Arangala Crista - Exploring calculus: labs and projects with mathematica

Exploring Calculus

Labs and Projects with Mathematica

TEXTBOOKS in MATHEMATICS

Series Editors: Al Boggess and Ken Rosen

PUBLISHED TITLES

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TEXTBOOKS in MATHEMATICS

Exploring Calculus

Labs and Projects with Mathematica

Crista Arangala

Elon University
North Carolina, USA

Karen A. Yokley

Elon University
North Carolina, USA

CRC Press

Taylor & Francis Group

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Library of Congress Cataloging-in-Publication Data

Names: Arangala, Crista. | Yokley, Karen A., 1976

Title: Exploring calculus : labs and projects with Mathematica / Crista Arangala and Karen A. Yokley.

Description: Boca Raton : Taylor & Francis, 2017. | Series: Textbooks in mathematics ; 42 | A CRC title. | Includes bibliographical references and index.

Identifiers: LCCN 2016010816 | ISBN 9781498771016 (alk. paper)

Subjects: LCSH: Calculus--Computer-assisted instruction. | Calculus--Data processing. | Mathematica (Computer file)

Classification: LCC QA303.5.C65 A73 2017 | DDC 515.0285/53--dc23

LC record available at https://lccn.loc.gov/2016010816

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Contents

This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus, or on occasion to emphasize a particular topic. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections.

The exercise sections integrate problems, technology, Mathematica visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way.

For those just starting with Mathematica, Lab 0 gives a good introduction to how to use the algebra system as it relates to beginning calculus curriculum and is a great place for first year calculus students to start. Note that if commands in labs are in bold, then they should be typed exactly as they are provided.

Following each chapter is a project set. Each project set consists of application-driven projects that emphasize the material in the chapter. Projects in each chapter have been ordered in the project set roughly in order of difficulty. Many of these projects foreshadow future topics of study, such as partial derivatives, center of mass, Fourier series, and Laplace transforms; and students should be encouraged to use many of these projects as the basis for further undergraduate research.

Related to the context of the text, we are aware that some choose to do transcendental functions earlier than others. We have chosen to put an introduction to exponential functions in : Lab 25 after learning some basic integration techniques. We believe that this is an appropriate place to introduce this material.