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CALCULUS AND ANALYTIC GEOMETRY : FOR ENGINEERING TECHNOLOGY
₹9176
CALCULUS AND ANALYTIC GEOMETRY : FOR ENGINEERING TECHNOLOGY
This book is an outgrowth of our Technical Mathematics with Calculus. It is in¬tended for students enrolled in an engineering technology curriculum. The material is presented under the assumption that the student has a working knowledge of col¬lege-level algebra and trigonometry.
The primary objective of a technical calculus book is to relate mathematical concepts to practical engineering technology problems. We have attempted to attain this goal by using physical problems that are well within the scope of the beginning student as a springboard to mathematical concepts. Our approach is exemplified in Chapters 2 and 6 in connection with the concepts of the derivative and the definite integral, respectively. Both chapters are designed to lead the student to the desired mathematical concept by identifying the common thread in several apparently unre¬lated physical problems. For example, in Chapter 2, the similarity in the solutions to the slope of a tangent line, the velocity of a particle, and the current in a circuit is used to motivate the definition of the derivative.
The scope of topics covered in the text is standard for technical calculus books. Algebraic functions are discussed in the preliminary chapters and are fol¬lowed by the transcendental functions. Selected topics from differential equations and infinite series are presented in the concluding chapters.
Analytic geometry is presented as it is needed to facilitate an understanding of calculus applications. Except in Chapters 1 and 11, the two subjects are inter¬woven. The conic sections of Chapter 11 can be taught at any time after Chapter 1 is covered, but they are delayed in the arrangement of topics to allow earlier coverage of the transcendental functions. The book is designed to satisfy the needs of a two semester course; however, those desiring a one-semester coverage of calculus will find the first seven chapters ideal for this purpose.
The presentation features a variety of learning aids. Numerous worked ex¬amples are included in each section, many of which have step-by-step comments to lead students through the solution. Because repetition is an important part of the learning process, we have included an abundant supply of graded problems in the end-of-section exercise sets. In addition, each chapter concludes with a set of review exercises. Exercises with application to a specific technology are "called-out" with a distinctive logo. (A key to the application symbols follows the Table of Contents.) Answers to the odd-numbered exercises are provided at the end of the book.
Comment and Warning statements are included throughout the book to alert the student to important ideas and processes and to warn of common pitfalls. Also, many of the mathematical procedures are presented in an easy-to-follow, step¬by-step format. These procedural steps are boxed - as ar~ key formulas, equations, and definitions - for emphasis and for easy reference. An additional learning aid is the Glossary of Important Terms at the back of the book.
Several important concepts in the book are reinforced through the use of simple computer programs. These interactive programs are written in BASIC lan¬guage for the Apple lIe computer. They occur at the ends of selected sections and are highlighted with the application symbol shown at the left. The programs will help the student understand the process or concept being presented in the section. We are grateful to Professor 1. W. Friel for permitting us to use these programs. Anyone interested in further information on these programs may contact Professor Friel at the University of Dayton.
Finally, we wish to acknowledge the contributions of the following individ¬uals who reviewed the manuscript for this text: Henry D. Davison, St. Petersburg Junior College; David Sherren, Fairmont State College; Donald W. Sibrel, Nashville State Technical Institute; Lawrence A. Trivieri, Mohawk Valley Community College; Roman Voronka, New Jersey Institute of Technology. Thanks also to our editor at Breton Publishers, George J. Horesta, and to Sylvia Dovner and her staff at Techni¬cal Texts, Inc., for their efforts on behalf of this project.
Bernard 1. Rice Jerry D. Strange
CHAPTER Prerequisites for Calculus
1.1 The Real Number Line
1.2 The Cartesian Coordinate System
Exercises for Sections 1.1-1.2
1.3 Functions
Exercises for Section 1.3
1.4 Linear Functions: Straight Lines
Exercises for Section 1.4
1.5 Quadratic Functions: Parabolic Graphs
Exercises for Section 1.5
1.6 Rational Functions
Exercises for Section 1.6
1.7 Multirule Functions
Exercises for Section 1.7
Review Exercises for Chapter 1
CHAPTER 2 The Rate of Change of a Function
2.1 Limits and Continuity
Exercises for Section 2.1
2.2 More on Limits
Exercises for Section 2.2
2.3 Applications of the Limit Idea
Exercises for Section 2.3
2.4 The Derivative
Exercises for Section 2.4
Review Exercises for Chapter 2
CHAPTER 3 Formulas for Finding the Derivative
3.1 Derivatives of Polynomials
Exercises for Section 3.1
3.2 Composite Functions
Exercises for Section 3.2
3.3 Derivatives of Products and Quotients
Exercises for Section 3.3
3.4 Higher-Order Derivatives
Exercises for Section 3.4
3.5 Implicit Differentiation
Exercises for Section 3.5
Review Exercises for Chapter 3
CHAPTER 4 Applications of the Derivative
4.1 Applications to Mechanics
Exercises for Section 4.1
4.2 Applications to Electricity
Exercises for Section 4.2
4.3 Related Rates
Exercises for Section 4.3
4.4 Maximum and Minimum Values of a Function
Exercises for Section 4.4
4.5 The Second Derivative Test
Exercises for Section 4.5
4.6 Curve Sketching
Exercises for Section 4.6
4.7 Applied Maximum and Minimum Problems
Exercises for Section 4.7
4.8 Differentials
Exercises for Section 4.8
Review Exercises for Chapter 4
CHAPTERS The Antiderivative and Its Applications
5.1 The Antiderivative or Integral of a Function
Exercises for Section 5.1
5.2 The Intergralofundu
Exercises for Section 5.2
5.3 Linear Motion
Exercises for Section 5.3
5.4 Series and Parallel Circuits
Exercises for Section 5.4
Review Exercises for Chapter 5
CHAPTER 6 The Definite Integral
6.1 Summation Notation
Exercises for Section 6.1
6.2 Two Problems Involving the Summation of Elements
Exercises for Section 6.2
6.3 The Definite Integral
Exercises for Section 6.3
6.4 The Fundamental Theorem of Calculus
Exercises for Section 6.4
6.5 Properties of the Definite Integral
Exercises for Section 6.5
6.6 Approximate Integration
Exercises for Section 6.6
Review Exercises for Chapter 6
CHAPTER 7 Applications of the Definite Integral
7.1 Area
Exercises for Section 7.1
7.2 Area Between Two Curves
Exercises for Section 7.2
7.3 Centroids
Exercises for Section 7.3
7.4 Volumes of Revolution
Exercises for Section 7.4
7.5 Moments of Inertia
Exercises for Section 7.5
7.6 Force and Work
Exercises for Section 7.6
Review Exercises for Chapter 7
CHAPTER 8 Exponential and Logarithmic Functions
8.1 Review Topics
Exercises for Section 8.1
8.2 Derivatives of Logarithmic Functions
Exercises for Section 8.2
8.3 Logarithmic Differentiation
Exercises for Section 8.3
8.4 Derivatives of Exponential Functions
Exercises for Section 8.4
8.5 Integrals of Reciprocal Functions
Exercises for Section 8.5
8.6 Integrals of Exponential Functions
Exercises for Section 8.6
Review Exercises for Chapter 8
CHAPTER 9 Trigonometric Functions
9.1 Review Topics
Exercises for Section 9.1
9.2 Derivative Formulas for the Sine and the Cosine Functions
Exercises for Section 9.2
9.3 Derivatives of the Other Trigonometric Functions
Exercises for Section 9.3
9.4 Inverse Trigonometric Functions
Exercises for Section 9.4
9.5 Derivatives of Inverse Trigonometric Functions
Exercises for Section 9.5
9.6 Integrals of Trigonometric Functions
Exercises for Section 9.6
9.7 Using Identities to Simplify Trigonometric Integrands
Exercises for Section 9.7
9.8 Integrals that Yield Inverse Trigonometric Functions
Exercises for Section 9.8
Review Exercises for Chapter 9
CHAPTER 10 Integration Techniques and Improper Integrals
10.1 Changing the Variable of Integration
Exercises for Section 10.1
10.2 Integration by Parts
Exercises for Section 10.2
10.3 Partial Fractions
Exercises for Section 10.3
10.4 Improper Integrals
Exercises for Section 10.4
Review Exercises for Chapter 10
CHAPTER 11 Conic Sections
11.1 The Parabola
Exercises for Section 11.1
11.2 The Ellipse
Exercises for Section 11.2
11.3 The Hyperbola
Exercises for Section 11.3
11.4 Translation of Axes
Exercises for Section 11.4
11.5 The General Second-Degree Equation
Exercises for Section 11.5
Review Exercises for Chapter 11
CHAPTER 12 Calculus of Functions of Two Variables
12.1 Functions of Two Variables
Exercises for Section 12.1
12.2 Partial Differentiation
Exercises for Section 12.2
12.3 Total Differentials and Derivatives
Exercises for Section 12.3
12.4 Iterated Integrals
Exercises for Section 12.4
12.5 Area as an Iterated Integral
Exercises for Section 12.5
12.6 Double Integration
Exercises for Section 12.6
12.7 Volume as a Double Integral
Exercises for Section 12.7
Review Exercises for Chapter 12
CHAPTER 13 Differential Equations
13.1 Some Elementary Terminology
Exercises for Section 13.1
13.2 Separable Equations
Exercises for Section 13.2
13.3 Linear Equations of the First Order
Exercises for Section 13.3
13.4 Applications of Linear Equations
Exercises for Section 13.4
13.5 Differential Equations of the Form
Exercises for Section 13.5
13.6 Undamped Vibrations
Exercises for Section 13.6
13.7 Damped Vibrations
Exercises for Section 13.7
13.8 Laplace Transform
Exercises for Section 13.8
13.9 Solving Differential Equations
Exercises for Section 13.9
Review Exercises for Chapter 13
CHAPTER14 Vectors, Parametric Equations, and Polar Coordinates
14.1 Vectors in the Plane
Exercises for Section 14.1
14.2 Parametric Equations
Exercises for Section 14.2
14.3 Tangents to Curves
Exercises for Section 14.3
14.4 Length of Arc
Exercises for Section 14.4
14.5 Polar Coordinates
Exercises for Section 14.5
14.6 Area and Arc Length in Polar Coordinates
Exercises for Section 14.6
Review Exercises for Chapter 14
CHAPTER15 Infinite Series
15.1 Sequences
Exercises for Section 15.1
15.2 Convergence and Divergence
Exercises for Section 15.2
15.3 Infinite Series and the Integral Test
Exercises for Section 15.3
15.4 Other Tests for Convergence
Exercises for Section 15.4
15.5 Power Series
Exercises for Section 15.5
Review Exercises for Chapter 15
CHAPTER16 Expansion of Functions
16.1 Maclaurin Series
Exercises for Section 16.1
16.2 Operations with Power Series
Exercises for Section 16.2
16.3 Approximation by Truncated Series
Exercises for Section 16.3
16.4 Taylor Series
Exercises for Section 16.4
16.5 Fourier Series
Exercises for Section 16.5
Review Exercises for Chapter 16
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