functions
- definition and properties - see
Functions - Theory - Real
functions - Introduction
- functions and physics - see
this note
- absolute value - see absolute value
- addition - see
Functions - Theory - Real functions -
Operations
- approximation - see Derivatives -
Theory - Applications - Approximation of functions by tangent lines
and Derivatives -
Theory - Applications - Taylor polynomial, also
Derivatives -
Methods Survey - Applications - Taylor polynomial and approximation
- arcsin/arccos/arctan/arccot - see arcsin/arccos/arctan/arccot
- argsinh/argcosh/argtanh/argcoth - see argsinh/argcosh/argtanh/argcoth
- argument - see
Functions - Theory - Real
functions - Introduction
- asymptotes (horizontal, vertical, oblique) -
see Derivatives - Theory - Graphing functions - Asymptotes
and Derivatives - Methods Survey - Graphing functions - Asymptotes
- asymptotic - see Functions - Theory - Limit - Order of functions, asymptotes
- attaining extremes - see
extrema of functions
- average of a function - see Integrals - Theory - Applications - Average
- Beta function - see Integrals - Theory - Applications - Gamma and Beta functions
- bijective - see
Functions - Theory - Real
functions - Introduction
- bounded function (above/below) - see
boundedness of functions
- boxes for limits of
functions
- by cases - see
Functions - Theory - Real
functions - Introduction and split functions
- characteristic function 1M(x) - see
Functions - Theory -
Elementary functions - Identity function
- composition - see
Functions - Theory - Real functions -
Operations
- concave up/down function - see
concavity of functions
- converges - see Functions - Theory - Limit - Definition
- constant function - see
Functions - Theory -
Elementary functions - Polynomials
- convex function - see concave up,
concavity of functions
- continuity - see
continuity
- continuity, uniform - see
continuity
- cos - see cos
- cosh - see cosh
- cot - see cot
- coth - see coth
- csc - see csc
- decreasing - see
monotonicity of functions
- defined by cases - see
Functions - Theory - Real
functions - Introduction, also split functions
- delta function - see
Functions - Theory -
Elementary functions - Heaviside function
- derivative - see derivative
- differentiable - see Derivatives -
Theory - Introduction - Derivative
- Dirac delta function - see
Functions - Theory -
Elementary functions - Heaviside function
- Dirichlet function - see
Functions - Theory -
Elementary functions - Dirichlet function, also
this note
- discontinuity - see
continuity
- diverges - see Functions - Theory - Limit - Definition
- domain D( f ) - see
Functions - Theory - Real functions
- Introduction
and Functions - Methods Survey - Basic
properties - Domain
- elementary functions - see elementary functions
- epsilon-delta game - see
Functions - Theory - Real functions -
Continuity and Functions - Theory - Limits - Definition
- equality of functions - see
Functions - Theory - Real
functions - Introduction
- even - see
Functions - Theory - Real functions -
Basic properties
and Functions - Methods Survey - Basic
properties - Symmetry
- example - see
this note
- expanding functions - see
Series - Methods Survey -
Series of functions - Expanding in power series
and
Series - Methods Survey -
Series of functions - Expanding in Fourier series
and
Taylor polynomial and series
and
Fourier series
- exponential - see exponential
- extrema of functions - see
extrema of functions
- factorial - see
factorial
- Frac(x) - see
Functions - Theory -
Elementary functions - Int and Frac
- Gamma function - see Integrals - Theory - Applications - Gamma function
- general power - see
power
- global maximum - see
extrema of functions
- global minimum - see
extrema of functions
- graph - see
graph
- graph sketching - see Derivatives - Theory - Graphing functions - Introduction
and Derivatives - Methods Survey - Graphing functions - Overview
- Heaviside function - see
Functions - Theory -
Elementary functions - Heaviside function
- hyperbolic functions - see hyperbolic functions
- hyperbolic functions, inverse - see argsinh/argcosh/argtgh/argcotgh
- identity function IM(x) - see
Functions - Theory -
Elementary functions - Identity function
- implicit functions - see Functions - Theory - Implicit and parametric functions - Implicit functions
and Derivatives -
Theory - Derivative of implicit and parametric functions - Implicit
functions, also
Derivatives -
Methods Survey - Implicit and parametric functions
- increasing - see
monotonicity of functions
- indicator function 1M(x) - see
Functions - Theory -
Elementary functions - Identity function
- inequality between functions - see
Functions - Theory - Real functions -
Operations
- infimum - see
extrema of functions
- inflection point - see
Functions - Theory - Real functions -
Concavity
- injection, injective function - see
1-1 function
- inside function - see composition in
Functions - Theory - Real functions -
Operations
- Int(x) - see
Functions - Theory -
Elementary functions - Int and Frac
- integrable - see Integrals - Theory - Introduction - Newton integral
- intercepts - see
Functions - Theory - Real functions -
Basic properties
- Intermediate value property (IVP) - see
Functions - Theory - Real functions -
Continuity
- inverse function - see inverse function
- inverse hyperbolic functions - see argsinh/argcosh/argtgh/argcotgh
- inverse trigonometric functions - see arcsin/arccos/arctg/arccotg
- invertible function - see
Functions - Theory - Real
functions - Introduction
- limit of a function - see Functions - Theory - Limit - Definition
and Functions - Methods Survey - Limit, also
limit of a function
- linear - see linear
function
- local maximum - see
extrema of functions
- local minimum - see
extrema of functions
- logarithm - see logarithm
- lower bound of a function - see
boundedness of functions
- maximum, global/local - see
extrema of functions
- mean of a function - see Integrals - Theory - Applications - Average
- minimum, global/local - see
extrema of functions
- monotone
monotonicity of functions
- multiplication - see
Functions - Theory - Real functions -
Operations
- non-decreasing - see
monotonicity of functions
- non-increasing - see
monotonicity of functions
- odd - see
Functions - Theory - Real functions -
Basic properties
and Functions - Methods Survey - Basic
properties - Symmetry
- 1-1 - see 1-1 function
- one-sided continuity - see
continuity
- onto - see
Functions - Theory - Real
functions - Introduction
- operations with functions - see
Functions - Theory - Real functions -
Operations
- order of functions (comparison of growth) - see Functions - Theory - Limit - Order of functions and
Functions - Theory - Limit - Intuitive evaluation
for application to limits
- order of evaluation - see
this note
- outside function - see composition in
Functions - Theory - Real functions -
Operations
- parametric functions - see parametric curve
- periodic - see
Functions - Theory - Real functions -
Basic properties
and Functions - Methods Survey - Basic
properties - Periodicity
- piecewise continuous - see this note
- piecewise-defined functions - see
Functions - Theory - Real
functions - Introduction
- point of inflection - see
Functions - Theory - Real functions -
Concavity
- polynomial - see
polynomial
- power - see
power
- proper rational function - see rational function
- range R( f ) - see
Functions - Theory - Real
functions - Introduction
- ratio of linear functions - see linear function
- rational function - see rational function
- real function - see
Functions - Theory - Real
functions - Introduction
- restriction of a function - see
Functions - Theory - Real
functions - Introduction
- Riemann integrable - see Integrals - Theory - Introduction - Riemann integral
- root - see
power
- root of a function - see
root of a function
- "saw-like" function - see
Functions - Theory -
Elementary functions - "Saw-like" functions
- scaling variable/value - see
Functions - Theory - Real functions -
Operations, also
Functions - Methods Survey -
Real functions - Transformations
- sec - see sec
- separated from 0 - see Functions - Theory - Real functions - Continuity, also
Functions - Theory - Limit - Basic properties and
Functions - Methods Survey - Basic properties - Boundedness
- shift of variable/value - see
Functions - Theory - Real functions -
Operations, also
Functions - Methods Survey -
Real functions - Transformations
- sign(x) - see
Functions - Theory -
Elementary functions - Sign
- sin - see sin
- sin(1/x) - see
Functions - Theory -
Elementary functions - sin(1/x)
- sinh - see sinh
- sketching graph - see Derivatives - Theory - Graphing functions - Introduction
and Derivatives - Methods Survey - Graphing functions - Overview
- split functions - see
Functions - Theory - Real
functions - Introduction and Derivatives - Theory - Graphing functions - Split functions
- split functions, derivative - see Derivatives - Methods Survey - Derivative
- split functions, graph - see Derivatives - Theory - Graphing functions - Split
functions
- strictly decreasing - see
monotonicity of functions
- strictly increasing - see
monotonicity of functions
- supremum - see
extrema of functions
- surjection, surjective function - see
Functions - Theory - Real
functions - Introduction
- symmetry of a function - see
Functions - Theory - Real functions -
Basic properties
and Functions - Methods Survey - Basic
properties - Symmetry
- systems of functions - see
Series - Theory -
Series of functions - Basic systems of functions
- tan - see tan
- tanh - see tanh
- test function for convergence tests - see
Integrals - Theory - Improper
integrals - Convergence tests (note on the best choice in Integrals - Methods Survey - Improper integrals)
- transformations - see
Functions - Theory - Real functions -
Operations
and Functions - Methods Survey - Basic
properties - Transformations
- trigonometric functions - see trigonometric functions
- trigonometric functions, inverse - see arcsin/arccos/arctg/arccotg
- unbounded function - see
boundedness of functions
- uniform continuity - see
continuity
- upper bound of a function - see
boundedness of functions
- value of a function - see
Functions - Theory - Real
functions - Introduction
- value of a function, scaling/shift - see
Functions - Theory - Real
functions - Operations, also
Functions - Methods Survey -
Real functions - Transformations
- variable - see
Functions - Theory - Real
functions - Introduction
- variable, scaling/shift - see
Functions - Theory - Real functions -
Operations, also
Functions - Methods Survey -
Real functions - Transformations
- zero point of a function - see
root of a function