Carla C. Morris - Fundamentals of Calculus

Copyright 2016 by John Wiley & Sons, Inc. All rights reserved

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

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Library of Congress Cataloging-in-Publication Data:

Morris, Carla C.

Fundamentals of Calculus / Carla C. Morris, Robert M. Stark.

pages cm

Includes bibliographical references and index.

ISBN 978-1-119-01526-0 (cloth)

1. CalculusTextbooks. I. Stark, Robert M., 1930- II. Title.

QA303.2.M67 2015

515dc23

2014042182

A fundamental calculus course is a staple for students in Business, Economics, and the Natural, Social, and Environmental Sciences, among others. Most topics within this book parallel conventional texts, and they appear here directly, unimpeded by lengthy examples, explanations, data, irrelevances, and redundancies. Examples are the primary means to illustrate concepts and techniques as students readily respond to them. While there are ample Exercises and Supplementary Exercises, distracting abundance is avoided. Arrow symbols interspersed in the text, UP ( ) and DOWN ( ), are used to signal student tips, insights, and general information much as an instructor might to students in class to help their understanding. UP arrows modestly increase text depth while DOWN arrows expand aid to students.

Students often question the importance and usefulness of calculus, and some find math courses confusing and difficult. To address such issues, one goal of the text is for students to understand that calculus techniques involve basic rules used in combinations to solve complex problems. The challenge to students is to disassemble problems into manageable components. For example, a derivative of [(f(x)g(x))/h(x)]r. The text encourages students to use power, quotient, and product rules for solutions. Another goal is to encourage students to understand calculus as the mathematics of change. To help, text examples guide students in modeling skills.

The elements of finite calculus lacking in most texts is a feature in this book, which serves multiple purposes. First, it offers an easier introduction by focusing on change and enables students to compare corresponding topics with differential calculus. Many may argue that it is the more natural calculus for social and other sciences. Besides, and equally important, finite calculus lends itself to modeling and spreadsheets. In Chapters 2 and 5, finite calculus is applied to marginal economic analysis, finance, growth, and decay.

Each chapter begins with an outline of sections, main topics of discussion, and examples. The outline displays topical chapter coverage and aids in finding items of particular interest. The Historical Notes sketch some of the rich 4000-year history of mathematics and its people.

Some students may skip Chapter 1, Linear Equations and Functions while others find it a useful review.

In Chapter 2, The Derivative finite differences are introduced naturally in forming derivatives and is a topic in its own right. Usually absent from applied calculus texts, finite calculus emphasizes understanding calculus as the mathematics of change (not simply rote techniques) and is an aid to popular spreadsheet modeling.

In Chapter 3, Using the Derivative students' newly acquired knowledge of a derivative appears in everyday contexts including marginal economic analysis. Early on, it shows students an application of calculus.

Chapter 4, Exponential and Logarithmic Functions delineates their principles. This chapter appears earlier than in other texts for two reasons. One, it allows for more complex derivatives to be discussed in Chapter 5 to include exponentials and logarithms. Two, it allows for the discussion on finite differences in Chapter 5 to be a lead in for integration in Chapter 6, Integral Calculus.

Chapter 5, Techniques of Differentiation treats the derivatives of products and quotients, maxima, and minima. Finite differences (or finite calculus) appear again in a brief section of this chapter. The anti-differences introduced in Chapter 5 anticipate the basics of integration in Chapter 6.

Chapters 7 and 8, Integration Techniques and Functions of Several Variables respectively, typify most texts. An exception is our inclusion of partial fractions.

Chapter 9, Series and Summations includes important insight to applications.

Chapter 10, Applications to Probability links calculus and probability.

The table below suggests sample topic choices for a basic calculus course:

A modestly priced Student Solutions Manual contains complete solutions.

Suggestions for improvements are welcome.