| Grundrechnungsarten |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Natürliche Zahlen | 0 1 2 3 4 5 6 7 8 9 | 3+5 |
|
| 34+2 |
|
| 67+33 |
|
| Gemischte Zahlen | # / | 2#2/7+1#1/2 |
|
| 3#1/2+5#2/3 |
|
| Dezimalzahl | , . | 0.345+0.34 |
|
| 0,45-0.74 |
|
| Periodische Dezimalzahl | . , | 0,3_7 |
|
| 3,2_6+2._8 |
|
| Prozent | % | % |
|
| 30% |
|
| 20%+2 |
|
| Addition | + | + |
|
| 3+7 |
|
| 3+4+2+6+23 |
|
| Subtraktion | - | - |
|
| 3-7 |
|
| 34-4-6-7 |
|
| Multiplikation | * | * |
|
| 3*7 |
|
| 2*4*5 |
|
| Division | / : | : |
|
| / |
|
| 3/x+2/x |
|
| 3/4+8/4 |
|
| Potenz | ^ | ^ |
|
| 3^4 |
|
| x^2=x^3 |
|
| Komplexe Zahlen | i | i |
|
| 3+6i+2-1i |
|
| 3i/(24-3I) |
|
| Klammern | { [ ( ) ]} } | ( |
|
| ) |
|
| [ |
|
| ] |
|
| {3*[5+2(2+3)]+1}+2 |
|
| (23+x)+(34-12) |
|
| Variablen und Gleichungen |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Variablen | a b c d n m q p r s t u v w x y z ?? ✕ | x |
|
| 3x+3y |
|
| x^2=1 |
|
| 3d+5d |
|
| Variablen | var | varx |
|
| var(what you like) |
|
| var(beliebig) |
|
| 5var(birds)+6var(birds) |
|
| 5m+6cm=var(paper)*20cm |
|
| Gleichung | = | = |
|
| 3x+3=9 |
|
| 9d=3 |
|
| 5y^2=y+3 |
|
| Ungleichung | <,>,<=,>= | < |
|
| > |
|
| <= |
|
| >= |
|
| 3x+3>9 |
|
| 9d<=3 |
|
| 5y^2>=y+3 |
|
| Gleichungssystem | ; | 3x+3=9d;9d=3x |
|
| 5y=z+3;z+y=3 |
|
| a+b+c+d=10; a-b+c+d=6; a+b-c+d=4; a+b+c-d=2 |
|
| Wert einsetzen | ..;n | 3x+3;6;7 |
|
| x^2+2x-3;11;4 |
|
| (x^3+x-1)";1;2;3 |
|
| Funktionen |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Absoluter Betrag | abs | abs |
|
| abs( |
|
| abs(-2) |
|
| abs(3-4) |
|
| abs(4) |
|
| Binomialkoeffizienten | n choose k/n über k/k aus n.. | 5 choose 6 |
|
| 3 aus 4 |
|
| 4 über 3 |
|
| 5 ueber 3 |
|
| 5 boven 3 |
|
| 5 parmi 3 |
|
| Signum | sgn | sgn |
|
| sgn( |
|
| sgn(-7) |
|
| sgn(7) |
|
| Runden | round | round |
|
| round( |
|
| round(1.2) |
|
| round(-0.002) |
|
| round(6.523) |
|
| Fakultät | ! | ! |
|
| 6! |
|
| 2! |
|
| 5!-3! |
|
| Sinus | sin | sin |
|
| sin( |
|
| sinPI |
|
| sin(3+4) |
|
| sin^2(3PI) |
|
| Kosinus | cos | cos |
|
| cos( |
|
| cosPI |
|
| cos(3+4) |
|
| cos^2(3PI) |
|
| Tangens | tan | tan |
|
| tan( |
|
| tanPI |
|
| tan(3+4) |
|
| tan^2(3PI) |
|
| Cotangens | cot | cot |
|
| cot( |
|
| cotPI |
|
| cot(3+4) |
|
| cot^2(3PI) |
|
| Arkussinus | asin | asin |
|
| asin( |
|
| asin0 |
|
| asin(3+4) |
|
| asin^2(3) |
|
| Arcuscosinus | acos | acos |
|
| acos( |
|
| acos0 |
|
| acos(3+4) |
|
| acos^2(3) |
|
| Arcustangens | atan | atan |
|
| atan( |
|
| atan0 |
|
| atan(3+4) |
|
| atan^2(3) |
|
| Arkuskotangens | acot | acot |
|
| acot( |
|
| acot0 |
|
| acot(3+4) |
|
| acot^2(3) |
|
| Wurzeln | sqrt | sqrt |
|
| √ |
|
| sqrt( |
|
| √( |
|
| sqrt4 |
|
| sqrt-9 |
|
| sqrtx^2 |
|
| Von | von/of | von |
|
| of |
|
| 3%von100 |
|
| 23.2%von100 |
|
| 20%von100 |
|
| Exponentialfunktion Basis E | exp,e | exp |
|
| e |
|
| exp( |
|
| exp1 |
|
| expx |
|
| exp(3+x) |
|
| e^4 |
|
| Logarithmus zur Basis | log_ | log_ |
|
| log_3(E) |
|
| log_5x |
|
| log_x(x+3) |
|
| Natürlicher Logarithmus | ln,log | ln |
|
| ln( |
|
| lnE |
|
| logE |
|
| ln(x+3) |
|
| Logarithmus zur Basis 10 | lg | lg |
|
| lg_ |
|
| lg8 |
|
| lg(x+3) |
|
| Logarithmus zur Basis 2 | lb | lb |
|
| lb_ |
|
| lb4 |
|
| lb(x+3) |
|
| Ableitung | ',",''' | ' |
|
| " |
|
| ''' |
|
| (4x^2+5x+1)' |
|
| (sin(x^2+1))";2 |
|
| (expx)' |
|
| (1/(1+x^2))' |
|
| Partielle Ableitung | d/dx, d^2/dx, d²/dx, d^3/dt | d/dx(4x^2+5x+1) |
|
| d/dt(sin(t^2+1)) |
|
| d/dx(d/dy(yx^2+xy^2)) |
|
| Konstanten |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Eulersche Konstante | E, e | E |
|
| Natürlicher Logarithmus von 2 | LN2 | LN2 |
|
| Natürliche Logarithmus von 10 | LN10 | LN10 |
|
| Konstanter Logarithmus von 2 | LOG2E | LOG2E |
|
| Logarithmus der Eulerschen Konstante E zur Basis 10 | LOG10E | LOG10E |
|
| Konstante Pi für Kreisberechnungen | PI,pi,π | pi |
|
| π |
|
| PI |
|
| sinpi |
|
| cos(3pi) |
|
| Maßeinheiten |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Beliebige Maßeinheit | unit | unit(dollar) |
|
| Ampere | A, kA, mA | A |
|
| kA |
|
| mA |
|
| Volt | V, MV, kV, mV | V |
|
| MV |
|
| 30MV |
|
| kV |
|
| mV |
|
| Ohm | Ohm, GOhm, MOhm, kOhm | Ohm |
|
| GOhm |
|
| MOhm |
|
| kOhm |
|
| mOhm |
|
| 4Ohm |
|
| Ohmmeter | Ohmm | Ohmm |
|
| 4Ohmm |
|
| Watt | W, GW, MW, kW, mW | W |
|
| GW |
|
| MW |
|
| kW |
|
| mW |
|
| 30MW |
|
| Pferdestärken | PS | PS |
|
| 10PS |
|
| Coulomb | C | C |
|
| 9C |
|
| Farad | F, kF, mF, µF, nF, pF | F |
|
| kF |
|
| mF |
|
| nF |
|
| µF |
|
| pF |
|
| 9F |
|
| Henry | H | H |
|
| 7H |
|
| Siemens | S,kS | S |
|
| kS |
|
| 4S |
|
| Gigameter | Gm | Gm |
|
| 30Gm |
|
| Megameter | Mm | Mm |
|
| 30Mm |
|
| Kilometer | km | km |
|
| 30km |
|
| Hektometer | hm | hm |
|
| 30hm |
|
| Dekameter | dam | dam |
|
| 30dam |
|
| Meter | m | m |
|
| 30m |
|
| Dezimeter | dm | dm |
|
| 30dm |
|
| Zentimeter | cm | cm |
|
| 30cm |
|
| Millimeter | mm | mm |
|
| 30mm |
|
| Mikrometer | µm | µm |
|
| 30µm |
|
| Nanometer | nm | nm |
|
| 30nm |
|
| Ångström | Å | Å |
|
| 30Å |
|
| Pikometer | pm | pm |
|
| 30pm |
|
| Femtometer | fm | fm |
|
| 30fm |
|
| Attometer | am | am |
|
| 30am |
|
| Zoll | in | in |
|
| 30in |
|
| Fuß | ft | ft |
|
| 30ft |
|
| Yard | yard | yard |
|
| 30yard |
|
| Seemeile | sm | sm |
|
| 30sm |
|
| Hektar | ha | ha |
|
| 30ha |
|
| Ar | Ar | Ar |
|
| 30Ar |
|
| Acre | Acre | Acre |
|
| 30Acre |
|
| Registertonne | RT | RT |
|
| 30RT |
|
| Radiant | °, rad | rad |
|
| sin30° |
|
| sin30rad |
|
| Liter | L | L |
|
| Kiloliter | kl | kl |
|
| 30kl |
|
| Hektoliter | hl | hl |
|
| 30hl |
|
| Dekaliter | dl | dl |
|
| 30dl |
|
| Zentiliter | cl | cl |
|
| 30cl |
|
| Milliliter | ml | ml |
|
| 30ml |
|
| Mikroliter | µl | µl |
|
| 30µl |
|
| Nanoliter | nl | nl |
|
| 30nl |
|
| Pikoliter | pl | pl |
|
| 30pl |
|
| Femtoliter | fl | fl |
|
| 30fl |
|
| Geschwindigkeit | v | v |
|
| 30v |
|
| Beschleunigung | Acc | Acc |
|
| 30Acc |
|
| Grad Celsius | °C | °C |
|
| 30°C |
|
| Grad Fahrenheit | °F | °F |
|
| 30°F |
|
| Kelvin | TKelvin | TKelvin |
|
| 30TKelvin |
|
| Tonnen | Ton | Ton |
|
| 30Ton |
|
| Kilogramm | kg | kg |
|
| 30kg |
|
| Gramm | gramm | gramm |
|
| 30gramm |
|
| Kilopond | kp | kp |
|
| 30kp |
|
| Hertz | Hz, THz, GHz, MHz, kHz | Hz |
|
| THz |
|
| GHz |
|
| MHz |
|
| kHz |
|
| 30Hz |
|
| Bel | B | B |
|
| 30B |
|
| Dezibel | dB | dB |
|
| 30dB |
|
| Neper | Np | Np |
|
| 30Np |
|
| Jahr | Jahr/years | year |
|
| 30years |
|
| Tag | day | day |
|
| 30day |
|
| Stunde | hour/std | hour |
|
| 30hour |
|
| Minute | min | min |
|
| 30min |
|
| Sekunde | s | sec |
|
| 30sec |
|
| Millisekunde | ms | ms |
|
| 30ms |
|
| Mikrosekunde | µs | µs |
|
| 30µs |
|
| Nanosekunde | ns | ns |
|
| 30ns |
|
| Pikosekunde | ps | ps |
|
| 30ps |
|
| Femtosekunde | fs | fs |
|
| 30fs |
|
| Joule | J,kJ | J |
|
| kJ |
|
| 30J |
|
| Nm | Nm | Nm |
|
| 5Nm |
|
| Lumen | lm | lm |
|
| 5lm |
|
| Lux | lx | lx |
|
| 5lx |
|
| Katal | kat | kat |
|
| 5kat |
|
| Pascal | Pa, GPa, MPa, hPa, kPa, dPa | Pa |
|
| MPa |
|
| hPa |
|
| kPa |
|
| dPa |
|
| 30Pa |
|
| Bar | bar | bar |
|
| 30bar |
|
| Technische Atmosphäre | at | at |
|
| 30at |
|
| Physikalische Atmosphäre | atm | atm |
|
| 30atm |
|
| Torr | Torr | Torr |
|
| 30Torr |
|
| Pound-Druck pro quadrat inch | psi | psi |
|
| 30psi |
|
| Millisievert | mSv | mSv |
|
| 30mSv |
|
| Mikrosievert | µSv | µSv |
|
| 30µSv |
|
| Sievert | Sv | Sv |
|
| 30Sv |
|
| Rem | rem | rem |
|
| 30rem |
|
| Becquerel | Bq | Bq |
|
| 30Bq |
|
| Curie | Ci | Ci |
|
| 30Ci |
|
| Tesla | T | T |
|
| 30T |
|
| Gauß | Gs | Gs |
|
| 30Gs |
|
| Gamma | γ | γ |
|
| 30γ |
|
| Nanotesla | nT | nT |
|
| 30nT |
|
| Weber | Wb | Wb |
|
| 30Wb |
|
| Mikroweber | µWb | µWb |
|
| 30µWb |
|
| Milliweber | mWb | mWb |
|
| 30mWb |
|
| Nanoweber | nWb | nWb |
|
| 30nWb |
|
| Maxwell | Mx | Mx |
|
| 30Mx |
|
| PH in der Chemie | pH | pH |
|
| 30pH |
|
| Euro | € | € |
|
| 30€ |
|
| Euro Cent | cent | cent |
|
| 30cent |
|
| Schweizer Franken | CHF | CHF |
|
| 30CHF |
|
| Schweizer Rappen | Rappen | Rappen |
|
| 30Rappen |
|
| US-Dollar | $, USD | $ |
|
| USD |
|
| 30$ |
|
| US Dollar Cent | cents | cents |
|
| 30cents |
|
| Pfund Sterling | €, GBP | £ |
|
| GBP |
|
| 30£ |
|
| Pence | pence | pence |
|
| 30pence |
|
| Yen | ¥, JPY | ¥ |
|
| JPY |
|
| 30¥ |
|
| Indische Rupie | Rupie | Rupie |
|
| 30Rupie |
|
| Indische Paise | Paise | Paise |
|
| 30Paise |
|
| Vorlagen |
|---|
| Art | Syntax | Beispiele | ergibt |
|---|
| Zufällige natürliche Zahl (n) Nr. m mit s Stellen | ?nsm | ?n11 |
|
| ?n22 |
|
| ?n11+?n22 |
|
| Zufällige ganze Zahl (z) Nr. m mit s Stellen | ?zsm | ?z11 |
|
| ?z22 |
|
| ?z11+?z22 |
|
| Zufällige ganze Zahl<=5 (k) Nr. m | ?km | ?k1 |
|
| ?k2 |
|
| ?k1+?k2 |
|
| Zufällige Variable (x) Nr. m | ?xm | ?x1 |
|
| ?x2 |
|
| ?x1+?x1^2+?x2 |
|
| M_4=m_1*m_2*m_3 wobei nr. 1/2/3 zufällig erzeugt werden | ?lsm | ?l11-?n32*?n33*?n34 |
|
| Die natürliche Zufallszahl m+1=m^2 | ?gsm | ?g11-(?n22)^2 |
|
steps2MATH Syntax