Calculus: Early Transcendental Functions

Chapter 0: Preliminaries

0.1, "Polynomials and Rational Functions"

0.2, "Graphing Calculators and Computer Algebra Systems"

0.3, "Inverse Functions"

0.4, "Trigonometric and Inverse Trigonometric Functions"

0.5, "Exponential and Logarithmic Functions"

0.6, "Transformations of Functions"

Chapter 1: Limits and Continuity

1.1, "A Brief Preview of Calculus: Tangent Lines and the Length of a Curve

1.2, "The Concept of Limit"

1.3, "Computation of Limits"

1.4, "Continuity and Its Consequences"

1.5, "Limits Involving Infinity; Asymptotes"

1.6, "Formal Definition of the Limit"

1.7, "Limits and Loss-of-Significance Errors"

Chapter 2: Differentiation

2.1, "Tangent Lines and Velocity"

2.2, "The Derivative"

2.3, "Computation of Derivatives: The Power Rule"

2.4, "The Product and Quotient Rules"

2.5, "The Chain Rule"

2.6, "Derivatives of Trigonometric Functions"

2.7, "Derivatives of Exponential and Logarithmic Functions"

2.8, "Implicit Differentiation and Inverse Trigonometric Functions"

2.9, "The Hyperbolic Functions"

2.10, "The Mean Value Theorem"

Chapter 3: Applications of the Derivative

3.1, "Linear Approximations and Newton's Method""

3.2, "Indeterminate Forms and L'Hpital's Rule "

3.3, "Maximum and Minimum Values"

3.4, "Increasing and Decreasing Functions"

3.5, "Concavity and the Second Derivative Test"

3.6, "Overview of Curve Sketching"

3.7, "Optimization"

3.8, "Related Rates"

3.9, "Rates of Change in Economics and the Sciences"

Chapter 4: Integration

4.1, "Antiderivatives"

4.2, "Sums and Sigma Notation"

4.3, "Area"

4.4, "The Definite Integral"

4.5, "The Fundamental Theorem of Calculus"

4.6, "Integration by Substitution"

4.7, "Numerical Integration"

4.8, "The Natural Logarithm as an Integral"

Chapter 5: Applications of the Definite Integral

5.1, "Area Between Curves"

5.2, "Volume: Slicing, Disks and Washers"

5.3, "Volumes by Cylindrical Shells"

5.4, "Arc Length and Surface Area"

5.5, "Projectile Motion"

5.6, "Applications of Integration to Physics and Engineering"

5.7, "Probability"

Chapter 6: Integration Techniques

6.1, "Review of Formulas and Techniques"

6.2, "Integration by Parts"

6.3, "Trigonometric Techniques of Integration"

6.4, "Integration of Rational Functions Using Partial Fractions"

6.5, "Integration Tables and Computer Algebra Systems"

6.6, "Improper Integrals"

Chapter 7: First-Order Differential Equations

7.1, "Modeling with Differential Equations"

7.2, "Separable Differential Equations"

7.3, ...