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

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