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Calculus Mind Map
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change。
Edited at 2020-10-10 11:38:32
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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