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