22M:25
Calculus I
Lecture JJJ
Fall 2005



Contact/class information

Instructor:         Dr. David Stewart
Phone: 335-3832
Email: dstewart -at- math dot uiowa dot edu
WWW URL: http://www.math.uiowa.edu/~dstewart/
Office: MLH 325B
Office hours: 10:30 - 11:30am MWF
Class times: JJJ: 2:30 - 3:20pm MWF
Discussion sections: J17: 2:30pm TuTh 3083 LIB; J18: 1:30pm TuTh 3083 LIB
Class location: JJJ: 217 MLH

You can see me outside the office hours provided it is mutually convenient. You can use email to set up an appointment time.

Resources

Information about other resources will be posted on ICON.

Homework 

Description

This course is about the basics of differential and integral calculus. After starting with some basic ideas (particularly real numbers and functions) we will introduce limits and then derivatives. After seeing how to compute derivatives and using them for finding minima and maxima of functions, we will introduce integrals and then link integrals and derivatives through the Fundamental Theorem of Calculus.

Textbook

Calculus (Early Transcendentals Single Variable) by J. Stewart, 5th Edition, 2003; Published by Brooks/Cole. This textbook is available through the University bookstore.

Syllabus

  1. Chapter 1: Functions and models. Functions and their representations; mathematical models; familiar functions (linear, polynomial, and rational functions); trigonometric functions; exponential and logarithmic functions.
  2. Chapter 2: Limits and derivatives. What is a limit? Velocity as a limit; computing limits; limit laws; the precise definition of limit; continuity of functions; limits at infinity; tangents, velocities and derivatives; the derivative of a function is a function.
  3. Chapter 3: Differentiation rules. Sum and power rules; product and quotient rules; derivatives of trig functions; chain rule; implicit differentiation; higher derivatives; derivatives of logarithmic functions and exponential functions; hyperbolic functions and their derivatives; linear approximation and derivatives.
  4. Chapter 4: Applications of differentiation. Maxima and minima; mean value theorem; graph sketching; using derivatives to compute limits: l'Hospital's rule; optimization; economics; Newton's method.
  5. Chapter 5: Integrals. Areas and distances; integrals as ``areas under a curve''; the definite integral; the Fundamental Theorem of Calculus; indefinite integrals; substitutions and the chain rule; the logarithm function as an integral.
  6. Chapter 6: Applications of integrals. Areas between curves; volumes, volumes by shells.

Assessment

There will be weekly homework assignments, two mid-semester exams, and a final comprehensive exam. The homework will count for 30% of the final assessment, the mid-semester exams will count 20% of the final assessment each, and the final exam will count for the remaining 30% of the assessment. There will also be ungraded exercises to help you exercise your skills.

The homework is a vital part of the course. If you don't do it, you won't just miss out on 30% of the assessment, but you probably won't get the practice or learn what you need for doing the exams either.

Notes

  1. The course plan may be modified during the semester. Such modifications will be announced in advance during class periods; the student has responsibility for keeping up with such changes. You should also make a habit of reviewing the class web page, which is accessible via: 
    http://www.math.uiowa.edu/~dstewart/classes/ 
    This page will have homework details and other information posted to it as the class progresses.
  2. The Department of Mathematics offices are in 14 McLean Hall (MLH). You can contact the chair of the department through the Departmental Secretary at 14 MLH or by calling 335-0714.
  3. Please let you instructor know if you have a disability that requires special arrangements. I need to hear from anyone who has a disability which may require some modification of seating, testing or other class requirements so that appropriate arrangements can be made. Please see me after class or during my office hours.
  4. Be sure to read the section titled Student Complaints Concerning Faculty Actions on page 23 of the Schedule of Classes (Fall 1999).
  5. This course is given by the College of Liberal Arts and Sciences. This means that class policies on matters such as requirements, grading, and sanctions for academic dishonesty are governed by the College of Liberal Arts and Sciences. Students wishing to add or drop this course after the official deadline must receive the approval of the Dean of the College of Liberal Arts and Sciences. Details of the University policy of cross enrollments may be found at: http://www.uiowa.edu/~provost/deos/crossenroll.doc .
David Stewart 2005-08-18