1. 1.4 Parametric Equations
1.1. Relations
1.2. Circles
1.3. Ellipses
1.4. Lines & Other Curves
2. Functions
3. Average Rates of Change
4. Applications
5. 1.2 Functions & Graphs
5.1. Domain & Range
5.2. Viewing & Intrepreting Graphs
5.3. Even & Odd Functions
5.4. Piecewise Functions
5.5. Absolute Value Function
5.6. Composite Functions
6. Radian Measure
7. Slope of a line
8. 1.3 Exponential Functions
8.1. Exponential Growth & Decay
8.2. The Number e
8.3. Applications
9. Instantaneous rates of change
10. 3.1 Derivative of a Function
10.1. Definition of a derivative
10.2. Graphing Derivative from Data
10.3. One-sided derivatives
11. 3.4 Velocity and other rates of change
11.1. Motion along a line
11.1.1. Relationship between graphs of and the graph of their derivative
11.2. Sensitivity to change
11.3. Derivatives in Economics
12. Derivative Notation
13. Chapter 2
13.1. 2.1 Rates of Change and Limits
13.1.1. Average and Intantaneous Speed
13.1.2. Definition of a limit
13.1.3. Properties of Limits
13.1.3.1. Limit Examples
13.1.4. One sided and two sided limits
13.1.4.1. `1
13.1.5. Sandwich Theorem
13.2. 2.2 Limits involving infinity
13.2.1. Laws
13.2.2. Direct Substitution Property
13.2.3. Finite Limts
13.2.4. More Sandwichs
13.2.5. Infinte Limits
13.2.6. End Behavior models
13.2.7. Seeing Limits
13.3. 2.3 Continuity
13.3.1. Continuity at a point
13.3.2. Continuous Functions
13.3.3. Algebraic Combinations
13.3.4. Composites
13.3.5. Intermediate Value Theorm for continuous functions
13.4. 2.4 Rates of Change and Tanget Lines
13.4.1. Tanget to a Curve
13.4.2. Slope of a Curve
13.4.3. Normal to a Curve
13.4.4. Speed Revisited
13.5. Review
14. Chapter 3
14.1. 3.2 Differentiablity
14.1.1. Derivatives might not exist
14.1.2. differentiability implies local linearity
14.1.3. Derivatives on Calculator
14.1.4. Differentiability implies Continuity
14.1.5. Intermediate Value Theorem for Derivatives
14.2. 3.3 Rules for Differentiation
14.2.1. Postive integer powers, multiples, sums, and differences
14.2.2. Products and quotients
14.2.2.1. Derivative of the Sine Function
14.2.3. Negative integer powers of x
14.2.4. Second and higher order derivatives
14.3. 3.5 derivatives of trig functions
14.3.1. Derivative of the Cosine Function
14.3.2. Simple Harmonic Motion
14.3.3. Jerk
14.3.4. Derivatives of other Trig Functions
14.4. 3.6 Chain Rule
14.4.1. Derivative of a Composite Function
14.4.2. Outside-in rule
14.4.3. Repeated use of the chain rule
14.4.4. Slopes of parametric curves
14.4.5. Power chain rule
14.4.6. New node
14.4.7. New node
14.5. 3.7 Implicit Differentiation
14.5.1. Implicitly defined functions
14.5.2. Lenses, Tangents and Normal lines
14.5.3. Derivatives of higher order
14.5.4. Rational Powers of Differentiable functions
14.6. 3.8 Derivaties of Inverse trig functions
14.6.1. Derivatives of inverse functions
14.6.2. Derivatives of the arcsin
14.6.3. Derivative of the arctangent
14.6.4. Derivative of the arcsecant
14.6.5. Derivatives of the other three
14.7. 3.9 Derivaties of Exponential & Logarithmic Functions
14.7.1. Derivative of e^x
14.7.2. Derivative of a^x
14.7.3. Derivative of ln (x)
14.7.4. Derivative of log (x)
14.7.5. Power rule for arbitrary real powers
14.8. Key terms & Review
15. Chapter 4
16. Chapter 5
17. General
17.1. Sample Tests
17.2. Recommended Examples
17.2.1. Solutions
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