Calculus, Matrix Version

by Edwards, C. Henry; Penney, David E.

• ISBN13: 9780130084064
• ISBN10: 0130084069
• Edition: 6th
• Format: Hardcover
• Copyright: 2003-01-01
• Publisher: Pearson College Div

Summary

The Matrix version combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. This book contains an entire chapter on calculus of transcendental functions, a new chapter on matrices and eigenvalues, and increased coverage of differential equations. For professionals who need to brush up on their calculus skills.

Table of Contents

About the Authors	xiii
Preface	xv
Functions, Graphs, and Models	1	(52)
Functions and Mathematical Modeling	2	(10)
Project: A Square Wading Pool	11	(1)
Graphs of Equations and Functions	12	(12)
Project: A Broken Tree	23	(1)
Polynomials and Algebraic Functions	24	(9)
Project: A Leaning Ladder	33	(1)
Transcendental Functions	33	(12)
Project: A Spherical Asteroid	45	(1)
Preview: What Is Calculus?	45	(8)
Review: Definitions and Concepts	48	(5)
Prelude to Calculus	53	(48)
Tangent Lines and Slope Predictors	54	(9)
Project: Numerical Slope Investigations	63	(1)
The Limit Concept	63	(12)
Project: Limits, Slopes, and Logarithms	74	(1)
More About Limits	75	(13)
Project: Numerical Epsilon-Delta Limit Investigations	87	(1)
The Concept of Continuity	88	(13)
Review: Definitions, Concepts, Results	99	(2)
The Derivative	101	(92)
The Derivative and Rates of Change	102	(13)
Basic Differentiation Rules	115	(11)
The Chain Rule	126	(7)
Derivatives of Algebraic Functions	133	(9)
Maxima and Minima of Functions on Closed Intervals	142	(10)
Project: When Is Your Coffee Cup Stablest?	150	(2)
Applied Optimization Problems	152	(13)
Derivatives of Trigonometric Functions	165	(11)
Successive Approximations and Newton's Method	176	(17)
Project: How Deep Does a Floating Ball Sink?	188	(1)
Review: Formulas, Concepts, Definitions	189	(4)
Additional Applications of the Derivative	193	(78)
Implicit Functions and Related Rates	194	(10)
Project: Investigating the Folium of Descartes	203	(1)
Increments, Differentials, and Linear Approximation	204	(8)
Increasing and Decreasing Functions and the Mean Value Theorem	212	(10)
The First Derivative Test and Applications	222	(10)
Project: Constructing a Candy Box With Lid	232	(1)
Simple Curve Sketching	232	(10)
Higher Derivatives and Concavity	242	(14)
Curve Sketching and Asymptotes	256	(15)
Project: Locating Special Points on Exotic Graphs	267	(1)
Review: Definitions, Concepts, Results	267	(4)
The Integral	271	(94)
Introduction	272	(1)
Antiderivatives and Initial Value Problems	272	(14)
Elementary Area Computations	286	(12)
Riemann Sums and the Integral	298	(10)
Project: Calculator/Computer Riemann Sums	307	(1)
Evaluation of Integrals	308	(10)
The Fundamental Theorem of Calculus	318	(10)
Integration by Substitution	328	(8)
Areas of Plane Regions	336	(10)
Numerical Integration	346	(19)
Project: Trapezoidal and Simpson Approximations	359	(2)
Review: Definitions, Concepts, Results	361	(4)
Applications of the Integral	365	(62)
Riemann Sum Approximations	366	(10)
Volumes by the Method of Cross Sections	376	(11)
Volumes by the Method of Cylindrical Shells	387	(9)
Project: Design Your Own Ring!	395	(1)
Arc Length and Surface Area of Revolution	396	(9)
Force and Work	405	(11)
Centroids of Plane Regions and Curves	416	(11)
Review: Definitions, Concepts, Results	423	(4)
Calculus of Transcendental Functions	427	(62)
Exponential and Logarithmic Functions	428	(13)
Project: Discovering the Number e for Yourself	441	(1)
Indeterminate Forms and L'Hopital's Rule	441	(8)
More Indeterminate Forms	449	(6)
The Natural Logarithm as an Integral	455	(12)
Project: Natural Functional Equations	466	(1)
Inverse Trigonometric Functions	467	(10)
Hyperbolic Functions	477	(12)
Review: Formulas, Concepts, Definitions	485	(4)
Techniques of Integration	489	(56)
Introduction	490	(1)
Integral Tables and Simple Substitutions	490	(4)
Integration by Parts	494	(7)
Trigonometric Integrals	501	(7)
Rational Functions and Partial Fractions	508	(7)
Trigonometric Substitution	515	(6)
Integrals Involving Quadratic Polynomials	521	(5)
Improper Integrals	526	(19)
Summary	539	(6)
Differential Equations	545	(78)
Simple Equations and Models	546	(12)
Slope Fields and Euler's Method	558	(10)
Project: Computer-Assisted Slope Fields and Euler's Method	567	(1)
Separable Equations and Applications	568	(7)
Linear Equations and Applications	575	(12)
Population Models	587	(11)
Project: Predator-Prey Equations and Your Own Game Preserve	597	(1)
Linear Second-Order Equations	598	(9)
Mechanical Vibrations	607	(16)
Review: Definitions, Concepts, Results	618	(5)
Polar Coordinates and Parametic Curves	623	(58)
Analytic Geometry and the Conic Sections	624	(5)
Polar Coordinates	629	(9)
Area Computations in Polar Coordinates	638	(5)
Parametric Curves	643	(10)
Project: Trochoid Investigations	652	(1)
Integral Computations with Parametric Curves	653	(8)
Project: Moon Orbits and Race Tracks	660	(1)
Conic Sections and Applications	661	(20)
Review: Concepts and Definitions	679	(2)
Infinite Series	681	(90)
Introduction	682	(1)
Infinite Sequences	682	(9)
Project: Nested Radicals and Continued Fractions	691	(1)
Infinite Series and Convergence	691	(11)
Project: Numerical Summation and Geometric Series	701	(1)
Taylor Series and Taylor Polynomials	702	(13)
Project: Calculating Logarithms on a Deserted Island	715	(1)
The Integral Test	715	(7)
Project: The Number π, Once and for All	722	(1)
Comparison Tests for Positive-Term Series	722	(6)
Alternating Series and Absolute Convergence	728	(9)
Power Series	737	(13)
Power Series Computations	750	(8)
Project: Calculating Trigonometric Functions on a Deserted Island	758	(1)
Series Solutions of Differential Equations	758	(13)
Review: Definitions, Concepts, Results	767	(4)
Vectors and Matrices	771	(72)
Vectors in the Plane	772	(6)
Three-Dimensional Vectors	778	(10)
The Cross Product of Vectors	788	(8)
Lines and Planes in Space	796	(7)
Linear Systems and Matrices	803	(12)
Project: Automated Row Reduction	814	(1)
Matrix Operations	815	(15)
Project: Automated Solution of Linear Systems	829	(1)
Eigenvalues and Rotated Conics	830	(13)
Project: Eigenvalues and Rotated Conics	840	(1)
Review: Definitions, Concepts, Results	840	(3)
Curves and Surfaces in Space	843	(48)
Curves and Motion in Space	844	(14)
Project: Does a Pitched Baseball Really Curve?	857	(1)
Curvature and Acceleration	858	(13)
Cylinders and Quadric Surface	871	(10)
Cylindrical and Spherical Coordinates	881	(10)
Review: Definitions, Concepts, Results	889	(2)
Partial Differentiation	891	(100)
Introduction	892	(1)
Functions of Several Variables	892	(10)
Limits and Continuity	902	(8)
Partial Derivatives	910	(10)
Multivariable Optimization Problems	920	(11)
Linear Approximation and Matrix Derivatives	931	(11)
Project: Computer Algebra Implementation of Newton's Method	941	(1)
The Multivariable Chain Rule	942	(12)
Directional Derivatives and the Gradient Vector	954	(11)
Lagrange Multipliers and Constrained Optimization	965	(10)
Project: Numerical Solution of Lagrange Multiplier Systems	975	(1)
Critical Points of Multivariable Functions	975	(16)
Project: Critical Point Investigations	986	(1)
Review: Definitions, Concepts, Results	987	(4)
Multiple Integrals	991	(74)
Double Integrals	992	(7)
Project: Midpoint Sums Approximating Double Integrals	999	(1)
Double Integrals over More General Regions	999	(7)
Area and Volume by Double Integration	1006	(7)
Double Integrals in Polar Coordinates	1013	(7)
Applications of Double Integrals	1020	(11)
Project: Optimal Design of Downhill Race-Car Wheels	1030	(1)
Triple Integrals	1031	(9)
Project: Archimedes' Floating Paraboloid	1039	(1)
Integration in Cylindrical and Spherical Coordinates	1040	(8)
Surface Area	1048	(5)
Change of Variables in Multiple Integrals	1053	(12)
Review: Definitions, Concepts, Results	1061	(4)
Vector Calculus	1065
Vector Fields	1066
Line Integrals	1071
The Fundamental Theorem and Independence of Path	1082
Green's Theorem	1089
Surface Integrals	1099
Project: Surface Integrals and Rocket Nose Cones	1109
The Divergence Theorem	1109
Stokes' Theorem	1117
Review: Definitions, Concepts, Results	1124
APPENDICES	A-1
A: Real Numbers and Inequalities	A-1
B: The Coordinate Plane and Straight Lines	A-6
C: Review of Trigonometry	A-13
D: Proofs of the Limit Laws	A-19
E: The Completeness of the Real Number System	A-23
F: Existence of the Integral	A-28
G: Approximations and Riemann Sums	A-33
H: L'Hopital's Rule and Cauchy's Mean Value Theorem	A-36
I: Proof of Taylor's Formula	A-38
J: Conic Sections as Sections of a Cone	A-39
K: Proof of the Linear Approximation Theorem	A-40
L: Units of Measurement and Conversion Factors	A-41
M: Formulas from Algebra, Geometry, and Trigonometry	A-42
N: The Greek Alphabet	A-44
Answers to Odd-Numbered Problems	A-45
References for Further Study	A-100
Indices	I-1

Excerpts

Contemporary calculus instructors and students face traditional challenges as well as new ones that result from changes in the role and practice of mathematics by scientists and engineers in the world at large. As a consequence, this sixth edition of our calculus textbook is its most extensive revision since the first edition appeared in 1982. One chapter of the fifth edition has been replaced in the table of contents by two entirely new ones; most of the remaining chapters have been extensively rewritten. Nearly 160 of the book's over 800 worked examples are new for this edition and the 1850 figures in the text include 250 new computer-generated graphics. Almost 800 of its 7250 problems are new, and these are augmented by over 330 new conceptual discussion questions that now precede the problem sets. Moreover, almost 1100 new true/false questions are included in the Study Guides on the new CD-ROM that accompanies this edition. In summary, almost 2200 of these 8650-plus problems and questions are new, and the text discussion and explanations have undergone corresponding alteration and improvement. PRINCIPAL NEW FEATURES The current revision of the text features More unified treatment oftranscendental functionsin Semester I, Differential equationsand applications in Semester II, and Linear systems and matrices in Semester III. The new chapter on differential equations now appears immediately after Chapter 8 on techniques of integration. It includes both direction fields and Eider's method together with the more elementary symbolic methods (which exploit techniques from Chapter 8) and interesting applications of both first- and second-order equations. Chapter 11 (Infinite Series) now ends with a new section on power series solutions of differential equations, thus bringing full circle a unifying focus of second-semester calculus on elementary differential equations. Linear systems and matrices, ending with an elementary treatment of eigenvalues and eigenvectors, are now introduced in Chapter 12. The subsequent coverage of multivariable calculus now integrates matrix methods and terminology with the traditional notation and approach--including (for instance) introduction and extensive application of the chain rule in matrix-product form.