Calculus with Analytic Geometry / Edition 5

Calculus with Analytic Geometry / Edition 5

1.0 3
by Robert Ellis, Denny Gulick, Denny Gulick
     
 

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ISBN-10: 0030442249

ISBN-13: 9780030442247

Pub. Date: 01/28/1994

Publisher: Harcourt

Product Details

ISBN-13:
9780030442247
Publisher:
Harcourt
Publication date:
01/28/1994
Edition description:
5TH
Pages:
1024
Product dimensions:
8.02(w) x 10.00(h) x 1.61(d)

Table of Contents

1 FUNCTIONS
1(71)
1.1 The Real Numbers
2(9)
1.2 Points and Lines in the Plane
11(7)
1.3 Functions
18(8)
1.4 Graphs
26(9)
1.5 Aids to Graphing
35(8)
1.6 Combining Functions
43(8)
1.7 Trigonometric Functions
51(8)
1.8 Exponential and Logarithmic Functions
59(9)
Key Terms and Expressions
68(1)
Key Formulas
68(1)
Review Exercises
69(3)
2 LIMITS AND CONTINUITY
72(56)
2.1 Informal Discussion of Limit
72(8)
2.2 Definition of Limit
80(9)
2.3 Limit Theorems and Continuity
89(8)
2.4 The Squeezing Theorem and Substitution Rule
97(10)
2.5 One-Sided and Infinite Limits
107(9)
2.6 Continuity on Intervals and the Intermediate Value Theorem
116(8)
Key Terms and Expressions
124(1)
Key Formulas
124(1)
Key Theorems
125(1)
Review Exercises
125(2)
Topics for Discussion
127(1)
3 DERIVATIVES
128(76)
3.1 The Derivative
128(10)
3.2 Differentiable Functions
138(8)
3.3 Derivatives of Combinations of Functions
146(13)
3.4 The Chain Rule
159(10)
3.5 Higher Derivatives
169(4)
3.6 Implicit Differentiation
173(6)
3.7 Related Rates
179(10)
3.8 Approximations
189(11)
Key Terms and Expressions
200(1)
Key Formulas
200(1)
Review Exercises
200(2)
Topics for Discussion
202(1)
Cumulative Review, Chapters 1-2
202(2)
4 APPLICATIONS OF THE DERIVATIVE
204(73)
4.1 Maximum and Minimum Values
204(10)
4.2 The Mean Value Theorem
214(4)
4.3 Applications of the Mean Value Theorem
218(8)
4.4 Exponential Growth and Decay
226(7)
4.5 The First and Second Derivative Tests
233(7)
4.6 Extreme Values on an Arbitrary Interval
240(10)
4.7 Concavity and Inflection Points
250(7)
4.8 Limits at Infinity
257(9)
4.9 Graphing
266(5)
Key Terms and Expressions
271(1)
Key Theorems
272(1)
Review Exercises
272(3)
Topics for Discussion
275(1)
Cumulative Review, Chapters 1-3
276(1)
5 THE INTEGRAL
277(84)
5.1 Preparation for the Definite Integral
279(10)
5.2 The Definite Integral
289(13)
5.3 Special Properties of the Definite Integral
302(8)
5.4 The Fundamental Theorem of Calculus
310(12)
5.5 Indefinite Integrals and Integration Rules
322(7)
5.6 Integration by Substitution
329(8)
5.7 The Logarithm
337(9)
5.8 Another Look at Area
346(9)
5.9 Who Invented Calculus?
355(1)
Key Terms and Expressions
356(1)
Key Formulas
356(1)
Key Theorems
356(1)
Review Exercises
357(2)
Topics for Discussion
359(1)
Cumulative Review, Chapters 1-4
359(2)
6 INVERSE FUNCTIONS
361(69)
6.1 Inverse Functions
362(10)
6.2 The Natural Exponential Function
372(5)
6.3 General Exponential and Logarithmic Functions
377(8)
6.4 Hyperbolic Functions
385(5)
6.5 The Inverse Trigonometric Functions
390(11)
6.6 L'Hopital's Rule
401(9)
6.7 Introduction to Differential Equations
410(6)
6.8 Methods of Solving Differential Equations
416(9)
Key Terms and Expressions
425(1)
Key Formulas
425(1)
Key Theorems
425(1)
Review Exercises
426(2)
Topics for Discussion
428(1)
Cumulative Review, Chapters 1-5
428(2)
7 TECHNIQUES OF INTEGRATION
430(63)
7.1 Integration by Parts
431(9)
7.2 Trigonometric Integrals
440(9)
7.3 Trigonometric Substitutions
449(7)
7.4 Partial Fractions
456(10)
7.5 Integration by Tables and Symbolic Integration
466(4)
7.6 The Trapezoidal Rule and Simpson's Rule
470(1)
7.7 Improper Integrals
478(1)
Key Terms and Expressions
489(1)
Key Formulas
489(1)
Review Exercises
490(1)
Topics for Discussion
491(1)
Cumulative Review, Chapters 1-6
492(1)
8 APPLICATIONS OF THE INTEGRAL
493(51)
8.1 Volume: The Cross-Sectional Method
494(8)
8.2 Volume: The Shell Method
502(5)
8.3 Length of a Curve
507(5)
8.4 Area of a Surface
512(4)
8.5 Work
516(9)
8.6 Moments and Center of Gravity
525(8)
8.7 Hydrostatic Force
533(5)
Key Terms
538(1)
Key Theorem
538(1)
Formulas for Applications of the Integral
539(1)
Review Exercises
539(3)
Topics for Discussion
542(1)
Cumulative Review, Chapters 1-7
543(1)
9 SEQUENCES AND SERIES
544(92)
9.1 Polynomial Approximation
545(5)
9.2 Sequences
550(12)
9.3 Convergence Properties of Sequences
562(7)
9.4 Infinite Series
569(12)
9.5 Positive Series: The Integral Test and the Comparison Tests
581(9)
9.6 Positive Series: The Ratio Test and the Root Test
590(4)
9.7 Alternating Series and Absolute Convergence
594(8)
9.8 Power Series
602(12)
9.9 Taylor Series
614(12)
9.10 Binomial Series
626(5)
Summary of Convergence and Divergence Tests for Series
631(1)
Key Terms and Expressions
632(1)
Key Theorems
632(1)
Key Formulas
632(1)
Review Exercises
632(3)
Topics for Discussion
635(1)
Cumulative Review, Chapters 1-8
635(1)
10 CURVES IN THE PLANE
636(54)
10.1 Parametrized Curves
636(5)
10.2 Length and Surface Area for Parametrized Curves
641(8)
10.3 Polar Coordinates
649(9)
10.4 Length and Area in Polar Coordinates
658(5)
10.5 Conic Sections
663(14)
10.6 Rotation of Axes
677(4)
10.7 A Unified Description of Conic Sections
681(5)
Key Terms and Expressions
686(1)
Key Formulas
687(1)
Review Exercises
687(1)
Topics for Discussion
688(1)
Cumulative Review, Chapters 1-9
689(1)
11 VECTORS, LINES AND PLANES
690(47)
11.1 Cartesian Coordinates in Space
691(3)
11.2 Vectors in Space
694(12)
11.3 The Dot Product
706(8)
11.4 The Cross Product and Triple Products
714(7)
11.5 Lines in Space
721(6)
11.6 Planes in Space
727(6)
Key Terms and Expressions
733(1)
Key Formulas
733(1)
Review Exercises
733(2)
Topics for Discussion
735(1)
Cumulative Review, Chapters 1-10
735(2)
12 VECTOR-VALUED FUNCTIONS
737(60)
12.1 Definitions and Examples
737(8)
12.2 Limits and Continuity of Vector-Valued Functions
745(4)
12.3 Derivatives and Integrals of Vector-Valued Functions
749(13)
12.4 Space Curves and Their Lengths
762(9)
12.5 Tangents and Normals to Curves
771(9)
12.6 Curvature
780(6)
12.7 Kepler's Laws of Motion
786(8)
Key Terms and Expressions
794(1)
Key Formulas
794(1)
Review Exercises
794(1)
Topics for Discussion
795(1)
Cumulative Review, Chapters 1-11
795(2)
13 PARTIAL DERIVATIVES
797(82)
13.1 Functions of Several Variables
797(12)
13.2 Limits and Continuity
809(8)
13.3 Partial Derivatives
817(13)
13.4 The Chain Rule
830(10)
13.5 Directional Derivatives
840(4)
13.6 The Gradient
844(7)
13.7 Tangent Plane Approximations and Differentials
851(4)
13.8 Extreme Values
855(10)
13.9 Lagrange Multipliers
865(9)
Key Terms and Expressions
874(1)
Key Formulas
874(1)
Key Theorems
874(1)
Review Exercises
875(2)
Topics for Discussion
877(1)
Cumulative Review, Chapters 1-12
877(2)
14 MULTIPLE INTEGRALS
879(73)
14.1 Double Integrals
879(16)
14.2 Double Integrals in Polar Coordinates
895(8)
14.3 Surface Area
903(4)
14.4 Triple Integrals
907(11)
14.5 Triple Integrals in Cylindrical Coordinates
918(6)
14.6 Triple Integrals in Spherical Coordinates
924(8)
14.7 Moments and Centers of Gravity
932(6)
14.8 Change of Variables in Multiple Integrals
938(10)
Key Terms and Expressions
948(1)
Key Formulas
949(1)
Review Exercises
949(1)
Topics for Discussion
950(1)
Cumulative Review, Chapters 1-13
951(1)
15 CALCULUS OF VECTOR FIELDS
952
15.1 Vector Fields
953(13)
15.2 Line Integrals
966(11)
15.3 The Fundamental Theorem of Line Integrals
977(6)
15.4 Green's Theorem
983(8)
15.5 Surface Integrals
991(6)
15.6 Integrals over Oriented Surfaces
997(9)
15.7 Stokes's Theorem
1006(7)
15.8 The Divergence Theorem
1013(7)
Key Terms and Expressions
1020(1)
Key Formulas
1021(1)
Key Theorems
1021(1)
Evaluation of Integrals
1021(1)
Review Exercises
1022(1)
Topics for Discussion
1023(1)
Cumulative Review, Chapters 1-14
1023
APPENDIX A-1
Proofs of Selected Theorems A-1(22)
Table of Integrals A-23(7)
Answers to Odd-Numbered Exercises A-30
INDEX OF SYMBOLS I-1(2)
INDEX I-3

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Calculus with Analytic Geometry 1 out of 5 based on 0 ratings. 3 reviews.
Guest More than 1 year ago
This is a required textbook for a class that I'm taking. I found the book so confusing, that I ended up buying another textbook to help me understand calculus. I cannot recommend this book.
Guest More than 1 year ago
This is certainly one of those math books that you don't want to read. Get a better one! This book can barely teach you calculus. It's used in OSU!!
Guest More than 1 year ago
The book is so poorly written, that at times it is even hard to figure out what you're supposed to do in the exercise part. Do yourself a favor and stay away from this book.