Calculus – Howard Anton, Irl Bivens, Stephen Davis – 10th Edition

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Calculus, Tenth Edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. Calculus, Tenth Edition excels in increasing student comprehension and conceptual understanding of the mathematics.

The new edition retains the strengths of earlier editions: e.g., Anton’s trademark clarity of exposition; mathematics; excellent exercises and examples; and appropriate level, while incorporating more skill, a -based, for effective teaching and learning, continues Anton’s vision of student confidence in mathematics because it takes the guesswork out of studying by providing them with a clear roadmap: what to do, how to do it, and if they did it right.

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  • 1. FUNCTIONS
    1.1 Functions
    1.2 Graphing Functions Using Calculators and Computer Algebra Systems
    1.3 New Functions from Old
    1.4 Families of Functions4
    1.5 Inverse Functions; Inverse Trigonometric Functions
    1.6 Exponential and Logarithmic Functions
    1.7 Mathematical Models
    1.8 Parametric Equations

    2. LIMITS AND CONTINUITY
    2.1 Limits (An Intuitive Approach)
    2.2 Computing Limits
    2.3 Limits at Infinity; End Behavior of a Function
    2.4 Limits (Discussed More Rigorously)
    2.5 Continuity
    2.6 Continuity of Trigonometric and Inverse Functions

    3. THE DERIVATIVE
    3.1 Tangent Lines, Velocity, and General Rates of Change
    3.2 The Derivative Function
    3.3 Techniques of Differentiation9
    3.4 The Product and Quotient Rules
    3.5 Derivatives of Trigonometric Functions
    3.6 The Chain Rule
    3.7 Related Rates
    3.8 Local Linear Approximation; Differentials

    4. EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS
    4.1 Implicit Differentiation
    4.2 Derivatives of Logarithmic Functions
    4.3 Derivatives of Exponential and Inverse Trigonometric Functions
    4.4 L’Hôpital’s Rule; Indeterminate Forms

    5. THE DERIVATIVE IN GRAPHING AND APPLICATIONS
    5.1 Analysis of Functions I:Increase, Decrease, and Concavity
    5.2 Analysis of Functions II: Relative Extrema; Graphing Polynomials
    5.3 More on Curve Sketching: Rational Functions; Curves with Cusps and Vertical Tangent Lines; Using Technology
    5.4 Absolute Maxima and Minima
    5.5 Applied Maximum and Minimum Problems
    5.6 Newton’s Method
    5.7 Rolle’s Theorem; Mean-Value Theorem
    5.8 Rectilinear Motion

    6. INTEGRATION
    6.1 An Overview of the Area Problem
    6.2 The Indefinite Integral
    6.3 Integration by Substitution
    6.4 The Definition of Area as a Limit; Sigma Notation
    6.5 The Definite Integral
    6.6 The Fundamental Theorem of Calculus
    6.7 Rectilinear Motion Revisited Using Integration
    6.8 Evaluating Definite Integrals by Substitution
    6.9 Logarithmic Functions from the Integral Point of View

    7. APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING
    7.1 Area Between Two Curves
    7.2 Volumes by Slicing; Disks and Washers5
    7.3 Volumes by Cylindrical Shells
    7.4 Length of a Plane Curve
    7.5 Area of a Surface of Revolution
    7.6 Average Value of a Function and its Applications
    7.7 Work
    7.8 Fluid Pressure and Force9
    7.9 Hyperbolic Functions and Hanging Cables

    8. PRINCIPLES OF INTEGRAL EVALUATION
    8.1 An Overview of Integration Methods
    8.2 Integration by Parts
    8.3 Trigonometric Integrals
    8.4 Trigonometric Substitutions3
    8.5 Integrating Rational Functions by Partial Fractions
    8.6 Using Computer Algebra Systems and Tables of Integrals
    8.7 Numerical Integration; Simpson’s Rule
    8.8 Improper Integrals

    9. MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS
    9.1 First-Order Differential Equations and Applications
    9.2 Slope Fields; Euler’s Method
    9.3 Modeling with First-Order Differential Equations
    9.4 Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring

    10. INFINITE SERIES
    10.1 Sequences
    10.2 Monotone Sequences
    10.3 Infinite Series
    10.4 Convergence Tests
    10.5 The Comparison, Ratio, and Root Tests
    10.6 Alternating Series; Conditional Convergence
    10.7 Maclaurin and Taylor Polynomials
    10.8 Maclaurin and Taylor Series; PowerSeries
    10.9 Convergence of Taylor Series
    10.10 Differentiating and Integrating Power Series; Modeling with Taylor Series

    11. ANALYTIC GEOMETRY IN CALCULUS
    11.1 Polar Coordinates
    11.2 Tangent Lines and Arc Length for Parametric and Polar Curves
    11.3 Area in Polar Coordinates4
    11.4 Conic Sections in Calculus
    11.5 Rotation of Axes; Second-Degree Equations
    11.6 Conic Sections in Polar Coordinates
    Horizon Module: Comet Collision

    12. THREE-DIMENSIONAL SPACE; VECTORS
    12.1 Rectangular Coordinates in-Space; Spheres; Cylindrical Surfaces
    12.2 Vectors
    12.3 Dot Product; Projections
    12.4 Cross Product
    12.5 Parametric Equations of Lines
    12.6 Planes in-Space
    12.7 Quadric Surfaces
    12.8 Cylindrical and Spherical Coordinates5

    13. VECTOR-VALUED FUNCTIONS
    13.1 Introduction to Vector-Valued Functions
    13.2 Calculus of Vector-Valued Functions
    13.3 Change of Parameter; Arc Length
    13.4 Unit Tangent, Normal, and Binormal Vectors
    13.5 Curvature
    13.6 Motion Along a Curve
    13.7 Kepler’s Laws of Planetary Motion

    14. PARTIAL DERIVATIVES
    14.1 Functions of Two or More Variables
    14.2 Limits and Continuity
    14.3 Partial Derivatives
    14.4 Differentiability, Differentials, and Local Linearity
    14.5 The Chain Rule
    14.6 Directional Derivatives and Gradients
    14.7 Tangent Planes and Normal Vectors
    14.8 Maxima and Minima of Functions of Two Variables
    14.9 Lagrange Multipliers

    15. MULTIPLE INTEGRALS
    15.1 Double Integrals
    15.2 Double Integrals over Nonrectangular Regions
    15.3 Double Integrals in Polar Coordinates
    15.4 Parametric Surfaces; Surface Area
    15.5 Triple Integrals
    15.6 Centroid, Center of Gravity, Theorem of Pappus
    15.7 Triple Integrals in Cylindrical and Spherical Coordinates
    15.8 Change of Variables in Multiple Integrals; Jacobians

    16. TOPICS IN VECTOR CALCULUS
    16.1 Vector Fields
    16.2 Line Integrals
    16.3 Independence of Path; Conservative Vector Fields
    16.4 Green’s Theorem
    16.5 Surface Integrals
    16.6 Applications of Surface Integrals; Flux
    16.7 The Divergence Theorem
    16.8 Stokes' Theorem
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