Calculus

by Strauss, Monty J.; Bradley, Gerald L.; Smith, Karl J.

• ISBN13: 9780130918710
• ISBN10: 0130918717
• Edition: 3rd
• Format: Hardcover
• Copyright: 2002-01-01
• Publisher: Pearson College Div

Summary

Built from the ground up to meet the needs of today's calculus learners,Calculuswas the first book to pair a complete calculus syllabus with the best elements of reformlike extensive verbalization and strong geometric visualization. The Third Edition of this groundbreaking book has been crafted and honed, making itthebook of choice for those seeking the best of both worlds.Numerous chapters offer an exciting choice of problem sets and include topics such as functions and graphs, limits and continuity, differentiation, additional applications of the derivative, integration, additional applications of the integral, methods of integration, infinite series, vectors in the plane and in space, vector-valued functions, partial differentiation, multiple integration, introduction to vector analysis, and introduction to differential equations.For individuals in fields related to engineering, science, or mathematics.

Table of Contents

Preface	ix
Functions and Graphs	1	(48)
Preliminaries	2	(11)
Lines in the Plane	13	(6)
Functions and Graphs	19	(14)
Inverse Functions; Inverse Trigonometric Functions	33	(16)
Chapter 1 Review	42	(4)
Guest Essay: Calculus Was Inevitable, John Troutman	46	(2)
Mathematical Essays	48	(1)
Limits and Continuity	49	(48)
The Limit of a Function	50	(11)
Algebraic Computation of Limits	61	(9)
Continuity	70	(10)
Exponential and Logarithmic Functions	80	(17)
Chapter 2 Review	92	(5)
Differentiation	97	(86)
An Introduction to the Derivative: Tangents	98	(12)
Techniques of Differentiation	110	(9)
Derivatives of Trigonometric, Exponential, and Logarithmic Functions	119	(6)
Rates of Change: Modeling Rectilinear Motion	125	(13)
The Chain Rule	138	(8)
Implicit Differentiation	146	(11)
Related Rates and Applications	157	(8)
Linear Approximation and Differentials	165	(18)
Chapter 3 Review	177	(4)
Group Research Project: Chaos	181	(2)
Additional Applications of the Derivative	183	(88)
Extreme Values of a Continuous Function	184	(11)
The Mean Value Theorem	195	(6)
Using Derivatives to Sketch the Graph of a Function	201	(16)
Curve Sketching with Asympototes: Limits Involving Infinity	217	(12)
I'Hopital's Rule	229	(9)
Optimization in the Physical Sciences and Engineering	238	(12)
Optimization in Business, Economics, Economics, and the Life Sciences	250	(21)
Chapter 4 Review	263	(6)
Group Research Project: Wine Barrel Capacity	269	(2)
Integration	271	(84)
Antidifferentiation	272	(10)
Area as the Limit of a Sum	282	(8)
Riemann Sums and the Definite Integral	290	(12)
The Fundamental Theorems of Calculus	302	(7)
Integration by Substitution	309	(7)
Introduction to Differential Equations	316	(12)
The Mean Value Theorem for Integrals; Average Value	328	(6)
Numerical Integration: The Trapezoidal Rule and Simpson's Rule	334	(8)
An Alternative Approach: The Logarithm as an Integral	342	(13)
Chapter 5 Review	346	(5)
Guest Essay: Kinematics of Jogging, Ralph Boas	351	(1)
Mathematical Essays	352	(1)
Cumulative Review: Chapter 1--5	353	(2)
Additional Applications of the Integral	355	(70)
Area between two Curves	356	(6)
Volume	362	(13)
Polar Forms and Area	375	(10)
Arc Length and Surface Area	385	(10)
Physical Applications: Work, Liquid Force, and Centroids	395	(12)
Applications to Business, Economics, and Life Sciences	407	(18)
Chapter 6 Review	417	(7)
Group Research Project: Houdini's Excape	424	(1)
Methods of Integration	425	(68)
Review of Substitution and Integration by Table	426	(9)
Integration by Parts	435	(6)
Trigonometric Methods	441	(7)
Method of Partial Fractions	448	(9)
Summary of Integration Techniques	457	(4)
First-Order Differential Equations	461	(11)
Improper Integrals	472	(9)
Hyperbolic and Inverse Hyperbolic Functions	481	(12)
Chapter 7 Review	487	(4)
Group Research Project: Buoy Design	491	(2)
Infinite Series	493	(80)
Sequences and Their Limits	494	(11)
Introduction to Infinite Series: Geometric Series	505	(9)
The Integral Test; p-Series	514	(7)
Comparison Tests	521	(6)
The Ratio Test and the Root Test	527	(6)
Alternating Series; Absolute and Conditional Convergence	533	(11)
Power Series	544	(9)
Taylor and Maclaurin Series	553	(20)
Chapter 8 Review	566	(4)
Group Research Project: Elastic Tightrope	570	(1)
Cumulative Review: Chapters 6--8	571	(2)
Vectors in the Plane and in Space	573	(60)
Vectors in R2	574	(8)
Coordinates and Vectors in R3	582	(6)
The Dot Product	588	(9)
The Cross Product	597	(9)
Parametric Representation of Curves; Lines in R3	606	(9)
Planes in R3	615	(7)
Quadric Surfaces	622	(11)
Chapter 9 Review	628	(4)
Group Research Project: Star Trek	632	(1)
Vector-Valued Functions	633	(60)
Introduction to Vector Functions	634	(8)
Differentiation and Integration of Vector Functions	642	(9)
Modeling Ballistics and Planetary Motion	651	(9)
Unit Tangent and Principal Unit Normal Vectors; Curvature	660	(13)
Tangential and Normal Components of Acceleration	673	(20)
Chapter 10 Review	679	(5)
Guest Essay: The Stimulation of Science, Howard Eves	684	(3)
Mathematical Essays	687	(1)
Cumulative Review: Chapters 1--10	688	(5)
Partial Differentiation	693	(84)
Functions of Several Variables	694	(7)
Limits and Continuity	701	(9)
Partial Derivatives	710	(10)
Tangent Planes, Approximations, and Differentiability	720	(9)
Chain Rules	729	(8)
Directional Derivatives and the Gradient	737	(12)
Extrema of Functions of Two Variables	749	(12)
Lagrange Multipliers	761	(16)
Chapter 11 Review	770	(5)
Group Research Project: Desertification	775	(2)
Multiple Integration	777	(82)
Double Integration over Rectangular Regions	778	(9)
Double Integration over Nonrectangular Regions	787	(8)
Double Integrals in Polar Coordinates	795	(9)
Surface Area	804	(8)
Triple Integrals	812	(10)
Mass, Moments, and Probability Density Functions	822	(11)
Cylindrical and Spherical Coordinates	833	(10)
Jacobians: Change of Variables	843	(16)
Chapter 12 Review	852	(5)
Group Research Project: Space-Capsule Design	857	(2)
Vector Analysis	859	(76)
Properties of a Vector Field: Divergence and Curl	860	(7)
Line Integrals	867	(10)
The Fundamental Theorem and Path Independence	877	(10)
Green's Theorem	887	(11)
Surface Integrals	898	(10)
Stokes' Theorem	908	(8)
The Divergence Theorem	916	(19)
Chapter 13 Review	924	(5)
Guest Essay: Continuous vs. Discrete Mathematics	929	(1)
Cumulative Review: Chapters 11--13	930	(1)
Mathematical Essays	931	(1)
Cumulative Review: Chapters 11--13	932	(3)
Introduction to Differential Equations	935
First-Order Differential Equations	936
Second-Order Homogeneous Linear Differential Equations	947
Second-Order Nonhomogeneous Linear Differential Equations	957
Chapter 14 Review	966
Group Research Project: Save the Perch Project	969
Appendices
A Introduction to the Theory of Limits	A-1
B Selected Proofs	A-8
C Significant Digits	A-17
D Short Table of Integrals	A-21
E Trigonometric Formulas	A-31
F Answers to Selected Problems	A-34
G Credits	A-80
Index	A-85