An edition of Calculus, Early Transcendentals (1991)

Calculus

Early Transcendentals

Eighth Edition

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Cover of: Calculus by James Stewart, James Stewart
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Last edited by Drini
August 26, 2024 | History
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An edition of Calculus, Early Transcendentals (1991)

Calculus

Early Transcendentals

Eighth Edition

by

  • 48 Want to read
  • 4 Currently reading
  • 1 Have read

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Publish Date
Publisher
Cengage Learning
Language
English
Pages
1368

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Subjects

Calculus, Textbooks, Transcendental functions, Cálculo, Libros de texto
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Calculus: Early Transcendentals
2020, Cengage Learning
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Calculus: early transcendentals
2012, Brooks/Cole, Cengage Learning, Brand: Thomson Brooks/Cole, Cengage Learning
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Calculus: early transcendentals
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1991, Brooks/Cole Pub. Co.
in English - 2nd ed., Early transcendentals.
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Book Details

Table of Contents

Preface
Page xi
To The Student
Page xxiii
Calculators, Computers, And Other Graphing Devices
Page xxiv
Diagnostic Tests
Page xxvi
A Preview Of Calculus
Page 1
1. Functions And Models
Page 9
1.1. Four Ways To Represent A Function
Page 10
1.2. Mathematical Models: A Catalog Of Essential Functions
Page 23
1.3. New Functions From Old Functions
Page 36
1.4. Exponential Functions
Page 45
1.5. Inverse Functions And Logarithms
Page 55
Review
Page 68
Principles Of Problem Solving
Page 71
2. Limits And Derivatives
Page 77
2.1. The Tangent And Velocity Problems
Page 78
2.2. The Limit Of A Function
Page 83
2.3. Calculating Limits Using The Limit Laws
Page 95
2.4. The Precise Definition Of A Limit
Page 104
2.5. Continuity
Page 114
2.6. Limits At Infinity; Horizontal Asymptotes
Page 126
2.7. Derivatives And Rates Of Change
Page 140
Writing Project · Early Methods For Finding Tangents
Page 152
2.8. The Derivative As A Function
Page 152
Review
Page 165
Problems Plus
Page 169
3. Differentiation Rules
Page 171
3.1. Derivatives Of Polynomials And Exponential Functions
Page 172
Applied Project · Building A Better Roller Coaster
Page 182
3.2. The Product And Quotient Rules
Page 183
3.3. Derivatives Of Trigonometric Functions
Page 190
3.4. The Chain Rule
Page 197
Applied Project · Where Should A Pilot Start Descent?
Page 208
3.5. Implicit Differentiation
Page 208
Laboratory Project · Families Of Implicit Curves
Page 217
3.6. Derivatives Of Logarithmic Functions
Page 218
3.7. Rates Of Change In The Natural And Social Sciences
Page 224
3.8. Exponential Growth And Decay
Page 237
Applied Project · Controlling Red Blood Cell Loss During Surgery
Page 244
3.9. Related Rates
Page 245
3.10. Linear Approximations And Differentials
Page 251
Laboratory Project · Taylor Polynomials
Page 258
3.11. Hyperbolic Functions
Page 259
Review
Page 266
Problems Plus
Page 270
4. Applications Of Differentiation
Page 275
4.1. Maximum And Minimum Values
Page 276
Applied Project · The Calculus Of Rainbows
Page 285
4.2. The Mean Value Theorem
Page 287
4.3. How Derivatives Affect The Shape Of A Graph
Page 293
4.4. Indeterminate Forms And l'Hospital's Rule
Page 304
Writing Project · The Origins Of l'Hospital's Rule
Page 314
4.5. Summary Of Curve Sketching
Page 315
4.6. Graphing With Calculus And Calculators
Page 323
4.7. Optimization Problems
Page 330
Applied Project · The Shape Of A Can
Page 343
Applied Project · Planes And Birds: Minimizing Energy
Page 344
4.8. Newton's Method
Page 345
4.9. Antiderivatives
Page 350
Review
Page 358
Problems Plus
Page 363
5. Integrals
Page 365
5.1. Areas and Distances
Page 366
5.2. The Definite Integral
Page 378
Discovery Project · Area Functions
Page 391
5.3. The Fundamental Theorem of Calculus
Page 392
5.4. Indefinite Integrals and the Net Change Theorem
Page 402
Writing Project · Newton, Leibniz, and the Invention of Calculus
Page 411
5.5. The Substitution Rule
Page 412
Review
Page 421
Problems Plus
Page 425
6. Applications of Integration
Page 427
6.1. Areas Between Curves
Page 428
Applied Project · The Gini Index
Page 436
6.2. Volumes
Page 438
6.3. Volumes by Cylindrical Shells
Page 449
6.4. Work
Page 455
6.5. Average Value of a Function
Page 461
Applied Project · Calculus and Baseball
Page 464
Applied Project · Where to Sit at the Movies
Page 465
Review
Page 466
Problems Plus
Page 468
7. Techniques of Integration
Page 471
7.1. Integration by Parts
Page 472
7.2. Trigonometric Integrals
Page 479
7.3. Trigonometric Substitution
Page 486
7.4. Integration of Rational Functions by Partial Fractions
Page 493
7.5. Strategy for Integration
Page 503
7.6. Integration Using Tables and Computer Algebra Systems
Page 508
Discovery Project · Patterns in Integrals
Page 513
7.7. Approximate Integration
Page 514
7.8. Improper Integrals
Page 527
Review
Page 537
Problems Plus
Page 540
8. Further Applications of Integration
Page 543
8.1. Arc Length
Page 544
Discovery Project · Arc Length Contest
Page 550
8.2. Area of a Surface of Revolution
Page 551
Discovery Project · Rotating on a Slant
Page 557
8.3. Applications to Physics and Engineering
Page 558
Discovery Project · Complementary Coffee Cups
Page 568
8.4. Applications to Economics and Biology
Page 569
8.5. Probability
Page 573
Review
Page 581
Problems Plus
Page 583
9. Differential Equations
Page 585
9.1. Modeling with Differential Equations
Page 586
9.2. Direction Fields and Euler's Method
Page 591
9.3. Separable Equations
Page 599
Applied Project · How Fast Does a Tank Drain?
Page 608
Applied Project · Which Is Faster, Going Up or Coming Down?
Page 609
9.4. Models for Population Growth
Page 610
9.5. Linear Equations
Page 620
9.6. Predator-Prey Systems
Page 627
Review
Page 634
Problems Plus
Page 637
10. Parametric Equations and Polar Coordinates
Page 639
10.1. Curves Defined by Parametric Equations
Page 640
Laboratory Project · Running Circles Around Circles
Page 648
10.2. Calculus with Parametric Curves
Page 649
Laboratory Project · Bézier Curves
Page 657
10.3. Polar Coordinates
Page 658
Laboratory Project · Families of Polar Curves
Page 668
10.4. Areas and Lengths in Polar Coordinates
Page 669
10.5. Conic Sections
Page 674
10.6. Conic Sections in Polar Coordinates
Page 682
Review
Page 689
Problems Plus
Page 692
11. Infinite Sequences and Series
Page 693
11.1. Sequences
Page 694
Laboratory Project · Logistic Sequences
Page 707
11.2. Series
Page 707
11.3. The Integral Test and Estimates of Sums
Page 719
11.4. The Comparison Tests
Page 727
11.5. Alternating Series
Page 732
11.6. Absolute Convergence and the Ratio and Root Tests
Page 737
11.7. Strategy for Testing Series
Page 744
11.8. Power Series
Page 746
11.9. Representations of Functions as Power Series
Page 752
11.10. Taylor and Maclaurin Series
Page 759
Laboratory Project · An Elusive Limit
Page 773
Writing Project · How Newton Discovered the Binomial Series
Page 773
11.11. Applications of Taylor Polynomials
Page 774
Applied Project · Radiation from the Stars
Page 783
Review
Page 784
Problems Plus
Page 787
12. Vectors and the Geometry of Space
Page 791
12.1. Three-Dimensional Coordinate Systems
Page 792
12.2. Vectors
Page 798
12.3. The Dot Product
Page 807
12.4. The Cross Product
Page 814
Discovery Project · The Geometry of a Tetrahedron
Page 823
12.5. Equations of Lines and Planes
Page 823
Laboratory Project · Putting 3D in Perspective
Page 833
12.6. Cylinders and Quadric Surfaces
Page 834
Review
Page 841
Problems Plus
Page 844
13. Vector Functions
Page 847
13.1. Vector Functions and Space Curves
Page 848
13.2. Derivatives and Integrals of Vector Functions
Page 855
13.3. Arc Length and Curvature
Page 861
13.4. Motion in Space: Velocity and Acceleration
Page 870
Applied Project · Kepler's Laws
Page 880
Review
Page 881
Problems Plus
Page 884
14. Partial Derivatives
Page 887
14.1. Functions of Several Variables
Page 888
14.2. Limits and Continuity
Page 903
14.3. Partial Derivatives
Page 911
14.4. Tangent Planes and Linear Approximations
Page 927
Applied Project · The Speedo LZR Racer
Page 936
14.5. The Chain Rule
Page 937
14.6. Directional Derivatives and the Gradient Vector
Page 946
14.7. Maximum and Minimum Values
Page 959
Applied Project · Designing a Dumpster
Page 970
Discovery Project · Quadratic Approximations and Critical Points
Page 970
14.8. Lagrange Multipliers
Page 971
Applied Project · Rocket Science
Page 979
Applied Project · Hydro-Turbine Optimization
Page 980
Review
Page 981
Problems Plus
Page 985
15. Multiple Integrals
Page 987
15.1. Double Integrals over Rectangles
Page 988
15.2. Double Integrals over General Regions
Page 1001
15.3. Double Integrals in Polar Coordinates
Page 1010
15.4. Applications of Double Integrals
Page 1016
15.5. Surface Area
Page 1026
15.6. Triple Integrals
Page 1029
Discovery Project · Volumes of Hyperspheres
Page 1040
15.7. Triple Integrals in Cylindrical Coordinates
Page 1040
Discovery Project · The Intersection of Three Cylinders
Page 1044
15.8. Triple Integrals in Spherical Coordinates
Page 1045
Applied Project · Roller Derby
Page 1052
15.9. Change of Variables in Multiple Integrals
Page 1052
Review
Page 1061
Problems Plus
Page 1065
16. Vector Calculus
Page 1067
16.1. Vector Fields
Page 1068
16.2. Line Integrals
Page 1075
16.3. The Fundamental Theorem for Line Integrals
Page 1087
16.4. Green's Theorem
Page 1096
16.5. Curl and Divergence
Page 1103
16.6. Parametric Surfaces and Their Areas
Page 1111
16.7. Surface Integrals
Page 1122
16.8. Stokes' Theorem
Page 1134
Writing Project · Three Men and Two Theorems
Page 1140
16.9. The Divergence Theorem
Page 1141
16.10. Summary
Page 1147
Review
Page 1148
Problems Plus
Page 1151
17. Second-Order Differential Equations
Page 1153
17.1. Second-Order Linear Equations
Page 1154
17.2. Nonhomogeneous Linear Equations
Page 1160
17.3. Applications of Second-Order Differential Equations
Page 1168
17.4. Series Solutions
Page 1176
Review
Page 1181
Appendixes
Page A1
A. Numbers, Inequalities, and Absolute Values
Page A2
B. Coordinate Geometry and Lines
Page A10
C. Graphs of Second-Degree Equations
Page A16
D. Trigonometry
Page A24
E. Sigma Notation
Page A34
F. Proofs of Theorems
Page A39
G. The Logarithm Defined as an Integral
Page A50
H. Complex Numbers
Page A57
I. Answers to Odd-Numbered Exercises
Page A65
Index
Page A139

Edition Notes

Includes index.

Classifications

Library of Congress
QA303.2 .S7315 2016, QA303.2.S7315 2016

The Physical Object

Pagination
1 volume (various pagings)
Number of pages
1368

ID Numbers

Open Library
OL26884974M
Internet Archive
calculusearlytra0000stew_08th
ISBN 10
1285741552, 1305270363
ISBN 13
9781285741550, 9781305272354, 9781305270367
LCCN
2014951195
OCLC/WorldCat
884617308

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