Happy Valentine's Day!!

Harry_the_cat

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Mar 16, 2016
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940
What do you get if you graph these parametric equations?

\(\displaystyle x = 16 sin^3(t)\)

and

\(\displaystyle y = 13 cos(t) - 5 cos(2t) - 2 cos(3t) - cos(4t)\)
 

Otis

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Apr 22, 2015
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Yours looks better than this one (from a recent thread about a quadratic function and its inverse):

\(\displaystyle f(x) = 1 - 2x - x^2 \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} - \frac{\sqrt{13}}{2} \text{ , } -\frac{3}{2} + \frac{\sqrt{13}}{2}\bigg]\)

\(\displaystyle g(x) = -1 - \sqrt{2 - x} \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} - \frac{\sqrt{13}}{2} \text{ , } 2\bigg]\)

\(\displaystyle h(x) = -1 + \sqrt{2 - x} \quad\quad \text{Doma}\text{in: } \bigg[-\frac{3}{2} + \frac{\sqrt{13}}{2} \text{ , } 2\bigg]\)
 

Denis

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Feb 17, 2004
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1,444
Hearty day: celebrating nail event! (9)
 

Otis

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Apr 22, 2015
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Text Rebus

TV a LINE STAY (2)
 
Last edited by a moderator:

Otis

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dmv.JPG
 

mmm4444bot

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Another parametric, curvy thing.

Each axis: [-2000, 2000]

Parameter t: [0, 60∙Pi]

x(t) = ((-33/2 *sin(11/7 - 7*t) - 29/5 *sin(3/2 - 6*t) - 42/5 *sin(11/7 - 5*t) - 2442/5 *sin(11/7 - t) + 1073/5 *sin(2*t + 11/7) + 434/11 *sin(3*t + 8/5) + 273/4 *sin(4*t + 8/5) + 22/5 *sin(8*t + 11/7) + 19/5 *sin(9*t + 13/8) + 90/13 *sin(10*t + 8/5) + 5/4 *sin(11*t + 11/7) - 2019/10)*Heaviside(59*Pi - t)*Heaviside(t - 55*Pi) + (-18/5 *sin(14/9 - 11*t) - 51/7 *sin(11/7 - 10*t) - 49/9 *sin(11/7 - 9*t) - 7/3 *sin(14/9 - 6*t) - 85/3 *sin(11/7 - 5*t) - 50/3 *sin(11/7 - 4*t) - 1819/7 *sin(11/7 - t) + 1733/8 *sin(2*t + 11/7) + 170/3 *sin(3*t + 8/5) + 2/3 *sin(7*t + 9/5) + 1/6 *sin(8*t + 2/3) + 2404/7)*Heaviside(55*Pi - t)*Heaviside(t - 51*Pi) + (-6/7 *sin(11/7 - 10*t) - 3 *sin(11/7 - 9*t) - 79/6 *sin(11/7 - 6*t) - 2969/8 *sin(11/7 - t) + 191/6 *sin(2*t + 33/7) + 152/7 *sin(3*t + 33/7) + 107/5 *sin(4*t + 33/7) + 13/8 *sin(5*t + 11/7) + 2/7 *sin(7*t + 23/5) + 22/5 *sin(8*t + 33/7) + 13/4 *sin(11*t + 33/7) + 3085/6)*Heaviside(51*Pi - t)*Heaviside(t - 47*Pi) + (-7/4 *sin(3/2 - 10*t) - 37/8 *sin(3/2 - 9*t) - 373/9 *sin(11/7 - 4*t) - 267/4 *sin(11/7 - 2*t) - 3133/7 *sin(11/7 - t) + 541/5 *sin(3*t + 8/5) + 820/11 *sin(5*t + 8/5) + 47/6 *sin(6*t + 12/7) + 35/3 *sin(7*t + 8/5) + 10/3 *sin(8*t + 12/7) + 5/11 *sin(11*t + 1) + 942)*Heaviside(47*Pi - t)*Heaviside(t - 43*Pi) + (-49/11 *sin(11/7 - 24*t) - 35/8 *sin(3/2 - 22*t) - 29/4 *sin(3/2 - 18*t) - 40/9 *sin(4/3 - 17*t) - 13/3 *sin(11/7 - 14*t) - 94/7 *sin(13/9 - 13*t) - 141/4 *sin(3/2 - 12*t) - 31/16 *sin(16/11 - 11*t) - 792/5 *sin(14/9 - 8*t) - 17/7 *sin(3/5 - 7*t) - 239/3 *sin(14/9 - 6*t) - 734/5 *sin(11/7 - 5*t) - 535/7 *sin(14/9 - 4*t) - 473/6 *sin(11/7 - 3*t) - 219/8 *sin(11/7 - 2*t) + 89 *sin(t + 33/7) + 1861/19 *sin(9*t + 8/5) + 603/10 *sin(10*t + 13/8) + 83/8 *sin(15*t + 5/3) + 13/4 *sin(16*t + 14/3) + 31/8 *sin(19*t + 8/5) + 26/7 *sin(20*t + 14/3) + 14/15 *sin(21*t + 7/6) + 3/4 *sin(23*t + 5/4) + 9944/13)*Heaviside(43*Pi - t)*Heaviside(t - 39*Pi) + (-104/3 *sin(4/7 - t) + 2 *sin(2*t + 20/7) + 1629/2)*Heaviside(39*Pi - t)*Heaviside(t - 35*Pi) + (-19/5 *sin(5/9 - 2*t) - 349/8 *sin(2/5 - t) + 5581/4)*Heaviside(35*Pi - t)*Heaviside(t - 31*Pi) + (-760/9 *sin(5/6 - t) + 12/13 *sin(2*t + 49/16) + 1377/7)*Heaviside(31*Pi - t)*Heaviside(t - 27*Pi) + (-9 *sin(1/8 - 2*t) - 827/9 *sin(2/5 - t) + 75/8 *sin(3*t + 25/12) - 3133/12)*Heaviside(27*Pi - t)*Heaviside(t - 23*Pi) + (41 *sin(t + 2/7) + 26/7 *sin(2*t + 19/18) + 9/2 *sin(3*t + 1/2) + 11/5 *sin(4*t + 25/8) - 4065/7)*Heaviside(23*Pi - t)*Heaviside(t - 19*Pi) + (-17/6 *sin(1/15 - 2*t) - 276/5 *sin(5/4 - t) + 2764/5)*Heaviside(19*Pi - t)*Heaviside(t - 15*Pi) + ((1234 *sin(t))/7 + 43/7 *sin(2*t + 14/3) + 54/7 *sin(3*t + 23/9) + 44/7 *sin(4*t + 5/4) + 3721/5)*Heaviside(15*Pi - t)*Heaviside(t - 11*Pi) + (-14/3 *sin(7/8 - 53*t) - 7 *sin(5/4 - 52*t) - 6 *sin(10/7 - 45*t) - 9/10 *sin(7/13 - 43*t) - 62/9 *sin(1/6 - 37*t) - 151/9 *sin(1/2 - 33*t) - 22/5 *sin(3/2 - 31*t) - 38/11 *sin(14/9 - 30*t) - 21/2 *sin(11/10 - 27*t) - 44/5 *sin(9/8 - 25*t) - 201/8 *sin(6/5 - 24*t) - 12 *sin(3/4 - 21*t) - 404/13 *sin(11/7 - 18*t) - 375/7 *sin(1/2 - 13*t) - 65 *sin(4/3 - 8*t) - 262/3 *sin(2/3 - 5*t) + 41/9 *sin(26*t) + 2406/5 *sin(t + 31/7) + 2743/8 *sin(2*t + 11/9) + 1248/7 *sin(3*t + 3/5) + 861/10 *sin(4*t + 4/5) + 197/6 *sin(6*t + 3/4) + 918/11 *sin(7*t + 30/7) + 233/3 *sin(9*t + 7/2) + 126/5 *sin(10*t + 18/5) + 397/9 *sin(11*t + 2/7) + 391/8 *sin(12*t + 1/15) + 211/7 *sin(14*t + 22/7) + 1037/14 *sin(15*t + 13/5) + 239/8 *sin(16*t + 19/8) + 209/4 *sin(17*t + 2) + 5/6 *sin(19*t + 25/9) + 207/7 *sin(20*t + 11/6) + 137/8 *sin(22*t + 13/6) + 38/5 *sin(23*t + 75/19) + 121/9 *sin(28*t + 15/7) + 73/7 *sin(29*t + 19/8) + 51/10 *sin(32*t + 8/5) + 11/5 *sin(34*t + 31/10) + 13 *sin(35*t + 27/8) + 52/5 *sin(36*t + 101/25) + 6 *sin(38*t + 11/5) + 125/14 *sin(39*t + 3) + 27/7 *sin(40*t + 2/5) + 55/4 *sin(41*t + 87/22) + 39/7 *sin(42*t + 3/4) + 31/4 *sin(44*t + 1/2) + 51/8 *sin(46*t + 93/23) + 29/14 *sin(47*t + 4) + 49/9 *sin(48*t + 26/9) + 7/5 *sin(49*t + 22/5) + 29/5 *sin(50*t + 29/10) + 70/9 *sin(51*t + 46/15) + 14/5 *sin(54*t + 3/4) - 2201/5)*Heaviside(11*Pi - t)*Heaviside(t - 7*Pi) + (-103/34 *sin(10/11 - 21*t) - 7/4 *sin(2/5 - 17*t) - 104/15 *sin(1/10 - 15*t) - 20/3 *sin(1/4 - 10*t) - 593/5 *sin(1/3 - 4*t) - 239/3 *sin(16/17 - 2*t) + 2113/7 *sin(t + 10/7) + 151/4 *sin(3*t + 8/7) + 183/4 *sin(5*t + 4/3) + 52/3 *sin(6*t + 11/5) + 115/7 *sin(7*t + 28/9) + 94/11 *sin(8*t + 19/5) + 280/13 *sin(9*t + 68/23) + 29/6 *sin(11*t + 1/2) + 59/9 *sin(12*t + 19/7) + 47/7 *sin(13*t + 12/5) + 41/6 *sin(14*t + 4/5) + 28/5 *sin(16*t + 3/7) + 9/7 *sin(18*t + 1/2) + 9/5 *sin(19*t + 7/2) + 44/15 *sin(20*t + 30/7) + 5/3 *sin(22*t + 9/5) - 9793/9)*Heaviside(7*Pi - t)*Heaviside(t - 3*Pi) + (-8/5 *sin(2/3 - 41*t) - 4/3 *sin(2/7 - 39*t) - 11/6 *sin(17/11 - 35*t) - 53/7 *sin(14/13 - 23*t) - 144/7 *sin(3/7 - 11*t) - 97/5 *sin(3/2 - 8*t) - 158/3 *sin(5/6 - 7*t) - 503/12 *sin(5/7 - 4*t) - 221/3 *sin(11/10 - 3*t) + 6521/5 *sin(t + 33/32) + 3023/6 *sin(2*t + 12/5) + 325/7 *sin(5*t + 17/5) + 307/11 *sin(6*t + 19/7) + 614/15 *sin(9*t + 23/6) + 67/4 *sin(10*t + 19/9) + 110/3 *sin(12*t + 49/12) + 105/4 *sin(13*t + 31/9) + 15 *sin(14*t + 30/7) + 324/11 *sin(15*t + 17/5) + 31/3 *sin(16*t + 26/7) + 59/3 *sin(17*t + 37/12) + 77/5 *sin(18*t + 3/2) + 15/2 *sin(19*t + 11/5) + 209/14 *sin(20*t + 4/9) + 55/9 *sin(21*t + 23/6) + 39/4 *sin(22*t + 10/7) + 137/13 *sin(24*t + 9/5) + 19/3 *sin(25*t + 1/22) + 3/2 *sin(26*t + 9/2) + 73/24 *sin(27*t + 16/9) + 15/8 *sin(28*t + 4/3) + 9/2 *sin(29*t + 23/6) + 143/18 *sin(30*t + 2) + 43/14 *sin(31*t + 14/13) + 5/4 *sin(32*t + 4/5) + 3/4 *sin(33*t + 2/3) + 13/8 *sin(34*t + 5/4) + 34/33 *sin(36*t + 21/10) + 5/8 *sin(37*t + 13/5) + 5/3 *sin(38*t + 9/7) + 11/8 *sin(40*t + 1) + 39/38 *sin(42*t + 16/7) + 16/7 *sin(43*t + 10/9) - 71/3)*Heaviside(3*Pi - t)*Heaviside(t + Pi))*Heaviside(sqrt(signum(sin(t/2))))

vBulletin can't handle it all; continued in next post …
 

mmm4444bot

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y(t) = ((-24/5 *sin(11/7 - 10*t) - 17/5 *sin(3/2 - 9*t) - 143/6 *sin(11/7 - 8*t) - 87/4 *sin(11/7 - 6*t) - 275/23 *sin(14/9 - 4*t) - 394/3 *sin(11/7 - 3*t) - 1563/10 *sin(11/7 - 2*t) - 865/27 *sin(11/7 - t) + 647/34 *sin(5*t + 8/5) + 2/7 *sin(7*t + 4/7) + 13/5 *sin(11*t + 8/5) + 545)*Heaviside(59*Pi - t)*Heaviside(t - 55*Pi) + (-77/6 *sin(11/7 - 10*t) - 49/24 *sin(10/7 - 9*t) - 277/8 *sin(11/7 - 6*t) - 73/7 *sin(14/9 - 5*t) - 2385/7 *sin(11/7 - 2*t) - 1005/7 *sin(11/7 - t) + 230/7 *sin(3*t + 11/7) + 175/6 *sin(4*t + 33/7) + 12/7 *sin(7*t + 3/2) + 104/11 *sin(8*t + 33/7) + 7/4 *sin(11*t + 13/8) + 2691/2)*Heaviside(55*Pi - t)*Heaviside(t - 51*Pi) + (-94/11 *sin(11/7 - 6*t) - 68/3 *sin(11/7 - 4*t) - 116/5 *sin(11/7 - 2*t) + 98/3 *sin(t + 33/7) + 306/7 *sin(3*t + 11/7) + 107/7 *sin(5*t + 11/7) + 46/7 *sin(7*t + 11/7) + 53/13 *sin(8*t + 33/7) + 27/14 *sin(9*t + 11/7) + 1/9 *sin(11*t + 8/5) + 3367/4)*Heaviside(51*Pi - t)*Heaviside(t - 47*Pi) + (-70/23 *sin(7/5 - 11*t) - 23/4 *sin(17/11 - 10*t) - 75/7 *sin(17/11 - 8*t) - 31/8 *sin(10/7 - 7*t) - 122/7 *sin(3/2 - 5*t) - 329/3 *sin(14/9 - 4*t) - 390/11 *sin(20/13 - 3*t) - 753/7 *sin(11/7 - 2*t) + 385/3 *sin(t + 11/7) + 61/3 *sin(6*t + 8/5) + 57/7 *sin(9*t + 8/5) + 6733/12)*Heaviside(47*Pi - t)*Heaviside(t - 43*Pi) + (-17/7 *sin(3/2 - 17*t) - 57/4 *sin(19/13 - 12*t) - 244/9 *sin(3/2 - 11*t) - 449/7 *sin(11/7 - 7*t) - 611/11 *sin(11/7 - 5*t) - 1581/14 *sin(11/7 - 3*t) - 341/5 *sin(11/7 - t) + 223/16 *sin(2*t + 11/7) + 144/7 *sin(4*t + 11/7) + 410/3 *sin(6*t + 8/5) + 4537/42 *sin(8*t + 8/5) + 874/7 *sin(9*t + 8/5) + 118/7 *sin(10*t + 33/7) + 52/5 *sin(13*t + 5/3) + 343/18 *sin(14*t + 5/3) + 11/7 *sin(15*t + 2) + 19/6 *sin(16*t + 13/9) + 23/9 *sin(18*t + 7/4) + 175/22 *sin(19*t + 12/7) + 38/7 *sin(20*t + 8/5) + 4/3 *sin(21*t + 23/5) + 39/8 *sin(22*t + 13/8) + 2/5 *sin(23*t + 33/8) + 1/5 *sin(24*t + 5/7) - 965/2)*Heaviside(43*Pi - t)*Heaviside(t - 39*Pi) + (45 *sin(t + 41/9) + 13/9 *sin(2*t + 20/19) + 4066/5)*Heaviside(39*Pi - t)*Heaviside(t - 35*Pi) + (-26/9 *sin(1 - 2*t) - 307/5 *sin(5/4 - t) + 1475/3)*Heaviside(35*Pi - t)*Heaviside(t - 31*Pi) + (616/5 *sin(t + 9/2) + 5/7 *sin(2*t + 14/3) + 7504/5)*Heaviside(31*Pi - t)*Heaviside(t - 27*Pi) + (-325/6 *sin(3/2 - t) + 20/3 *sin(2*t + 18/5) + 17/3 *sin(3*t + 5/7) + 9325/9)*Heaviside(27*Pi - t)*Heaviside(t - 23*Pi) + (-7 *sin(3/4 - 3*t) - 558/7 *sin(9/7 - t) + 39/19 *sin(2*t + 2) + 7/4 *sin(4*t + 14/5) + 11717/18)*Heaviside(23*Pi - t)*Heaviside(t - 19*Pi) + (329/4 *sin(t + 21/5) + 13/6 *sin(2*t + 9/4) + 10651/15)*Heaviside(19*Pi - t)*Heaviside(t - 15*Pi) + (-26/3 *sin(2/7 - 2*t) - 989/7 *sin(4/3 - t) + 28/3 *sin(3*t + 6/5) + 3/4 *sin(4*t + 24/7) - 2177/5)*Heaviside(15*Pi - t)*Heaviside(t - 11*Pi) + (-15/7 *sin(1/2 - 54*t) - 29/8 *sin(1/6 - 52*t) - 35/6 *sin(14/9 - 45*t) - 5/4 *sin(15/16 - 43*t) - 69/8 *sin(1 - 39*t) - 23/5 *sin(13/12 - 37*t) - 29/6 *sin(10/11 - 34*t) - 117/5 *sin(10/7 - 30*t) - 222/13 *sin(13/9 - 25*t) - 67/2 *sin(17/11 - 22*t) - 146/3 *sin(5/4 - 18*t) - 268/5 *sin(6/11 - 14*t) - 337/12 *sin(4/3 - 10*t) - 131 *sin(5/6 - 8*t) + 2689/3 *sin(t + 3) + 235/8 *sin(2*t + 11/7) + 145/2 *sin(3*t + 1/5) + 552/5 *sin(4*t + 23/5) + 921/7 *sin(5*t + 5/6) + 220/7 *sin(6*t + 9/2) + 575/16 *sin(7*t + 38/37) + 1001/40 *sin(9*t + 7/9) + 342/7 *sin(11*t + 3/4) + 115/4 *sin(12*t + 23/5) + 43 *sin(13*t + 17/6) + 112/3 *sin(15*t + 17/5) + 799/19 *sin(16*t + 19/10) + 305/8 *sin(17*t + 23/7) + 286/7 *sin(19*t + 21/8) + 1513/28 *sin(20*t + 3) + 77/4 *sin(21*t + 17/4) + 301/15 *sin(23*t + 28/11) + 121/7 *sin(24*t + 7/4) + 66/7 *sin(26*t + 16/5) + 43/3 *sin(27*t + 18/5) + 35/4 *sin(28*t + 38/11) + 109/12 *sin(29*t + 23/8) + 39/7 *sin(31*t + 19/6) + 8 *sin(32*t + 16/5) + 7/4 *sin(33*t + 7/3) + 32/9 *sin(35*t + 19/5) + 3 *sin(36*t + 28/27) + 17/4 *sin(38*t + 9/5) + 29/6 *sin(40*t + 4/7) + 31/8 *sin(41*t + 19/6) + 38/7 *sin(42*t + 1/3) + 47/12 *sin(44*t + 5/3) + 26/9 *sin(46*t + 27/7) + 45/7 *sin(47*t + 13/10) + 23/12 *sin(48*t + 24/7) + 38/5 *sin(49*t + 22/7) + 19/5 *sin(50*t + 9/7) + 5/2 *sin(51*t + 31/7) + 36/7 *sin(53*t + 8/3) - 3366/5)*Heaviside(11*Pi - t)*Heaviside(t - 7*Pi) + (-4/5 *sin(4/5 - 21*t) - 8/5 *sin(1/4 - 20*t) - 2 *sin(5/4 - 15*t) + 1662/5 *sin(t + 34/9) + 197/5 *sin(2*t + 8/3) + 364/11 *sin(3*t + 3) + 212/3 *sin(4*t + 14/3) + 388/9 *sin(5*t + 2) + 43 *sin(6*t + 29/14) + 71/5 *sin(7*t + 1/4) + 165/7 *sin(8*t + 3/8) + 153/11 *sin(9*t + 25/6) + 94/9 *sin(10*t + 3/2) + 37/4 *sin(11*t + 32/11) + 30/7 *sin(12*t + 2/3) + 53/10 *sin(13*t + 41/9) + 9/5 *sin(14*t + 19/5) + 31/8 *sin(16*t + 10/7) + 13/4 *sin(17*t + 31/7) + 31/16 *sin(18*t + 4/7) + sin(19*t + 3/2) + 7/5 *sin(22*t + 23/8) - 5601/8)*Heaviside(7*Pi - t)*Heaviside(t - 3*Pi) + (-2/7 *sin(5/4 - 42*t) - 35/12 *sin(3/4 - 38*t) - 6/5 *sin(3/8 - 36*t) - 25/13 *sin(46/45 - 32*t) - 19/8 *sin(2/7 - 30*t) - 23/3 *sin(5/8 - 24*t) - 65/6 *sin(5/11 - 22*t) - 34/5 *sin(4/5 - 19*t) - 16 *sin(7/6 - 13*t) - 330/7 *sin(1/4 - 10*t) - 10765/7 *sin(1/8 - t) + 6479/18 *sin(2*t + 8/7) + 1300/7 *sin(3*t + 59/15) + 598/9 *sin(4*t + 17/8) + 413/4 *sin(5*t + 6/7) + 187/5 *sin(6*t + 14/3) + 534/11 *sin(7*t + 14/5) + 185/6 *sin(8*t + 13/7) + 371/9 *sin(9*t + 12/7) + 431/10 *sin(11*t + 23/5) + 121/7 *sin(12*t + 18/7) + 107/3 *sin(14*t + 14/5) + 174/5 *sin(15*t + 7/6) + 19/5 *sin(16*t + 41/9) + 160/11 *sin(17*t + 12/7) + 16/3 *sin(18*t + 4/3) + 45/4 *sin(20*t + 39/11) + 75/4 *sin(21*t + 6/5) + 34/33 *sin(23*t + 7/5) + 61/12 *sin(25*t + 40/9) + 39/5 *sin(26*t + 145/36) + 190/27 *sin(27*t + 21/8) + 2 *sin(28*t + 3/4) + 3/2 *sin(29*t + 8/7) + 8/5 *sin(31*t + 17/11) + 21/5 *sin(33*t + 5/2) + 38/7 *sin(34*t + 11/9) + 23/7 *sin(35*t + 1/4) + 24/7 *sin(37*t + 9/10) + 15/8 *sin(39*t + 13/4) + 13/5 *sin(40*t + 18/17) + 17/11 *sin(41*t + 2/5) + 23/11 *sin(43*t + 1/8) + 57/8)*Heaviside(3*Pi - t)*Heaviside(t + Pi))*Heaviside(sqrt(signum(sin(t/2))))
 

Denis

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Feb 17, 2004
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I memorized that in the 1970's....but "lost it"
shortly after, from a hockey stick on da noggin' :rolleyes:
 

Harry_the_cat

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Mar 16, 2016
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mmm4444bot, well I won't be typing that into my graphics calculator!
 

Jomo

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Dec 30, 2014
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I memorized that in the 1970's....but "lost it"
shortly after, from a hockey stick on da noggin' :rolleyes:
So that is what happened to you. Now I understand everything.
 

Denis

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So that is what happened to you. Now I understand everything.
Well I have my hockey stick excuse...you have none!!
 

mmm4444bot

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I memorized that in the 1970's … but "lost it" …
… I won't be typing that into my graphics calculator!
I'd thought interested folk would copy-n-paste to their favorite CAS. Now, I've realized that not all graphing software recognizes stuff like Heaviside() or signum() and there could be other issues with direct copying. Sorry 'bout that.

Here's the parametric plot, as produced using MVR5.

heartPlot.JPG
 

Harry_the_cat

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Mar 16, 2016
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940
I'd thought interested folk would copy-n-paste to their favorite CAS. Now, I've realized that not all graphing software recognizes stuff like Heaviside() or signum() and there could be other issues with direct copying. Sorry 'bout that.

Here's the parametric plot, as produced using MVR5.

View attachment 11073
Wonderful! BTW what does Heaviside and signum do?
 

mmm4444bot

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…what [do] Heaviside and signum do?
Heaviside is a step function; you can read about it at wikipedia. I learned its use only as it's applied in Laplace transforms (i.e., solving differential equations). I just learned that multiple Heaviside versions exist.

\(\displaystyle H(n) = \begin{cases} 0, \; n < 0 \\ 1, \; n \ge 0 \end{cases}\)

Signum is a function that returns the sign of its argument. It also has an entry at wikipedia.

\(\displaystyle signum(x) = \begin{cases} -1, \; x < 0 \\ \;\; 0, \; x = 0 \\ \;\; 1, \; x > 0 \end{cases}\)

For non-zero inputs, I've also seen signum defined as x/|x|.
 

Subhotosh Khan

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Heaviside is a step function; you can read about it at wikipedia. I learned its use only as it's applied in Laplace transforms (i.e., solving differential equations). I just learned that multiple Heaviside versions exist.

\(\displaystyle H(n) = \begin{cases} 0, \; n < 0 \\ 1, \; n \ge 0 \end{cases}\)

Signum is a function that returns the sign of its argument. It also has an entry at wikipedia.

\(\displaystyle signum(x) = \begin{cases} -1, \; x < 0 \\ \;\; 0, \; x = 0 \\ \;\; 1, \; x > 0 \end{cases}\)

For non-zero inputs, I've also seen signum defined as x/|x|.
Heaviside - an electrical engineer - used Heaviside's operational methods of electric circuit analysis, where Laplace transform was used "intuitively". It is said that Heaviside was asked to "prove" that his method, he reportedly said that "It works". Later somebody else discovered that Laplace had formalised the method ~100 years before him.
 

Harry_the_cat

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Thanks mmm and Subho.
 

mmm4444bot

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… Heaviside was asked to "prove" [his] method, he reportedly said that "It works" …
Gotta love those engineer and physicist types! They get my Valentines. :cool:
 
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