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

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Designed for the I-II-III sequence, the seventh edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and needs of all kinds.

The new edition retains the strengths of earlier editions–its trademark clarity of exposition, mathematics, excellent exercises and examples, and appropriate level–while incorporating new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors. For the first time, the Seventh Edition is available in both Late Transcendentals and versions.

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  • 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
  • Citation

Download now Calculus: Early Transcendentals

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