Calculus Early Transcendentals – Howard Anton, Irl Bivens, Stephen Davis – 7th Edition

chapter one FUNCTIONS 11.1 Functions 1
1.2 Graphing Functions Using Calculators and Computer Algebra Systems16
1.3 New Functions from Old 27
1.4 Families of Functions40
1.5 Inverse Functions; Inverse Trigonometric Functions 51
1.6 Exponential and Logarithmic Functions 65
1.7 Mathematical Models 76
1.8 Parametric Equations 86
chapter two LIMITS AND CONTINUITY 101
2.1 Limits (An Intuitive Approach) 101
2.2 Computing Limits 113
2.3 Limits at Infinity; End Behavior of a Function 122
2.4 Limits (Discussed More Rigorously) 134
2.5 Continuity 144
2.6 Continuity of Trigonometric and Inverse Functions 155
chapter three THE DERIVATIVE 165
3.1 Tangent Lines, Velocity, and General Rates of Change 165
3.2 The Derivative Function 178
3.3 Techniques of Differentiation 190
3.4 The Product and Quotient Rules 198
3.5 Derivatives of Trigonometric Functions 204
3.6 The Chain Rule 209
3.7 Related Rates 217
3.8 Local Linear Approximation; Differentials 224
chapter four EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS 235
4.1 Implicit Differentiation 235
4.2 Derivatives of Logarithmic Functions 243
4.3 Derivatives of Exponential and Inverse Trigonometric Functions 248
4.4 L’Hôpital’s Rule; Indeterminate Forms 256
chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS 267
5.1 Analysis of Functions I:Increase, Decrease, and Concavity 267
5.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials 279
5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology 289
5.4 Absolute Maxima and Minima 301
5.5 Applied Maximum and Minimum Problems 309
5.6 Newton’s Method 323
5.7 Rolle’s Theorem; Mean-Value Theorem 329
5.8 Rectilinear Motion 336
chapter six INTEGRATION 349
6.1 An Overview of the Area Problem 349
6.2 The Indefinite Integral 355
6.3 Integration by Substitution 365
6.4 The Definition of Area as a Limit; Sigma Notation373
6.5 The Definite Integral 386
6.6 The Fundamental Theorem of Calculus 396
6.7 Rectilinear Motion Revisited Using Integration 410
6.8 Evaluating Definite Integrals by Substitution 419
6.9 Logarithmic Functions from the Integral Point of View 425
chapter 7 APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 442
7.1 Area Between Two Curves 442
7.2 Volumes by Slicing; Disks and Washers 450
7.3 Volumes by Cylindrical Shells 459
7.4 Length of a Plane Curve 465
7.5 Area of a Surface of Revolution 471
7.6 Average Value of a Function and its Applications 476
7.7 Work 481
7.8 Fluid Pressure and Force 490
7.9 Hyperbolic Functions and Hanging Cables 496
chapter eight PRINCIPLES OF INTEGRAL EVALUATION 510
8.1 An Overview of Integration Methods 510
8.2 Integration by Parts 513
8.3 Trigonometric Integrals 522
8.4 Trigonometric Substitutions 530
8.5 Integrating Rational Functions by Partial Fractions 537
8.6 Using Computer Algebra Systems and Tables of Integrals 545
8.7 Numerical Integration; Simpson’s Rule 556
8.8 Improper Integrals 569
chapter 9 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 582
9.1 First-Order Differential Equations and Applications 582
9.2 Slope Fields; Euler’s Method 596
9.3 Modeling with First-Order Differential Equations 603
9.4 Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring 612
chapter ten INFINITE SERIES 624
10.1 Sequences 624
10.2 Monotone Sequences 635
10.3 Infinite Series 643
10.4 Convergence Tests652
10.5 The Comparison, Ratio, and Root Tests 659
10.6 Alternating Series; Conditional Convergence 666
10.7 Maclaurin and Taylor Polynomials 675
10.8 Maclaurin and Taylor Series; PowerSeries 685
10.9 Convergence of Taylor Series 694
10.10 Differentiating and Integrating Power Series; Modeling with Taylor Series 704
chapter eleven ANALYTIC GEOMETRY IN CALCULUS 717
11.1 Polar Coordinates 717
11.2 Tangent Lines and Arc Length for Parametric and Polar Curves 731
11.3 Area in Polar Coordinates 740
11.4 Conic Sections in Calculus 746
11.5 Rotation of Axes; Second-Degree Equations 765
11.6 Conic Sections in Polar Coordinates 771
Horizon Module: Comet Collision 783
chapter twelve THREE-DIMENSIONAL SPACE; VECTORS 786
12.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 786
12.2 Vectors 792
12.3 Dot Product; Projections 804
12.4 Cross Product 813
12.5 Parametric Equations of Lines 824
12.6 Planes in 3-Space 831
12.7 Quadric Surfaces 839
12.8 Cylindrical and Spherical Coordinates 850
chapter thirteen VECTOR-VALUED FUNCTIONS 859
13.1 Introduction to Vector-Valued Functions 859
13.2 Calculus of Vector-Valued Functions 865
13.3 Change of Parameter; Arc Length 876
13.4 Unit Tangent, Normal, and Binormal Vectors 886
13.5 Curvature 892
13.6 Motion Along a Curve 901
13.7 Kepler’s Laws of Planetary Motion 914
chapter fourteen PARTIAL DERIVATIVES 924
14.1 Functions of Two or More Variables 924
14.2 Limits and Continuity 936
14.3 Partial Derivatives 945
14.4 Differentiability, Differentials, and Local Linearity 959
14.5 The Chain Rule 968
14.6 Directional Derivatives and Gradients 978
14.7 Tangent Planes and Normal Vectors 989
14.8 Maxima and Minima of Functions of Two Variables 996
14.9 Lagrange Multipliers 1008
chapter fifteen MULTIPLE INTEGRALS 1018
15.1 Double Integrals 1018
15.2 Double Integrals over Nonrectangular Regions 1026
15.3 Double Integrals in Polar Coordinates 1035
15.4 Parametric Surfaces; Surface Area 1043
15.5 Triple Integrals 1056
15.6 Centroid, Center of Gravity, Theorem of Pappus 1065
15.7 Triple Integrals in Cylindrical and Spherical Coordinates 1076
15.8 Change of Variables in Multiple Integrals; Jacobians 1087
Chapter sixteen TOPICS IN VECTOR CALCULUS 1102
16.1 Vector Fields 1102
16.2 Line Integrals 1112
16.3 Independence of Path; Conservative Vector Fields 1129
16.4 Green’s Theorem 1139
16.5 Surface Integrals 1147
16.6 Applications of Surface Integrals; Flux 1155
16.7 The Divergence Theorem 1164
16.8 Stokes' Theorem 1173