Calculus with Early Transcendentals, 2nd Edition

1.1 Functions and How We Represent Them

1.2 Common Functions

1.3 Transforming and Combining Functions

1.4 Inverse Functions

1.5 Calculus, Calculators, and Computer Algebra Systems

2.1 Rates of Change and Tangent Lines

2.2 Limits All around the Plane

2.3 The Mathematical Definition of Limit

2.4 Determining Limits of Functions

2.5 Continuity

2.6 Rate of Change Revisited: The Derivative

3.1 Differentiation Notation and Consequences

3.2 Derivatives of Polynomials, Exponentials, Products, and Quotients

3.3 Derivatives of Trigonometric Functions

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Inverse Functions

3.7 Rates of Change in Use

3.8 Related Rates

3.9 Linearization and Differentials

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 The First and Second Derivative Tests

4.4 L'Hôpital's Rule

4.5 Calculus and Curve Sketching

4.6 Optimization Problems

4.7 Antiderivatives

5.1 Area, Distance, and Riemann Sums

5.2 The Definite Integral

5.3 The Fundamental Theorem of Calculus

5.4 Indefinite Integrals and the Substitution Rule

5.5 The Substitution Rule and Definite Integration

6.1 Finding Volumes Using Slices

6.2 Finding Volumes Using Cylindrical Shells

6.3 Arc Length and Surface Area

6.4 Moments and Centers of Mass

6.5 Force, Work, and Pressure

6.6 Hyperbolic Functions

7.1 Integration by Parts

7.2 The Partial Fractions Method

7.3 Trigonometric Integrals

7.4 Trigonometric Substitutions

7.5 Integration Summary and Integration Using Computer Algebra Systems

7.6 Numerical Integration

7.7 Improper Integrals

8.1 Separable Differential Equations

8.2 First-Order Linear Differential Equations

8.3 Autonomous Differential Equations and Slope Fields

8.4 Second-Order Linear Differential Equations

9.1 Parametric Equations

9.2 Calculus and Parametric Equations

9.3 Polar Coordinates

9.4 Calculus in Polar Coordinates

9.5 Conic Sections in Cartesian Coordinates

9.6 Conic Sections in Polar Coordinates

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 The Ratio and Root Tests

10.6 Absolute and Conditional Convergence

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Further Applications of Series

11.1 Three-Dimensional Cartesian Space

11.2 Vectors and Vector Algebra

11.3 The Dot Product

11.4 The Cross Product

11.5 Describing Lines and Planes

11.6 Cylinders and Quadric Surfaces

12.1 Vector-Valued Functions

12.2 Arc Length and the Unit Tangent Vector

12.3 The Unit Normal and Binormal Vectors, Curvature, and Torsion

12.4 Planetary Motion and Kepler's Laws

13.1 Functions of Several Variables

13.2 Limits and Continuity of Multivariable Functions

13.3 Partial Derivatives

13.4 The Chain Rule for Multivariable Functions

13.5 Directional Derivatives and Gradient Vectors

13.6 Tangent Planes and Differentials

13.7 Extreme Values of Functions of Two Variables

13.8 Lagrange Multipliers

14.1 Double Integrals

14.2 Applications of Double Integrals

14.3 Double Integrals in Polar Coordinates

14.4 Triple Integrals

14.5 Triple Integrals in Cylindrical and Spherical Coordinates

14.6 Substitutions and Multiple Integrals

15.1 Vector Fields

15.2 Line Integrals

15.3 The Fundamental Theorem for Line Integrals

15.4 Green's Theorem

15.5 Parametric Surfaces and Surface Area

15.6 Surface Integrals

15.7 Stokes' Theorem

15.8 The Divergence Theorem