Calculus I. Spring Instructor: Daniel Stein Warren Weaver

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1 Calculus I Spring 2006 Class Times/Location: MW 8:55-10:45 AM Silver 512 Instructor: Daniel Stein Warren Weaver daniel.stein@nyu.edu Note: Calculus I is taught in groups of three sections. The two other sections of this group will be taught by Dr. Zhiwu Lin and Mr. Yakov Kerzhner. All lectures are given at the same time. There will be a common set of homeworks and exams, and grading policies will be uniform throughout this group. Instructor Office Hours: Mondays 1:00-2:00 PM Tuesdays 1:00-2:00 PM or by appointment Grader: Yu Ning Wallice Ao wallice.ao@nyu.edu Primary Text: Calculus I: One Variable by Salas, Hille, and Etgen (Wiley Custom Services). Supplementary Text: Differential Calculus I, II by R. Courant (Wiley). Course Information Announcements, information, and occasional printed materials will be available via Blackboard. Login to NYU Home at: click on the "Academics" Tab in the top right-hand corner of NYU Home, and under the "Classes" channel, click on the link to Calculus I. Course Goals The goals of this course are for you to understand the central ideas underlying the calculus of functions with one variable and be able to solve problems that arise naturally within this subject. The course is designed to help you develop general ``math skills'', which include not just solving problems (though especially that), but also how to approach a problem, break it down into smaller parts, understand the concepts behind the methods, analyze the meaning of your answer, and judge whether the answer you arrive

2 CALCULUS I 2 at is reasonable. We will discuss applications to other sciences whenever possible. We hope that you will be able to repeatedly use the skills you acquire in this course for years to come. Reading You will need to complete assigned readings before class each day, as indicated on the course schedule, and come to class prepared to participate in activities and discussions about those topics. You will benefit enormously if you reread the assigned sections after the week's lectures. Lectures The lectures are a central part of the course. They will not be a simple following of the book. I will use alternative derivations when possible, give lots of examples and do sample problems not in the book, occasionally introduce topics not covered (or covered later) in the book, and, of course, answer questions. Come with questions --- class participation is strongly encouraged (and rewarded)! Tutoring There is free tutoring available, provided both by the Math Department and by the University through the College Learning Center. Hours for the Math Department tutoring sessions are posted on the 7 th floor of WWH, and will also appear on the course's Blackboard page. Free help specifically for Calculus I is available through the College Learning Center in Weinstein Hall; for tutoring hours, go to click on Schedule, and follow the appropriate links. Using available tutoring facilities is optional, of course, but strongly encouraged when extra help would be useful with the weekly readings, problem sets, or studying. Problem Sets You will be given weekly homework assignments, to be handed in at the beginning of class each Wednesday. Solution sets will be posted on Blackboard within 24 hours of each homework's due date. If you encounter a problem where you cannot complete an assignment by its due date, then you must see me in advance to ask for an extension. You should do this only if urgent problems (e.g., medical, family emergency) arise. Unexcused late homeworks will not be accepted. You are welcome (and encouraged) to form study groups and to discuss the

3 CALCULUS I 3 problems with other students. However, you must turn in your own work, both as a matter of academic honesty and also because if you don't, you are guaranteed to do poorly on the exams. Examinations There will be three (non-cumulative) 50-minute exams during the semester, and a cumulative 1-hour, 50-minute final exam. The subjects covered and the exam dates are given below. Each in-class exam will test you on material covered in class, homework, or readings since the previous exam and up to one week prior to the exam date. The final exam will be comprehensive and cover every topic over the entire semester. If you have to miss an exam for any non-medical reason, you must make arrangements with me in advance. A missed exam (with no medical excuse or special arrangement) will receive a grade of zero. The in-class examination dates will be Monday, February 13; Wednesday, March 8; and Wednesday, April 12. Student Assessment As just mentioned, there will be three fifty-minute exams during the semester, plus a cumulative one-hour, fifty-minute final exam. The score for each aspect of the course will be normalized to 100, and the final scores will be calculated using the following weighting: Problem Sets 20% In-Class Exams (best 2 out of 3) 40% Final Exam 40% Note that your lowest exam score (excluding the final) will be dropped. Course Resources Please do not be afraid to ask for help. There are many resources available to help you be successful in this course. In no particular order, these include: o Instructor s office hours o to instructor o Student-formed study groups o Math Department tutoring o College Learning Center tutoring

4 CALCULUS I 4 Feedback Please ask questions during lectures and sections. If there is something you don't understand, I guarantee you that many others are having the same problem. Plus, an interactive class is more fun for both the students and the instructor. If there is some aspect about the pace, content, or structure of the course you don't like, or other feedback you'd like to give, please let me know as soon as possible. Remember, this course is for you! The tentative course schedule appears on p. 5.

5 CALCULUS I 5 Course Schedule Week Lecture Chapter Topics Limits 2 2.4, 3.1 The derivative Differentiation formulas The derivative as a rate of change The chain rule 1 2.5, 3.6 Derivatives of trigonometric functions 2 3.7, 3.9 Implicit differentiation, differentials, and linear approximations Mean value theorem, maxima and minima 2 4.3, 4.8 Curve sketching Endpoints, extreme values Optimization Area as a definite integral Antidifferentiation Fundamental theorem of calculus Indefinite integrals Integration by substitution Applications of the integral Applications of the integral (continued) Logarithmic functions Logarithmic and exponential functions Integrals involving logs and exponentials Exponential growth and decay Inverse trigonometric functions Integration by parts Integration by parts (continued) Final Exam (cumulative) Tuesday, May 9, :00-11:50 AM

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Math 181, Calculus I

Math 181, Calculus I [Semester] [Class meeting days/times] [Location] INSTRUCTOR INFORMATION: Name: Office location: Office hours: Mailbox: Phone: Email: Required Material and Access: Textbook: Stewart,