Calculus Mind Map

Calculus-Mind-Map
3.4 Velocity and other rates of change
Motion along a line
Relationship between graphs
of and the graph of their
derivative
Sensitivity to change
Derivatives in Economics
3.1 Derivative of a Function
Definition of a derivative
Graphing Derivative from Data
Onesided derivatives
1.2 Functions & Graphs
Domain & Range
Viewing & Intrepreting Graphs
Even & Odd Functions
Piecewise Functions
Absolute Value Function
Composite Functions
1.3 Exponential Functions
Exponential Growth & Decay
The Number e
Applications
Chapter 1
1.1 Lines
Increments
Parallel Lines
Perpendicular lines
Finding Inverse Functions
Equations of Lines
1.5 Functions & Logarithms
Onetoone functions
Inverse Functions
Logarithmic Functions
Properties of Logarithms
Applications
1.6 Trigonometric Functions
Graphs of Trigonometric
Functions
Peroid of trigonometric functions
Even & Odd Trig Functions
Transformations of Trig Functions
Inverse Trig functions
1.4 Parametric Equations
Relations
Circles
Ellipses
Lines & Other Curves
Chapter 3
3.2 Differentiablity
Derivatives might not exist
differentiability implies
local linearity
Derivatives on Calculator
Differentiability implies
Continuity
Intermediate Value
Theorem for Derivatives
3.3 Rules for Differentiation
Postive integer powers,
multiples, sums, and
differences
Products and quotients
Derivative of the Sine Function
Negative integer powers of x
Second and higher order
derivatives
3.5 derivatives of trig functions
Derivative of the Cosine
Function
Simple Harmonic Motion
Jerk
Derivatives of other
Trig Functions
3.6 Chain Rule
Derivative of a Composite Function
Outsidein rule
Repeated use of the chain rule
Slopes of parametric curves
Power chain rule
New node
New node
3.7 Implicit Differentiation
Implicitly defined functions
Lenses, Tangents and
Normal lines
Derivatives of higher order
Rational Powers of
Differentiable functions
3.8 Derivaties of
Inverse trig functions
Derivatives of inverse functions
Derivatives of the arcsin
Derivative of the arctangent
Derivative of the arcsecant
Derivatives of the other three
3.9 Derivaties of
Exponential & Logarithmic
Functions
Derivative of e^x
Derivative of a^x
Derivative of ln (x)
Derivative of log (x)
Power rule for arbitrary
real powers
Chapter 2
2.1 Rates of Change and Limits
Average and Intantaneous Speed
Definition of a limit
Properties of Limits
Limit Examples
One sided and two sided limits
Sandwich Theorem
2.2 Limits involving infinity
Laws
Direct Substitution Property
Finite Limts
More Sandwichs
Infinte Limits
End Behavior models
Seeing Limits
2.3 Continuity
Continuity at a point
Continuous Functions
Algebraic Combinations
Composites
Intermediate Value Theorm
for continuous functions
2.4 Rates of Change
and Tanget Lines
Tanget to a Curve
Slope of a Curve
Normal to a Curve
Speed Revisited
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