0. Functions

1. 0.1 Functions and Their Graphs
2. 0.2 Some Important Functions
3. 0.3 The Algebra of Functions
4. 0.4 Zeros of Functions - The Quadratic Formula and Factoring
5. 0.5 Exponents and Power Functions
6. 0.6 Functions and Graphs in Applications

1. The Derivative

• 1.1 The Slope of a Straight Line
• 1.2 The Slope of a Curve at a Point
• 1.3 The Derivative and Limits
• 1.4 Limits and the Derivative
• 1.5 Differentiability and Continuity
• 1.6 Some Rules for Differentiation
• 1.8 The Derivative as a Rate of Change
• 2. Applications of the Derivative
• 2.1 Describing Graphs of Functions
• 2.2 The First and Second Derivative Rules
• 2.3 The First and Section Derivative Tests and Curve Sketching
• 2.4 Curve Sketching (Conclusion)
• 2.5 Optimization Problems
• 2.6 Further Optimization Problems
• 2.7 Applications of Derivatives to Business and Economics

3. Techniques of Differentiation

• 3.1 The Product and Quotient Rules
• 3.2 The Chain Rule
• 3.3 Implicit Differentiation and Related Rates

4. The Exponential and Natural Logarithm Functions

• 4.1 Exponential Functions
• 4.2 The Exponential Function ex
• 4.3 Differentiation of Exponential Functions
• 4.4 The Natural Logarithm Function
• 4.5 The Derivative of ln x
• 4.6 Properties of the Natural Logarithm Function

5. Applications of the Exponential and Natural Logarithm Functions

• 5.1 Exponential Growth and Decay
• 5.2 Compound Interest
• 5.3. Applications of the Natural Logarithm Function to Economics
• 5.4. Further Exponential Models

6. The Definite Integral

• 6.1 Antidifferentiation
• 6.2 The Definite Integral and Net Change of a Function
• 6.3 The Definite Integral and Area Under a Graph
• 6.4 Areas in the xy-Plane
• 6.5 Applications of the Definite Integral

7. Functions of Several Variables

• 7.1 Examples of Functions of Several Variables
• 7.2 Partial Derivatives
• 7.3 Maxima and Minima of Functions of Several Variables
• 7.4 Lagrange Multipliers and Constrained Optimization
• 7.5 The Method of Least Squares
• 7.6 Double Integrals

8. The Trigonometric Functions

• 8.1 Radian Measure of Angles
• 8.2 The Sine and the Cosine
• 8.3 Differentiation and Integration of sin t and cos t
• 8.4 The Tangent and Other Trigonometric Functions

9. Techniques of Integration

• 9.1 Integration by Substitution
• 9.2 Integration by Parts
• 9.3 Evaluation of Definite Integrals
• 9.4 Approximation of Definite Integrals
• 9.5 Some Applications of the Integral
• 9.6 Improper Integrals

10. Differential Equations

• 10.1 Solutions of Differential Equations
• 10.2 Separation of Variables
• 10.3 First-Order Linear Differential Equations
• 10.4 Applications of First-Order Linear Differential Equations
• 10.5 Graphing Solutions of Differential Equations
• 10.6 Applications of Differential Equations
• 10.7 Numerical Solution of Differential Equations

11. Taylor Polynomials and Infinite Series

• 11.1 Taylor Polynomials
• 11.2 The Newton-Raphson Algorithm
• 11.3 Infinite Series
• 11.4 Series with Positive Terms
• 11.5 Taylor Series

12. Probability and Calculus

• 12.1 Discrete Random Variables
• 12.2 Continuous Random Variables
• 12.3 Expected Value and Variance
• 12.4 Exponential and Normal Random Variables
• 12.5 Poisson and Geometric Random Variables