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Calculus : Concepts and Applications,9781559536547
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Calculus : Concepts and Applications

by
Edition:
2nd
ISBN13:

9781559536547

ISBN10:
1559536543
Format:
Hardcover
Pub. Date:
5/1/2004
Publisher(s):
Kendall Hunt
List Price: $126.06
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  • Calculus : Concepts and Applications
    Calculus : Concepts and Applications




Summary

The acclaimed Calculus: Concepts and Applications is now available in a new edition, revised to reflect important changes in the Advanced Placement curriculum, and updated to incorporate feedback from instructors throughout the U.S.With over 40 years of experience teaching AP Calculus, Paul Foerster developed Calculus: Concepts and Applications with the high school student in mind, but with all the content of a college-level course. Like the previous edition, the second edition follows the AP Calculus curriculum for both AB and BC levels.In Calculus: Concepts and Applications, students start off with calculus! Review of precalculus occurs at various points when it's needed. The text combines graphing-calculator technology with a unique, real-world application approach, and presents calculus as a study of just four fundamental concepts: limits, derivatives, definite integrals, and indefinite integrals. Students learn these concepts using algebraic, numerical, graphical, and verbal approaches. As a result, students with a wider range of abilities can be successful in calculus, not just those who are strong in algebra. The accompanying set of Explorations in the Instructor's Resource Book, designed for cooperative group work, gives students hands-on experience with new topics before they are formally introduced.In this new edition, derivatives of transcendental functions, related rates, as well as area and volume applications of the definite integral are introduced earlier. Additionally, the Instructor's Resource Book includes projects utilizing the CBL', The Geometer's Sketchpad ®, and Fathom Dynamic Statistics' software, giving students extended opportunities to explore and understand calculus in depth.

Table of Contents

A Note to the Student from the Author xiii
Limits, Derivatives, Integrals, and Integrals
1(30)
The Concept of Instantaneous Rate
3(3)
Rate of Change by Equation, Graph, or Table
6(8)
One Type of Integral of a Function
14(4)
Definite Integrals by Trapezoids, from Equations and Data
18(6)
Calculus Journal
24(1)
Chapter Review and Test
25(6)
Properties of Limits
31(40)
Numerical Approach to the Definition of Limit
33(1)
Graphical and Algebraic Approaches to the Definition of Limit
34(6)
The Limit Theorems
40(5)
Continuity and Discontinuity
45(7)
Limits Involving Infinity
52(8)
The Intermediate Value Theorem and Its Consequences
60(4)
Chapter Review and Test
64(7)
Derivatives, Antiderivatives, and Indefinite Integrals
71(58)
Graphical Interpretation of Derivative
73(1)
Difference Quotients and One Definition of Derivative
74(4)
Derivative Functions, Numerically and Graphically
78(7)
Derivative of the Power Function and Another Definition of Derivative
85(7)
Displacement, Velocity, and Acceleration
92(8)
Introduction to Sine, Cosine, and Composite Functions
100(2)
Derivatives of Composite Functions---The Chain Rule
102(5)
Proof and Application of Sine and Cosine Derivatives
107(8)
Exponential and Logarithmic Functions
115(7)
Chapter Review and Test
122(7)
Products, Quotients, and Parametric Functions
129(58)
Combinations of Two Functions
131(1)
Derivative of a Product of Two Functions
132(5)
Derivative of a Quotient of Two Functions
137(5)
Derivatives of the Other Trigonometric Functions
142(4)
Derivatives of Inverse Trigonometric Functions
146(7)
Differentiability and Continuity
153(7)
Derivatives of a Parametric Function
160(9)
Graphs and Derivatives of Implicit Relations
169(5)
Related Rates
174(6)
Chapter Review and Test
180(7)
Definite and Indefinite Integrals
187(80)
A Definite Integral Problem
189(1)
Linear Approximations and Differentials
190(7)
Formal Definition of Antiderivative and Indefinite Integral
197(7)
Riemann Sums and the Definition of Definite Integral
204(7)
The Mean Value Theorem and Rolle's Theorem
211(10)
The Fundamental Theorem of Calculus
221(6)
Definite Integral Properties and Practice
227(6)
Definite Integrals Applied to Area and Other Problems
233(9)
Volume of a Solid by Plane Slicing
242(10)
Definite Integrals Numerically by Grapher and by Simpson's Rule
252(7)
Chapter Review and Test
259(8)
The Calculus of Exponential and Logarithmic Functions
267(48)
Integral of the Reciprocal Function: A Population Growth Problem
269(1)
Antiderivative of the Reciprocal Function and Another Form of the Fundamental Theorem
270(10)
The Uniqueness Theorem and Properties of Logarithmic Functions
280(8)
The Number e, Exponential Functions, and Logarithmic Differentiation
288(7)
Limits of Indeterminate Forms: l'Hospital's Rule
295(6)
Derivative and Integral Practice for Transcendental Functions
301(5)
Chapter Review and Test
306(5)
Cumulative Review: Chapters 1--6
311(4)
The Calculus of Growth and Decay
315(54)
Direct Proportion Property of Exponential Functions
317(1)
Exponential Growth and Decay
318(6)
Other Differential Equations for Real-World Applications
324(9)
Graphical Solution of Differential Equations by Using Slope Fields
333(8)
Numerical Solution of Differential Equations by Using Euler's Method
341(7)
The Logistic Function, and Predator-Prey Population Problems
348(11)
Chapter Review and Test
359(6)
Cumulative Review: Chapters 1-7
365(4)
The Calculus of Plane and Solid Figures
369(62)
Cubic Functions and Their Derivatives
371(1)
Critical Points and Points of Inflection
372(13)
Maxima and Minima in Plane and Solid Figures
385(10)
Volume of a Solid of Revolution by Cylindrical Shells
395(6)
Length of a Plane Curve---Arc Length
401(6)
Area of a Surface of Revolution
407(7)
Lengths and Areas for Polar Coordinates
414(9)
Chapter Review and Test
423(8)
Algebraic Calculus Techniques for the Elementary Functions
431(68)
Introduction to the Integral of a Product of Two Functions
433(1)
Integration by Parts---A Way to Integrate Products
434(4)
Rapid Repeated Integration by Parts
438(6)
Reduction Formulas and Computer Algebra Systems
444(5)
Integrating Special Powers of Trigonometric Functions
449(5)
Integration by Trigonometric Substitution
454(6)
Integration of Rational Functions by Partial Fractions
460(6)
Integrals of the Inverse Trigonometric Functions
466(3)
Calculus of the Hyperbolic and Inverse Hyperbolic Functions
469(12)
Improper Integrals
481(7)
Miscellaneous Integrals and Derivatives
488(5)
Integrals in Journal
493(1)
Chapter Review and Test
494(5)
The Calculus of Motion---Averages, Extremes, and Vectors
499(46)
Introduction to Distance and Displacement for Motion Along a Line
501(1)
Distance, Displacement, and Acceleration for Linear Motion
502(6)
Average Value Problems in Motion and Elsewhere
508(6)
Minimal Path Problems
514(6)
Maximum and Minimum Problems in Motion and Elsewhere
520(2)
Vector Functions for Motion in a Plane
522(16)
Chapter Review and Test
538(7)
The Calculus of Variable-Factor Products
545(42)
Review of Work---Force Times Displacement
547(1)
Work Done by a Variable Force
548(5)
Mass of a Variable-Density Object
553(5)
Moments, Centroids, Center of Mass, and the Theorem of Pappus
558(9)
Force Exerted by a Variable Pressure---Center of Pressure
567(6)
Other Variable-Factor Products
573(7)
Chapter Review and Test
580(7)
The Calculus of Functions Defined by Power Series
587(68)
Introduction to Power Series
589(1)
Geometric Sequences and Series as Mathematical Models
590(7)
Power Series for an Exponential Function
597(1)
Power Series for Other Elementary Functions
598(7)
Taylor and Maclaurin Series, and Operations on These Series
605(8)
Interval of Convergence for a Series---The Ratio Technique
613(8)
Convergence of Series at the Ends of the Convergence Interval
621(14)
Error Analysis for Series---The Lagrange Error Bound
635(8)
Chapter Review and Test
643(5)
Cumulative Reviews
648(7)
Final Examination: A Guided Tour Through Calculus 655(4)
Appendix: Summary of Properties of Trigonometric Functions 659(2)
Answers to Selected Problems 661(94)
Glossary 755(6)
Index of Problem Titles 761(6)
General Index 767(10)
Photograph Credits 777


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