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

Title

The Lafayette College Calculus Laboratories--Third 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 required for these notebooks can be found in the file Packages.zip under the entry for the first semester of this course (Resource Library Database item 4304).

Description

These laboratory materials represent the third 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.

The third semester truly exploits the capabilities of Mathematica for great 3D graphics. See the linear programming Lab for a powerful example.

Topics:

Introduction to Second Order Differential Equations

Applications of Second Order Differential Equations

Geometric Linear Programming

Scalar Fields and Singularities

Critical Points for Scalar Fields

The Gradient

The Lagrange Multiplier Method

Multiple Integration

Storage Tank Design

Subject

Mathematics > Calculus and Analysis > Calculus

Related items

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

Downloads

README.txt (2.2 KB) - Author notes

Lab-01.nb (40.2 KB) - Introduction to Second Order Differential Equations

Lab-02.nb (54.5 KB) - Applications of Second Order Differential Equations

Lab-03.nb (36 KB) - Geometric Linear Programming

Lab-04.nb (27.8 KB) - Scalar Fields and Singularities

Lab-05.nb (55.3 KB) - Critical Points for Scalar Fields

Lab-06.nb (54.5 KB) - The Gradient

Lab-07.nb (41.9 KB) - The Lagrange Multiplier Method

Lab-08.nb (88.7 KB) - Multiple Integration

Lab-09.nb (118.3 KB) - Storage Tank Design

Files specific to Mathematica 2.2 version:

Lab-01.ma (15.4 KB) - Introduction to Second Order Differential Equations

Lab-02.ma (21.2 KB) - Applications of Second Order Differential Equations

Lab-03.ma (18.7 KB) - Geometric Linear Programming

Lab-04.ma (16.4 KB) - Scalar Fields and Singularities

Lab-05.ma (29.2 KB) - Critical Points for Scalar Fields

Lab-06.ma (20.1 KB) - The Gradient

Lab-07.ma (16.8 KB) - The Lagrange Multiplier Method

Lab-08.ma (40 KB) - Multiple Integration

Lab-09.ma (59.6 KB) - Storage Tank Design