The Lafayette College Calculus Laboratories--First Semester -- from Wolfram Library Archive

Title

The Lafayette College Calculus Laboratories--First Semester

Author

Robert Root

Organization:

Lafayette College

Department:

Mathematics

Education level

College

Objectives

The course differs from other Computer Algebra System-based Calculus sequences in several ways. The CAS is not in daily use by the students, they still must do most of their computations and algebra by hand. The CAS is included in a weekly laboratory only. This more conservative approach allows our laboratory with only 28 machines to serve a population of 250-300 calculus students a semester, with availability for occasional use by students in upper level courses as well. The laboratory is typically used to introduce students heuristically to a new topic before they encounter it in lecture or homework. We attempt to use the CAS to expose students to the concepts and techniques of calculus in (the now platitudinous) three ways: graphically, numerically, and symbolically.

Another goal of some labs is to introduce our students to applications that were previously too complex for beginning calculus students computational skills. Our sizable contingent of engineers are effectively motivated by this exposure, and increasingly are returning to Mathematica to solve their computational problems in courses beyond the calculus sequence.

Materials

Calculus, 5th edition by Swokowski (PWS)
Calculus, 4th edition by Stewart (Brooks Cole)

See below for the Mathematica notebook files for each of the laboratories. The packages in Packages.zip are required for all three semesters of this course.

Description

These laboratory materials represent the first semester in a three semester scientific and engineering calculus sequence developed at Lafayette College in Easton, Pennsylvania. These materials were assembled from a sequence of courses taught from Swokowski's Calculus, 5th edition, but they have been adapted and modified to fit the course taught from Stewart's text in its third and now its fourth edition. Throughout the changes in text the course has met three times per week in a conventional classroom setting and a fourth time in a Mathematica lab.

This course is meant to be only an incremental change from a traditional calculus course, introducing a CAS rather than a graphing calculator. While many of the labs could be implemented on a calculator, the graphics available on the computer screen are much better, and there are certain labs that use Mathematica's sophisticated graphical tools. For an example, see the rational functions lab or the Newton's method lab.

Topics:

Some Basics of Mathematics and Mathematica

Comparing Graphs of Functions

Estimating Limits

Secant Lines & Difference Quotients

Properties of Derivatives

Newton's Method of finding Roots

Extreme Values of Functions

Concavity & Derivatives

Rational Functions

Optimization

Area of a Region with Curved Boundary

Integrals, Areas and Average Temperatures

How Far to Harvard Square?

Subjects

	Applied Mathematics > Optimization
	Mathematics > Calculus and Analysis > Calculus

Related items

	The Lafayette College Calculus Laboratories--Second Semester [in Courseware and Class Materials]
	The Lafayette College Calculus Laboratories--Third Semester [in Courseware and Class Materials]

Downloads

LabReportSuggestions.txt (3.3 KB) - Plain-text file

PackagesREADME.txt (957 B) - Text file

README.txt (2.2 KB) - Author notes

Lab-01.nb (35.4 KB) - Some Basics of Mathematics and Mathematica

Lab-02.nb (66.6 KB) - Comparing Graphs of Functions

Lab-03.nb (37.6 KB) - Estimating Limits

Lab-04.nb (24 KB) - Secant Lines and Difference Quotients

Lab-05.nb (29.4 KB) - Properties of Derivatives

Lab-06.nb (35.9 KB) - Newton's Method for Finding Roots

Lab-07.nb (31 KB) - Extreme Values of Functions

Lab-08.nb (36.4 KB) - Concavity and Derivatives

Lab-09.nb (31 KB) - Rational Functions

Lab-10.nb (231.7 KB) - Optimization

Lab-11.nb (34.7 KB) - Area of a Region with Curved Boundary

Lab-12.nb (39.1 KB) - Integrals, Areas and Average Temperatures

Lab-13.nb (24.2 KB) - How Far to Harvard Square?

LabReportSuggestions.hqx (8.9 KB) - Macintosh format Word document

Mystery.m (1.2 KB) - For use with Lab-07.ma

Packages.zip (8.2 KB) - ZIP archive

RationalGraphics.m (18 KB) - For use with Lab-09.ma includes a command for putting rational functions in proper form.

Files specific to Mathematica 2.2 version:

Lab-01.ma (17.4 KB) - Some Basics of Mathematics and Mathematica

Lab-02.ma (29.5 KB) - Comparing Graphs of Functions

Lab-03.ma (22 KB) - Estimating Limits

Lab-04.ma (14.1 KB) - Secant Lines and Difference Quotients

Lab-05.ma (12.8 KB) - Properties of Derivatives

Lab-06.ma (17.4 KB) - Newton's Method for Finding Roots

Lab-07.ma (15.3 KB) - Extreme Values of Functions

Lab-08.ma (18.4 KB) - Concavity and Derivatives

Lab-09.ma (16.1 KB) - Rational Functions

Lab-10.ma (194.7 KB) - Optimization

Lab-11.ma (19 KB) - Area of a Region with Curved Boundary

Lab-12.ma (22.1 KB) - Integrals, Areas and Average Temperatures

Lab-13.ma (18.1 KB) - How Far to Harvard Square?