listed.

Text: Single Variable Calculus Early Transcendentals, 6th edition. James Stewart, Thomson Brooks/Cole, 2003. ISBN-10: 049501169X ISBN-13: 978-0495011699

Calculator: The TI-83+ or TI-84+ calculator or functional equivalent is required for this course.

Student Learning Outcomes: Having successfully completed this course you will be expected to demonstrate:

• an understanding of the basic theory of functions in several classes, including polynomial functions, algebraic functions, trigonometric functions, exponential functions, and logarithmic functions
• an ability to select appropriate techniques, and perform the computation required, for the integration of functions in the above classes
• an understanding of functions presented in parametric form or polar form
• an ability to select appropriate techniques, and perform the computations required, for the differentiation and integration of functions presented in the above forms
• an understanding of the basic theory of infinite sequences and series
• an ability to select appropriate techniques, and perform the computation required, to test infinite sequences and series for convergence
• an ability to select and apply appropriate models from among those listed above in order to solve applied problems from a variety of disciplines
• an ability to communicate the processes used in the above analyses (and the results of those analyses) in a concise, coherent, and mathematically correct manner

Outcomes Assessment: You will be required to complete in-class weekly quizzes, three exams during the semester, and a cumulative final exam at the end of the course. All problems assigned in these exercises will be designed to assess your progress in one or more of the following areas:

• the ability to select he appropriate model needed to solve an applied problem
• the ability to select the appropriate technique to work within a model
• the ability to perform the basic computations necessary for a given technique within a model
• the ability to give a written account of the analysis used and a interpretation of the results of that analysis

The grading methodology will be as follows: the lowest two quiz grades will be dropped and the remaining quiz grades averaged. This grade will be combined with the three exam grades, giving four major scores. The lowest of these four scores will be dropped; the remaining three scores averaged will represent 70% of the course grade. The cumulative final examination will account for the remaining 30% of the course grade. There is one exception: in the case where the final examination score is higher than the average of the (highest) three main scores obtained earlier, the final exam score will represent 100% of the course grade. 

Policies:

• I will assign homework most class days. Homework will not generally be graded, but is intended to provide you with problems similar to those that you will be expected to complete on quizzes and exams.
• Quizzes will be given on Wednesdays beginning January 23rd. Missed quizzes may not be made up under any circumstances and will receive a grade of zero. Remember two quiz grades will be dropped in computing your quiz average.
• Exams will be given on Wednesday February 20th, Wednesday April 2nd, and Wednesday April 30th. Missed exams may not be made up under any circumstances, and will receive a grade of zero. Remember that one exam will be dropped in computing your exam average.
• Work on examinations is of course expected to be solely your own. You should be familiar with the Marist College Academic Honesty Policy in the student handbook.
• I do not take formal attendance. More than three absences from class will be cause for concern on my part, and should be on yours. You are only hurting yourself by not being in class.
• I do not discuss grades by e-mail or by phone. I will not respond to e-mails or phone messages with inquires about grading. If you wish to discuss your grade at any point, please see me during office hours. While I will never assign a grade that is lower than the numerical average indicates, I reserve the right to raise grades to account for special circumstances such as (but not limited to) steady improvement over the course of the semester.
• Please be sure to turn off all electronic devices other than a graphing calculator during class. This includes laptops.
• Habitually arriving to class late, or habitually leaving class and returning`, is distracting and rude to all others in the class. Please be on time and expect to remain for the entire period.

Suggestions:

• Do not miss class.
• Do the homework consistently.
• Ask questions and participate in class.
• I strongly encourage you to work with others in the class on homework problems. Study groups are an excellent way to help learn the material.
• Take advantage of my office hours, I am there to help.
• Take advantage of the MATHLAB. It is a good place to work and have someone to answer questions from time to time as you work. It is also a good place to meet and work with others in class.
• Do not fall behind. It can be very difficult to catch up in a course such as this where later material builds directly on earlier material.

Chapter and Section Outline: What follows is a tentative outline of the sections we will cover this semester. It is ambitious and we may not be able to cover all material.

Section	Topic
5.5	The Substitution Rule - Review
6.1	Areas Between Curves
6.2	Volumes
6.3	Volumes by Cylindrical Shells
7.1	Integration by Parts
7.3	Trigonometric Substitution
7.4	Integration of Rational Functions by Partial Fractions
7.5	Strategy for Integration
4.4	Indeterminate Forms and L'Hospital's Rule
7.8	Improper Integrals
11.1	Sequences
11.2	Series
11.3	The Integral Test and Estimates of Sums
11.4	The Comparison Tests
11.5	Alternating Series
11.6	Absolute Convergence and the Ratio and Root Tests
11.7	Strategy for Testing Series
11.8	Power Series
11.9	Representations of Functions as Power Series
11.10	Taylor and Maclaurin Series
7.7	Approximate Integration
10.1	Curves Defined by Parametric Equations
10.2	Tangents and Areas
10.3	Polar Coordinates
10.4	Areas and Lengths in Polar Coordinates
6.4	Work
6.5	Average Value of a Function
8.1	Arc Length
8.2	Area of a Surface of Revolution
8.4	Applications to Economics and Biology

Note: The Final Exam will be announced as soon as the registrar announces the schedule.

I reserve the right to change this syllabus.

Last Modified January 3, 2008