EBOOK - Calculus 6th edition by SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE



The NEW 6th edition of Calculus blends the best aspects of calculus reform along with the goals and methodology of traditional calculus. The format of this text is enhanced, but is not dominated by new technology. Its innovative presentation includes: Conceptual Understanding through Verbalization Mathematical Communication Cooperative Learning Group Research Projects Integration of Technology Greater Text Visualization Supplementary Materials Calculus features: Interactive art -Many pieces of art in the book link online to dynamic art to illustrate such topics as limits, slopes, areas, and direction fields An early presentation of transcendental functions: Logarithms, exponential functions, and trigonometric functions Differential equations in a natural and reasonable way Utilization of the humanness of mathematics Precalculus mathematics being taught at most colleges and universities correctly reflected Think Tank problems to prove the proposition true or to find a counterexample to disprove the proposition Exploration Problems that go beyond the category of counterexample problem to provide opportunities for innovative thinking Journal Problems have been reprinted from leading mathematics journals in an effort to show that "mathematicians work problems too" Modeling Problems requires the reader to make assumptions about the real world in order to come up with the necessary formula or information to answer the question A student solutions manual, instructor's manual, and accompanying website.


CONTENTS:


1 Functions and Graphs

1 (72)

1.1 What Is Calculus?

2 (13)

1.2 Preliminaries

15 (12)

1.3 Lines in the Plane; Parametric Equations

27 (9)

1.4 Functions and Graphs

36 (15)

1.5 Inverse Functions; Inverse Trigonometric Functions

51 (22)

Chapter 1 Review

62 (9)

Book Report Ethnomathematics by Marcia Ascher

71 (1)

Chapter 1 Group Research Project

72 (1)

2 Limits and Continuity

73 (58)

2.1 The Limit of a Function

74 (11)

2.2 Algebraic Computation of Limits

85 (10)

2.3 Continuity

95 (12)

2.4 Exponential and Logarithmic Functions

107 (24)

Chapter 2 Review

122 (7)

Chapter 2 Group Research Project

129 (2)

3 Differentiation

131 (94)

3.1 An Introduction to the Derivative: Tangents

132 (13)

3.2 Techniques of Differentiation

145 (9)

3.3 Derivatives of Trigonometric, Exponential, and Logarithmic Functions

154 (7)

3.4 Rates of Change: Modeling Rectilinear Motion

161 (12)

3.5 The Chain Rule

173 (8)

3.6 Implicit Differentiation

181 (12)

3.7 Related Rates and Applications

193 (9)

3.8 Linear Approximation and Differentials

202 (23)

Chapter 3 Review

215 (2)

Book Report Fermat's Enigma by Simon Singh

217 (6)

Chapter 3 Group Research Project

223 (2)

4 Additional Applications of the Derivative

225 (98)

4.1 Extreme Values of a Continuous Function

226 (11)

4.2 The Mean Value Theorem

237 (7)

4.3 Using Derivatives to Sketch the Graph of a Function

244 (17)

4.4 Curve Sketching with Asymptotes: Limits Involving Infinity

261 (12)

4.5 L'Hopital's Rule

273 (9)

4.6 Optimization in the Physical Sciences and Engineering

282 (16)

4.7 Optimization in Business, Economics, and the Life Sciences

298 (25)

Chapter 4 Review

313 (9)

Chapter 4 Group Research Project

322 (1)

5 Integration

323 (98)

5.1 Antidifferentiation

324 (12)

5.2 Area as the Limit of a Sum

336 (8)

5.3 Riemann Sums and the Definite Integral

344 (13)

5.4 The Fundamental Theorems of Calculus

357 (7)

5.5 Integration by Substitution

364 (8)

5.6 Introduction to Differential Equations

372 (13)

5.7 The Mean Value Theorem for Integrals; Average Value

385 (7)

5.8 Numerical Integration: The Trapezoidal Rule and Simpson's Rule

392 (10)

5.9 An Alternative Approach: The Logarithm as an Integral

402 (19)

Chapter 5 Review

409 (8)

Chapter 5 Group Research Project

417 (1)

Cumulative Review Problems -

Chapters 1--5

418 (3)

6 Additional Applications of the Integral

421 (88)

6.1 Area Between Two Curves

422 (8)

6.2 Volume

430 (17)

6.3 Polar Forms and Area

447 (11)

6.4 Arc Length and Surface Area

458 (11)

6.5 Physical Applications: Work, Liquid Force, and Centroids

469 (15)

6.6 Applications to Business, Economics, and Life Sciences

484 (25)

Chapter 6 Review

497 (9)

Book Report To Infinity and Beyond, A Cultural History of the Infinite, by Eli Maor

506 (1)

Chapter 6 Group Research Project

507 (2)

7 Methods of Integration

509 (74)

7.1 Review of Substitution and Integration by Table

510 (8)

7.2 Integration By Parts

518 (6)

7.3 Trigonometric Methods

524 (7)

7.4 Method of Partial Fractions

531 (9)

7.5 Summary of Integration Techniques

540 (5)

7.6 First-Order Differential Equations

545 (12)

7.7 Improper Integrals

557 (11)

7.8 Hyperbolic and Inverse Hyperbolic Functions

568 (15)

Chapter 7 Review

576 (6)

Chapter 7 Group Research Project

582 (1)

8 Infinite Series

583 (92)

8.1 Sequences and Their Limits

584 (12)

8.2 Introduction to Infinite Series; Geometric Series

596 (10)

8.3 The Integral Test; p-series

606 (7)

8.4 Comparison Tests

613 (6)

8.5 The Ratio Test and the Root Test

619 (8)

8.6 Alternating Series; Absolute and Conditional Convergence

627 (12)

8.7 Power Series

639 (10)

8.8 Taylor and Maclaurin Series

649 (26)

Chapter 8 Review

664 (6)

Chapter 8 Group Research Project

670 (1)

Cumulative Review Problems---Chapters 6--8

671 (4)

9 Vectors in the Plane and in Space

675 (76)

9.1 Vectors in R2

676 (10)

9.2 Coordinates and Vectors in R3

686 (9)

9.3 The Dot Product

695 (11)

9.4 The Cross Product

706 (10)

9.5 Lines in R3

716 (10)

9.6 Planes in R3

726 (9)

9.7 Quadric Surfaces

735 (16)

Chapter 9 Review

742 (8)

Chapter 9 Group Research Project

750 (1)

10 Vector-Valued Functions

751 (68)

10.1 Introduction to Vector Functions

752 (8)

10.2 Differentiation and Integration of Vector Functions

760 (10)

10.3 Modeling Ballistics and Planetary Motion

770 (12)

10.4 Unit Tangent and Principal Unit Normal Vectors; Curvature

782 (14)

10.5 Tangential and Normal Components of Acceleration

796 (23)

Chapter 10 Review

805 (7)

Chapter 10 Group Research Project

812 (4)

Cumulative Review Problems---Chapters 1--10

816 (3)

11 Partial Differentiation

819 (100)

11.1 Functions of Several Variables

820 (9)

11.2 Limits and Continuity

829 (10)

11.3 Partial Derivatives

839 (10)

11.4 Tangent Planes, Approximations, and Differentiability

849 (11)

11.5 Chain Rules

860 (10)

11.6 Directional Derivatives and the Gradient

870 (14)

11.7 Extrema of Functions of Two Variables

884 (13)

11.8 Lagrange Multipliers

897 (22)

Chapter 11 Review

908 (8)

Book Report Heritage by Margaret Alic

916 (1)

Chapter 11 Group Research Project

917 (2)

12 Multiple Integration

919 (98)

12.1 Double Integration over Rectangular Regions

920 (11)

12.2 Double Integration over Nonrectangular Regions

931 (10)

12.3 Double Integrals in Polar Coordinates

941 (10)

12.4 Surface Area

951 (9)

12.5 Triple Integrals

960 (13)

12.6 Mass, Moments, and Probability Density Functions

973 (13)

12.7 Cylindrical and Spherical Coordinates

986 (12)

12.8 Jacobians: Change of Variables

998 (19)

Chapter 12 Review

1008 (8)

Chapter 12 Group Research Project

1016 (1)

13 Vector Analysis

1017 (94)

13.1 Properties of a Vector Field: Divergence and Curl

1018 (9)

13.2 Line Integrals

1027 (12)

13.3 The Fundamental Theorem and Path Independence

1039 (11)

13.4 Green's Theorem

1050 (13)

13.5 Surface Integrals

1063 (12)

13.6 Stokes' Theorem and Applications

1075 (10)

13.7 Divergence Theorem and Applications

1085 (26)

Chapter 13 Review

1097 (6)

Chapter 13 Group Research Project

1103 (4)

Cumulative Review Problems---Chapters 11--13

1107 (4)

14 Introduction to Differential Equations

1111 (42)

14.1 First-Order Differential Equations

1112 (11)

14.2 Second-Order Homogeneous Linear Differential Equations

1123 (13)

14.3 Second-Order Nonhomogeneous Linear Differential Equations

1136 (17)

Chapter 14 Review

1146 (5)

Book Report Mathematical Experience by Philip J. Davis and Reuben Hersh

1151 (1)

Chapter 14 Group Research Project

1152 (1)

Appendices

1153 (96)

A Introduction to the Theory of Limits

1153 (6)

B Selected Proofs

1159 (10)

C Significant Digits

1169 (5)

D Short Table of Integrals

1174 (10)

E Trigonometry

1184 (7)

F Determinants

1191 (5)

G Answers to Selected Problems

1196 (53)


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