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Math 221 - Calculus and Analytic Geometry I     vanvleck.gif (8145 bytes)
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Timetable Information
Current Syllabus
Older Calculus Sequence Syllabus (out of date in many ways but contains more details)
Catalog Description

Introduction to differential and integral calculus and plane analytic geometry; applications; transcendental functions.

Catalog Prerequisites: (I) Advanced mathematical competence-algebra & suitable placement scores, or Math 112, and (II) Advanced mathematical competence-trigonometry & suitable placement scores, or Math 113; or Math 114. Open to Freshmen. May not receive credit for both Math 211 & 221.

Course Prerequisite(s)

Mathematics 112 and 113, or Mathematics 114, or appropriate placement test scores. (For further information see the statement on preparation for UW Madison mathematics courses and description of UW System mathematics placement tests.)

Prerequisite knowledge and/or skills

Algebra skills for manipulating polynomials and functions, trigonometry skills including elementary functions in radian measure and knowledge of trigonometric identities and formulas.

Textbook(s) and/or other required material
Calculus 8th edition, by Varberg, Purcell, and Rigdon, Prentice Hall, 1999 (Linked to publisher's web pages)
Course objectives

Students who complete this course will be able to use the techniques of single variable calculus to solve problems, and be able to expand their knowledge as needed to confront new situations. As specific skills, the student will be able to:

Read and learn additional mathematics from a text or reference book
Use the notation and terminology of functions
Use limits in an informal setting
Calculate and apply derivatives of elementary functions
Use the derivative to find rates of change, tangent lines, linear and quadratic approximations, and relative and absolute extrema, in abstract as well as applied situations
Find and apply antiderivatives, indefinite integrals, and definite integrals
Solve simple differential equations and initial value problems for position, velocity, acceleration, and exponential growth and decay
Set up and evaluate a Riemann sum describing an application and leading to a definite integral
Evaluate indefinite integrals using substitution
Use the Fundamental Theorem of Calculus to find derivatives of functions given by integrals
Use the Fundamental Theorem of Calculus and substitution to evaluate definite integrals
Topics covered
Functions and graphing
Limits, intuitively and with an idea of how they can be formalized, including limits at infinity and infinite limits and l'Hopital's rule
Derivatives of first and higher order, differentiation formulas, rates of change, the chain rule and implicit differentiation, related rates and differentials, Newton's method
Inverse functions, exponential and logarithmic functions, inverse trigonometric functions, hyperbolic functions, and applications of these functions
Geometric implications of the first and second derivative and applications to finding extrema
Antiderivatives, summation and the definite integral, the Fundamental Theorem of Calculus, and substitution in integration
Applications of integration to finding area, volume, work, and average value
Class/laboratory schedule

Three hours of lecture each week (either 50 minutes MWF or 75 minutes TR) and two hours in discussion section.

Contribution of course to professional development of engineers and scientists:

This course contributes primarily to the students' knowledge of college-level mathematics and/or basic sciences, but does not provide experimental evidence.
(Some laboratory exercises will make use of real data from experiments, but they are provided to the student rather than being measured by the student personally.)

Calculus is a fundamental tool both in science and engineering courses which the student will take and also in professional applications. Even though the practicing engineer may use a calculator or computer to carry out a calculation, it is important that he/she knows what the technology is being asked to perform and how to tell if the answer is reasonable.This material is also key to understanding much of human thought for the last several hundred years. This course is the first in a sequence and provides basic skills and understanding which later courses will build on.

Relationship of course to undergraduate engineering objectives:

This course serves students in a variety of engineering majors. The paragraph below describes how the course contributes to the college's educational objectives.

The skills learned in this course are essential to success in most science and engineering courses the student will be taking, and the course uses examples which feed into those courses. In addition, the course builds an understanding of how abstract foundations support and frequently evolve into concrete technologies.

Assessment of student progress toward course objectives
Two or three examinations during the semester (typically 90 minutes, given in the evenings) and a two hour final examination
Homework, participation in discussion section, and quiz grades from discussion section
(some sections) Computer laboratory assignments, done in small groups and handed in as a group effort
(some sections) Term projects, which may be term papers or in-depth mathematical investigations
Person(s) who prepared this description
Robert L. Wilson