Wacker Art Basic Functions

Wacker Art

Basic Functions

Bild: "Kellerwald"

Mathematical Functions

Exponential Function: y = e^x

Taylor Series of the Exponential Function

Exponential Function Taylor Series

Even Part of the Exponential Function - The Hyperbolic Cosine

Cosinus Hyperbolicus Function

A function is called even if f(x) = f(-x)

Odd Part of the Exponential Function - The Hyperbolic Sine

Hyperbolic Sine Function

A function is called odd if f(x) = -f(-x)

Taylor Series of the Hyperbolic Cosine Function

Hyperbolic Cosine Function Taylor Series

Taylor Series of the Hyperbolic Sine Function

Hyperbolic Sine Function Taylor Series

Relation between Hyperbolic Cosine Function and Cosine Function

Cosine Function

Relation between Hyperbolic Sine Function and Sine Function

Sine Function

Taylor Series of the Cosine Function

Cosine Function Taylor Series

Taylor Series of the Sine Function

Sine Function Taylor Series

Basic Relations

Exponential Function

Definition of Sine and Cosine Functions with the Complex Exponential Function

Cosine Function

Sine Function

Definition of Tangent and Cotangent Functions with Sine and Cosine Functions

Tanget Function

Cotangent Function

Hyperbolic Tangent and Hyperbolic Cotangent Functions

Hyperbolic Tangent Function

Hyperbolic Cotangent Function

Logarithm Function: y = ln(x)

Gauß Function: y = e^-x²

Taylor Series

Gauss Function Taylor Series

Hyperbolic Sine Function - Sinus Hyperbolicus: y = sinh(x)

Taylor Series

Hyperbolic Sine Function Taylor Series

Inverse Hyperbolic Sine Function - Area Sinus Hyperbolicus: y = arcsinh(x)

Hyperbolic ArcSine Function

Hyperbolic Cosine Function - Cosinus Hyperbolicus: y = cosh(x)

Taylor Series

Hyperbolic Cosine Function Taylor Series

Invers Hyperbolic Cosine Function - Area Cosinus Hyperbolicus: y = arcosh(x)

Inverse hyperbolic cosine Function

Hyperbolic Tangent Function - Tangens Hyperbolicus: y = tanh(x)

Hyperbolic Tangent Function

Hyperbolic Cotangent Function - Cotangens Hyperbolicus: y = coth(x)

Hyperbolic Cotangent Function

Sine Function: y = sin(x)

Sine Function Taylor Series

Inverse Sine Function - Arcus Sine: y = arcsin(x)

Cosine Function: y = cos(x)

Cosine Function Taylor Series

Inverse Cosine Function - Arcus Cosine: y = arccos(x)

Tangent Function: y = tan(x)

Tangent Function

Inverse Tangent Function: y = atan(x)

Cotangent Function: y = cot(x)

Cotangent Function

Invers Cotangent Function: y = arccot(x)

Power Functions: y = xⁿ

y = x^-4	y = x^-3
y = x^-2	y = x^-1
y = x⁰ = 1	y = x¹ = x
y = x²	y = x³
y = x⁴	y = x⁵
y = x²⁴	y = x²⁵

Bild: "Edersee"

Visit the Geometric Algebra page for an overview on Geometric Algebra.

Geometric Algebra

27. August 2017 Version 1.0

Mathematical Functions

Exponential Function: y = ex

Taylor Series of the Exponential Function

Even Part of the Exponential Function - The Hyperbolic Cosine

Odd Part of the Exponential Function - The Hyperbolic Sine

Taylor Series of the Hyperbolic Cosine Function

Taylor Series of the Hyperbolic Sine Function

Relation between Hyperbolic Cosine Function and Cosine Function

Relation between Hyperbolic Sine Function and Sine Function

Taylor Series of the Cosine Function

Taylor Series of the Sine Function

Basic Relations

Definition of Sine and Cosine Functions with the Complex Exponential Function

Definition of Tangent and Cotangent Functions with Sine and Cosine Functions

Hyperbolic Tangent and Hyperbolic Cotangent Functions

Logarithm Function: y = ln(x)

Gauß Function: y = e-x2

Taylor Series

Hyperbolic Sine Function - Sinus Hyperbolicus: y = sinh(x)

Taylor Series

Inverse Hyperbolic Sine Function - Area Sinus Hyperbolicus: y = arcsinh(x)

Hyperbolic Cosine Function - Cosinus Hyperbolicus: y = cosh(x)

Taylor Series

Invers Hyperbolic Cosine Function - Area Cosinus Hyperbolicus: y = arcosh(x)

Hyperbolic Tangent Function - Tangens Hyperbolicus: y = tanh(x)

Hyperbolic Cotangent Function - Cotangens Hyperbolicus: y = coth(x)

Sine Function: y = sin(x)

Inverse Sine Function - Arcus Sine: y = arcsin(x)

Cosine Function: y = cos(x)

Inverse Cosine Function - Arcus Cosine: y = arccos(x)

Tangent Function: y = tan(x)

Inverse Tangent Function: y = atan(x)

Cotangent Function: y = cot(x)

Invers Cotangent Function: y = arccot(x)

Power Functions: y = xn

y = x-4

y = x-3

y = x-2

y = x-1

y = x0 = 1

y = x1 = x

y = x2

y = x3

y = x4

y = x5

y = x24

y = x25

Exponential Function: y = e^x

Gauß Function: y = e^-x²

Power Functions: y = xⁿ

y = x^-4

y = x^-3

y = x^-2

y = x^-1

y = x⁰ = 1

y = x¹ = x

y = x²

y = x³

y = x⁴

y = x⁵

y = x²⁴

y = x²⁵