Mathematik
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== Analysis == | == Analysis == | ||
| - | <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> | + | <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> |
| + | '''Binome, Trinome''' | ||
| + | |||
| + | {| | ||
| + | |<math>(a+b)^2=a^2+2ab+b^2</math> | ||
| + | |<math>(a+b)^3=a^3+3a^2b+3ab^2+b^3</math> | ||
| + | |- | ||
| + | |<math>(a-b)^2=a^2-2ab+b^2</math> | ||
| + | |<math>(a-b)^3=a^3-3a^2b+3ab^2-b^3</math> | ||
| + | |- | ||
| + | |<math>(a+b+c)^2=a^2+b^2+c^2+2ab+2ac+2bc</math> | ||
| + | |<math>a^3+b^3=(a+b)(a^2-ab+b^2)</math> | ||
| + | |- | ||
| + | |<math>a^2-b^2=(a+b)(a-b)</math> | ||
| + | |<math>a^3-b^3=(a-b)(a^2+ab+b^2)</math> | ||
| + | |} | ||
| + | <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> | ||
| + | |||
| + | <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> | ||
| + | |||
| + | Satz des Pythagoras: | ||
| + | |||
| + | <math>a^2+b^2=c^2</math> | ||
== komplexe Zahlen == | == komplexe Zahlen == | ||
Current revision
Analysis
Binome, Trinome
Geometrie
Satz des Pythagoras:
komplexe Zahlen
Normalform
| Summe | |
| Produkt |
Polarform:
| Produkt: | |
| Quotient: | |
| Potenz: |
-Rechenregeln:
konjungierte komplexe Zahlen:
