Calculus Early Transcendentals: Single Variable – Howard Anton, Irl Bivens, Stephen Davis – 10th Edition

0 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 4386.5 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 4676.9 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