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Calculus by Mind Map: Calculus

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