Mathematik

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(Geometrie)
 
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== Analysis ==
== Analysis ==
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<math>a \cdot x^2 + b \cdot x + c = 0 \Rightarrow x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4\cdot a\cdot c}} {2\cdot a}</math>
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<math>a \cdot x^2 + b \cdot x + c = 0 \quad \Rightarrow \quad x_{1,2} = \frac{-b \pm \sqrt{b^2 - 4\cdot a\cdot c}} {2\cdot a}</math>
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'''Binome, Trinome'''
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{|
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|<math>(a+b)^2=a^2+2ab+b^2</math>
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|<math>(a+b)^3=a^3+3a^2b+3ab^2+b^3</math>
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|-
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|<math>(a-b)^2=a^2-2ab+b^2</math>
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|<math>(a-b)^3=a^3-3a^2b+3ab^2-b^3</math>
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|-
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|<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc</math>
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|<math>a^3+b^3=(a+b)(a^2-ab+b^2)</math>
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|-
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|<math>a^2-b^2=(a+b)(a-b)</math>
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|<math>a^3-b^3=(a-b)(a^2+ab+b^2)</math>
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|}
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<math>a^n-b^n=(a-b)(a^{n-1}+a^{n-2}b+a^{n-3}b^2+\cdots+ab^{n-2}+b^{n-1})</math>
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<math>n!=1\cdot2\cdot3\cdot...\cdot(n-1)\cdot n,\ n\in N\setminus\{1\}</math>
== Geometrie ==
== Geometrie ==
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<math>U = \pi \cdot D = 2 \cdot \pi \cdot r</math>
<math>U = \pi \cdot D = 2 \cdot \pi \cdot r</math>
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Satz des Pythagoras:
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<math>a^2+b^2=c^2</math>
== komplexe Zahlen ==
== komplexe Zahlen ==

Current revision

Analysis

MathImage

Binome, Trinome

MathImage MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage

MathImage

MathImage

Geometrie

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Satz des Pythagoras:

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komplexe Zahlen

Normalform

MathImage MathImage:=MathImage
MathImage MathImage
Summe MathImage
Produkt MathImage

Polarform:

MathImage MathImage
MathImage MathImage
Produkt: MathImage
Quotient: MathImage
Potenz: MathImage

MathImage-Rechenregeln:

MathImage MathImage
MathImage MathImage
MathImage
MathImage MathImage

konjungierte komplexe Zahlen:

MathImage
MathImage MathImage
MathImage MathImage
MathImage MathImage MathImage
MathImage MathImage
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