
1. Instantaneous rates of change
2. Chapter 5
3. Chapter 4
4. General
4.1. Sample Tests
4.2. Recommended Examples
4.2.1. Solutions
5. 1.4 Parametric Equations
5.1. Relations
5.2. Circles
5.3. Ellipses
5.4. Lines & Other Curves
6. Functions
7. Average Rates of Change
8. Applications
9. 1.2 Functions & Graphs
9.1. Domain & Range
9.2. Viewing & Intrepreting Graphs
9.3. Even & Odd Functions
9.4. Piecewise Functions
9.5. Absolute Value Function
9.6. Composite Functions
10. Radian Measure
11. Slope of a line
12. 1.3 Exponential Functions
12.1. Exponential Growth & Decay
12.2. The Number e
12.3. Applications
13. 3.1 Derivative of a Function
13.1. Definition of a derivative
13.2. Graphing Derivative from Data
13.3. One-sided derivatives
14. 3.4 Velocity and other rates of change
14.1. Motion along a line
14.1.1. Relationship between graphs of and the graph of their derivative
14.2. Sensitivity to change
14.3. Derivatives in Economics
15. Derivative Notation
16. Chapter 2
16.1. 2.1 Rates of Change and Limits
16.1.1. Average and Intantaneous Speed
16.1.2. Definition of a limit
16.1.3. Properties of Limits
16.1.3.1. Limit Examples
16.1.4. One sided and two sided limits
16.1.4.1. `1
16.1.5. Sandwich Theorem
16.2. 2.2 Limits involving infinity
16.2.1. Laws
16.2.2. Direct Substitution Property
16.2.3. Finite Limts
16.2.4. More Sandwichs
16.2.5. Infinte Limits
16.2.6. End Behavior models
16.2.7. Seeing Limits
16.3. 2.3 Continuity
16.3.1. Continuity at a point
16.3.2. Continuous Functions
16.3.3. Algebraic Combinations
16.3.4. Composites
16.3.5. Intermediate Value Theorm for continuous functions
16.4. 2.4 Rates of Change and Tanget Lines
16.4.1. Tanget to a Curve
16.4.2. Slope of a Curve
16.4.3. Normal to a Curve
16.4.4. Speed Revisited
16.5. Review
17. Chapter 3
17.1. 3.2 Differentiablity
17.1.1. Derivatives might not exist
17.1.2. differentiability implies local linearity
17.1.3. Derivatives on Calculator
17.1.4. Differentiability implies Continuity
17.1.5. Intermediate Value Theorem for Derivatives
17.2. 3.3 Rules for Differentiation
17.2.1. Postive integer powers, multiples, sums, and differences
17.2.2. Products and quotients
17.2.2.1. Derivative of the Sine Function
17.2.3. Negative integer powers of x
17.2.4. Second and higher order derivatives
17.3. 3.5 derivatives of trig functions
17.3.1. Derivative of the Cosine Function
17.3.2. Simple Harmonic Motion
17.3.3. Jerk
17.3.4. Derivatives of other Trig Functions
17.4. 3.6 Chain Rule
17.4.1. Derivative of a Composite Function
17.4.2. Outside-in rule
17.4.3. Repeated use of the chain rule
17.4.4. Slopes of parametric curves
17.4.5. Power chain rule
17.4.6. New node
17.4.7. New node
17.5. 3.7 Implicit Differentiation
17.5.1. Implicitly defined functions
17.5.2. Lenses, Tangents and Normal lines
17.5.3. Derivatives of higher order
17.5.4. Rational Powers of Differentiable functions
17.6. 3.8 Derivaties of Inverse trig functions
17.6.1. Derivatives of inverse functions
17.6.2. Derivatives of the arcsin
17.6.3. Derivative of the arctangent
17.6.4. Derivative of the arcsecant
17.6.5. Derivatives of the other three
17.7. 3.9 Derivaties of Exponential & Logarithmic Functions
17.7.1. Derivative of e^x
17.7.2. Derivative of a^x
17.7.3. Derivative of ln (x)
17.7.4. Derivative of log (x)
17.7.5. Power rule for arbitrary real powers
17.8. Key terms & Review
18. Chapter 1
18.1. 1.1 Lines
18.1.1. Increments
18.1.2. Parallel Lines
18.1.2.1. Perpendicular lines
18.1.3. Finding Inverse Functions
18.1.4. Equations of Lines
18.2. 1.5 Functions & Logarithms
18.2.1. One-to-one functions
18.2.2. Inverse Functions
18.2.3. Logarithmic Functions
18.2.4. Properties of Logarithms
18.2.5. Applications
18.3. Key Terms & Review
18.4. 1.6 Trigonometric Functions
18.4.1. Graphs of Trigonometric Functions
18.4.2. Peroid of trigonometric functions
18.4.3. Even & Odd Trig Functions
18.4.4. Transformations of Trig Functions
18.4.5. Inverse Trig functions