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Full Description
Anton, Bivens & Davis latest issue of Calculus Early Transcendentals Single Variable continues to build upon previous editions to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The text continues to focus on and incorporate new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students. This 10th edition retains Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level.
Contents
BEFORE CALCULUS 1
0.1 Functions 1
0.2 New Functions from Old 15
0.3 Families of Functions 27
0.4 Inverse Functions; Inverse Trigonometric Functions
38
0.5 Exponential and Logarithmic Functions 52
1 LIMITS AND CONTINUITY 67
1.1 Limits (An Intuitive Approach) 67
1.2 Computing Limits 80
1.3 Limits at Infinity; End Behavior of a Function
89
1.4 Limits (Discussed More Rigorously) 100
1.5 Continuity 110
1.6 Continuity of Trigonometric, Exponential, and Inverse
Functions 121
2 THE DERIVATIVE 131
2.1 Tangent Lines and Rates of Change 131
2.2 The Derivative Function 143
2.3 Introduction to Techniques of Differentiation
155
2.4 The Product and Quotient Rules 163
2.5 Derivatives of Trigonometric Functions 169
2.6 The Chain Rule 174
3 TOPICS IN DIFFERENTIATION 185
3.1 Implicit Differentiation 185
3.2 Derivatives of Logarithmic Functions 192
3.3 Derivatives of Exponential and Inverse Trigonometric
Functions 197
3.4 Related Rates 204
3.5 Local Linear Approximation; Differentials
212
3.6 L?Hôpital?s Rule; Indeterminate
Forms 219
4 THE DERIVATIVE IN GRAPHING AND APPLICATIONS 232
4.1 Analysis of Functions I: Increase, Decrease, and
Concavity 232
4.2 Analysis of Functions II: Relative Extrema; Graphing
Polynomials 244
4.3 Analysis of Functions III: Rational Functions, Cusps,
and Vertical Tangents 254
4.4 Absolute Maxima and Minima 266
4.5 Applied Maximum and Minimum Problems 274
4.6 Rectilinear Motion 288
4.7 Newton?s Method 296
4.8 Rolle?s Theorem; Mean-Value Theorem
302
5 INTEGRATION 316
5.1 An Overview of the Area Problem 316
5.2 The Indefinite Integral 322
5.3 Integration by Substitution 332
5.4 The Definition of Area as a Limit; Sigma Notation
340
5.5 The Definite Integral 353
5.6 The Fundamental Theorem of Calculus 362
5.7 Rectilinear Motion Revisited Using Integration
376
5.8 Average Value of a Function and its Applications
385
5.9 Evaluating Definite Integrals by Substitution
390
5.10 Logarithmic and Other Functions Defined by Integrals
396
6 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE,
AND ENGINEERING 413
6.1 Area Between Two Curves 413
6.2 Volumes by Slicing; Disks and Washers 421
6.3 Volumes by Cylindrical Shells 432
6.4 Length of a Plane Curve 438
6.5 Area of a Surface of Revolution 444
6.6 Work 449
6.7 Moments, Centers of Gravity, and Centroids
458
6.8 Fluid Pressure and Force 467
6.9 Hyperbolic Functions and Hanging Cables
474
7 PRINCIPLES OF INTEGRAL EVALUATION 488
7.1 An Overview of Integration Methods 488
7.2 Integration by Parts 491
7.3 Integrating Trigonometric Functions 500
7.4 Trigonometric Substitutions 508
7.5 Integrating Rational Functions by Partial Fractions
514
7.6 Using Computer Algebra Systems and Tables of
Integrals 523
7.7 Numerical Integration; Simpson?s Rule
533
7.8 Improper Integrals 547
8 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
561
8.1 Modeling with Differential Equations 561
8.2 Separation of Variables 568
8.3 Slope Fields; Euler?s Method 579
8.4 First-Order Differential Equations and Applications
586
9 INFINITE SERIES 596
9.1 Sequences 596
9.2 Monotone Sequences 607
9.3 Infinite Series 614
9.4 Convergence Tests 623
9.5 The Comparison, Ratio, and Root Tests 631
9.6 Alternating Series; Absolute and Conditional
Convergence 638
9.7 Maclaurin and Taylor Polynomials 648
9.8 Maclaurin and Taylor Series; Power Series
659
9.9 Convergence of Taylor Series 668
9.10 Differentiating and Integrating Power Series;
Modeling with Taylor Series 678
10 PARAMETRIC AND POLAR CURVES; CONIC SECTIONS 692
10.1 Parametric Equations; Tangent Lines and Arc Length
for Parametric Curves 692
10.2 Polar Coordinates 705
10.3 Tangent Lines, Arc Length, and Area for Polar Curves
719
10.4 Conic Sections 730
10.5 Rotation of Axes; Second-Degree Equations
748
10.6 Conic Sections in Polar Coordinates 754
A APPENDICES
A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA
SYSTEMS A1
B TRIGONOMETRY REVIEW A13
C SOLVING POLYNOMIAL EQUATIONS A27
D SELECTED PROOFS A34
ANSWERS TO ODD-NUMBERED EXERCISES A45
INDEX I-1
WEB APPENDICES (online only)
Available for download
atwww.wiley.com/college/anton or
atwww.howardanton.com and in WileyPLUS.
E REAL NUMBERS, INTERVALS, AND INEQUALITIES
F ABSOLUTE VALUE
G COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS
H DISTANCE, CIRCLES, AND QUADRATIC EQUATIONS
I EARLY PARAMETRIC EQUATIONS OPTION
J MATHEMATICAL MODELS
K THE DISCRIMINANT
L SECOND-ORDER LINEAR HOMOGENEOUS DIFFERENTIAL
EQUATIONS
WEB PROJECTS: Expanding the Calculus Horizon (online
only)
Available for download
atwww.wiley.com/college/anton or
atwww.howardanton.com and in WileyPLUS.
COMET COLLISION ITERATION AND DYNAMICAL SYSTEMS RAILROAD
DESIGN ROBOTICS
