## Calculus Mind Map

Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change。

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Calculus-Mind-Map

Chapter 1

1.1 Lines

Increments

Parallel Lines

Perpendicular lines

Finding Inverse Functions

Equations of Lines

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

1.4 Parametric Equations

Relations

Circles

Ellipses

Lines & Other Curves

1.5 Functions & Logarithms

Onetoone functions

Inverse Functions

Logarithmic Functions

Properties of Logarithms

Applications

1.6 Trigonometric Functions

Graphs of TrigonometricFunctions

Peroid of trigonometric functions

Even & Odd Trig Functions

Transformations of Trig Functions

Inverse Trig functions

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 Theormfor continuous functions

2.4 Rates of Changeand Tanget Lines

Tanget to a Curve

Slope of a Curve

Normal to a Curve

Speed Revisited

Chapter 3

3.1 Derivative of a Function

Definition of a derivative

Graphing Derivative from Data

Onesided derivatives

3.2 Differentiablity

Derivatives might not exist

differentiability implieslocal linearity

Derivatives on Calculator

Differentiability impliesContinuity

Intermediate ValueTheorem for Derivatives

3.3 Rules for Differentiation

Postive integer powers,multiples, sums, anddifferences

Products and quotients

Derivative of the Sine Function

Negative integer powers of x

Second and higher orderderivatives

3.4 Velocity and other rates of change

Motion along a line

Relationship between graphsof and the graph of theirderivative

Sensitivity to change

Derivatives in Economics

3.5 derivatives of trig functions

Derivative of the CosineFunction

Simple Harmonic Motion

Jerk

Derivatives of otherTrig 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 andNormal lines

Derivatives of higher order

Rational Powers ofDifferentiable functions

3.8 Derivaties ofInverse 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 ofExponential & LogarithmicFunctions

Derivative of e^x

Derivative of a^x

Derivative of ln (x)

Derivative of log (x)

Power rule for arbitraryreal powers