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Single Variable Calculus : Early Transcendentals,9780534355630
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Single Variable Calculus : Early Transcendentals

by
Edition:
4th
ISBN13:

9780534355630

ISBN10:
0534355633
Format:
Paperback
Pub. Date:
2/19/1999
Publisher(s):
Brooks Cole

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Summary

This best-selling text differs from Calculus, 4/e in that the exponential and logarithmic functions are covered earlier. These functions are introduced in the first chapter and their limits and derivatives are found in Chapters 2 and 3 at the same time as polynomials and the other elementary functions.

Table of Contents

A Preview of Calculus 2(8)
1 Functions and Models
10(74)
1.1 Four Ways to Represent a Function
11(13)
1.2 Mathematical Models
24(14)
1.3 New Functions from Old Functions
38(12)
1.4 Graphing Calculators and Computers
50(6)
1.5 Exponential Functions
56(8)
1.6 Inverse Functions and Logarithms
64(11)
Review
75(3)
Principles of Problem Solving
78(6)
2 Limits and Derivatives
84(96)
2.1 The Tangent and Velocity Problems
85(5)
2.2 The Limit of a Function
90(12)
2.3 Calculating Limits Using the Limit Laws
102(10)
2.4 The Precise Definition of a Limit
112(10)
2.5 Continuity
122(11)
2.6 Limits at Infinity; Horizontal Asymptotes
133(14)
2.7 Tangents, Velocities, and Other Rates of Change
147(9)
2.8 Derivatives
156(7)
Writing Project Early Methods for Finding Tangents
162(1)
2.9 The Derivative as a Function
163(11)
Review
174(4)
Problems Plus
178(2)
3 Differentiation Rules
180(96)
3.1 Derivatives of Polynomials and Exponential Functions
181(9)
3.2 The Product and Quotient Rules
190(6)
3.3 Rates of Change in the Natural and Social Sciences
196(12)
3.4 Derivatives of Trigonometric Functions
208(7)
3.5 The Chain Rule
215(9)
3.6 Implicit Differentiation
224(9)
3.7 Higher Derivatives
233(7)
Applied Project Where Should a Pilot Start Descent?
240(1)
3.8 Derivatives of Logarithmic Functions
240(6)
3.9 Hyperbolic Functions
246(7)
3.10 Related Rates
253(6)
3.11 Linear Approximations and Differentials
259(8)
Laboratory Project Taylor Polynomials
266(1)
Review
267(4)
Problems Plus
271(5)
4 Applications of Differentiation
276(90)
4.1 Maximum and Minimum Values
277(11)
Applied Project The Calculus of Rainbows
286(2)
4.2 The Mean Value Theorem
288(6)
4.3 How Derivatives Affect the Shape of a Graph
294(11)
4.4 Indeterminate Forms and L'Hospital's Rule
305(9)
Writing Project The Origins of L'Hospital's Rule
313(1)
4.5 Summary of Curve Sketching
314(8)
4.6 Graphing with Calculus and Calculators
322(7)
4.7 Optimization Problems
329(11)
Applied Project The Shape of a Can
339(1)
4.8 Applications to Economics
340(5)
4.9 Newton's Method
345(6)
4.10 Antiderivatives
351(8)
Review
359(4)
Problems Plus
363(3)
5 Integrals
366(66)
5.1 Areas and Distances
367(11)
5.2 The Definite Integral
378(13)
Discovery Project Area Functions
390(1)
5.3 The Fundamental Theorem of Calculus
391(10)
5.4 Indefinite Integrals and the Total Change Theorem
401(9)
Writing Project Newton, Leibniz, and the Invention of Calculus
409(1)
5.5 The Substitution Rule
410(8)
5.6 The Logarithm Defined as an Integral
418(7)
Review
425(4)
Problems Plus
429(3)
6 Applications of Integration
432(36)
6.1 Areas between Curves
433(7)
6.2 Volumes
440(11)
6.3 Volumes by Cylindrical Shells
451(5)
6.4 Work
456(4)
6.5 Average Value of a Function
460(3)
Applied Project Where to Sit at the Movies
463(1)
Review
463(2)
Problems Plus
465(3)
7 Techniques of Integration
468(72)
7.1 Integration by Parts
469(7)
7.2 Trigonometric Integrals
476(7)
7.3 Trigonometric Substitution
483(7)
7.4 Integration of Rational Functions by Partial Fractions
490(9)
7.5 Strategy for Integration
499(6)
7.6 Integration Using Tables and Computer Algebra Systems
505(7)
Discovery Project Patterns in Integrals
511(1)
7.7 Approximate Integration
512(11)
7.8 Improper Integrals
523(11)
Review
534(3)
Problems Plus
537(3)
8 Further Applications of Integration
540(40)
8.1 Arc Length
541(7)
8.2 Area of a Surface of Revolution
548(7)
Discovery Project Rotating on a Slant
554(1)
8.3 Applications to Physics and Engineering
555(9)
8.4 Applications to Economics and Biology
564(5)
8.5 Probability
569(7)
Review
576(2)
Problems Plus
578(2)
9 Differential Equations
580(60)
9.1 Modeling with Differential Equations
581(5)
9.2 Direction Fields and Euler's Method
586(9)
9.3 Separable Equations
595(8)
Applied Project Which Is Faster, Going Up or Coming Down?
602(1)
9.4 Exponential Growth and Decay
603(10)
Applied Project Calculus and Baseball
612(1)
9.5 The Logistic Equation
613(9)
9.6 Linear Equations
622(6)
9.7 Predator-Prey Systems
628(6)
Review
634(4)
Problems Plus
638(2)
10 Parametric Equations and Polar Coordinates
640(52)
10.1 Curves Defined by Parametric Equations
641(7)
Laboratory Project Families of Hypocycloids
648(1)
10.2 Tangents and Area
648(7)
Laboratory Project Bezier Curves
655(1)
10.3 Arc Length and Surface Area
655(13)
10.4 Polar Coordinates
668(102)
10.5 Areas and Lengths in Polar Coordinates
770(5)
10.6 Conic Sections
775(7)
10.7 Conic Sections in Polar Coordinates
782(6)
Review
788(2)
Problems Plus
790
11 Infinite Sequences and Series
692
11.1 Sequences
693
Laboratory Project Logistic Sequences
704(1)
11.2 Series
704(10)
11.3 The Integral Test and Estimates of Sums
714(7)
11.4 The Comparison Tests
721(5)
11.5 Alternating Series
726(5)
11.6 Absolute Convergence and the Ratio and Root Tests
731(7)
11.7 Strategy for Testing Series
738(2)
11.8 Power Series
740(5)
11.9 Representations of Functions as Power Series
745(6)
11.10 Taylor and Maclaurin Series
751(11)
11.11 The Binomial Series
762(4)
Writing Project How Newton Discovered the Binomial Series
765(1)
11.12 Applications of Taylor Polynomials
766(9)
Applied Project Radiation from the Stars
774(1)
Review
775(3)
Problems Plus
778
Appendixes A1(106)
A Intervals, Inequalities, and Absolute Values A2(8)
B Coordinate Geometry and Lines A10(6)
C Graphs of Second-Degree Equations A16(8)
D Trigonometry A24(13)
E Sigma Notation A37(5)
F Proofs of Theorems A42(8)
G Complex Numbers A50(8)
H Answers to Odd-Numbered Exercises A58(49)
Index A107


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