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(1)

2D

D @ ArcSin @ Cos @ x DD , x D

- €€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ •!!!!!!!!!!!!!!!!!!!!!!!!!!! 1 Sin - Cos @ x @ D x D

2

Plot[-Sin[x]/Sqrt[1-Cos[x]^2],{x,-10,10},AspectRatio®Automatic];

-10 -5 -0.5 -1 5 10

0.5 1

Plot @ ArcSin @ Cos @ x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 5 10

-1.5 -1 -0.5 0.5 1 1.5

Plot @ Evaluate @ D @ ArcSin @ Cos @ x DD , x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 -0.5 -1 5 10

0.5 1

Plot @ ArcCos @ Cos @ x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 5 10

0.5 1 1.5 2 2.5 3

Plot @ Evaluate @ D @ ArcCos @ Cos @ x DD , x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 -0.5 -1 5 10

0.5 1

(2)

Plot @ Evaluate @ D @ ArcSin @ Sin @ x DD , x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 -0.5 -1 5 10

0.5 1

Plot @ ArcSin @ Sin @ x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 5 10

-1.5 -1 -0.5 0.5 1 1.5

Plot @ ArcTan @ Tan @ x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 5 10

-1.5 -1 -0.5 0.5 1 1.5

Plot @ ArcTan @ Cot @ x DD , 8 x, -10, 10 < , AspectRatio ® Automatic D ;

-10 -5 5 10

-1.5 -1 -0.5 0.5 1 1.5

Plot @8 ArcTan @ Cot @ x DD ArcTan @ Tan @ x DD < , 8 x, -10, 10 < , AspectRatio ® Automatic, Axes ® False D ;

Plot @8 ArcTan @ Cot @ x DD , ArcTan @ Tan @ x DD< , 8 x, -10, 10 < , AspectRatio ® Automatic, Axes ® False D ;

Plot @8 ArcTan @ Cot @ x DD , ArcTan @ Tan @ x DD , Sin @ x D • Sqrt @ 1 - Cos @ x D ^ 2 D< ,

8 x, -10, 10 < , AspectRatio ® Automatic, Axes ® False D ;

(3)

Plot @ ArcTan @ Sin @ x DD , 8 x, -10, 10 <D ;

-10 -5 5 10

-0.75 -0.5 -0.25 0.25 0.5 0.75

Plot @ 2 ArcSin @ E ^ H -x ^ 2 LD * Sign @ Floor @ ArcSin @ E ^ H -x ^ 2 LD DD , 8 x, -1, 1 < , PlotRange ® 8 -Pi, Pi <D ;

-1 -0.5 0.5 1

-3 -2 -1 1 2 3

Plot @ 2 ArcSin @ E ^ H -x ^ 2 LD * Sign @ Floor @ 2 ArcSin @ E ^ H -x ^ 2 LD DD , 8 x, -1, 1 < , PlotRange ® 8 0, Pi <D ;

-1 -0.5 0.5 1

0.5

1

1.5

2

2.5

3

(4)

Plot @ 2 ArcSin @ E ^ H -x ^ 2 LD * Sign @ Floor @ 2 ArcSin @ E ^ H - H x - 0.5 L ^ 2 LD DD , 8 x, -1, 1 < , PlotRange ® 8 -Pi, 2 Pi <D ;

-1 -0.8 -0.6 -0.4 -0.2 0.2

-2 2 4 6

Plot @ 2 ArcSin @ E ^ H -x ^ 2 LD * Sign @ Floor @ ArcSin @ E ^ H -x ^ 2 LD DD + ArcSin @ Cos @ x DD , 8 x, -1, 1 < , PlotRange ® 8 -Pi, 2 Pi <D ;

-1 -0.5 0.5 1

-2

2

4

6

(5)

3D

p0=Plot3D[ ArcTan[Tan[x]] ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

-4

-2

0

2

4

-4 -2

0 2

4 -2

-1 0 1 2

-4

-2

0

2

4

p0=Plot3D[ ArcTan[Tan[x]]+ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

-4

-2

0

2

4

-4 -2

0 2

4 -2

0 2

-4

-2

0

2

4

(6)

p0=Plot3D[-Sin[x]/Sqrt[1.0001-Cos[x]^2]+ArcSin[Sin[y]],{x,-5,5},{y,-5, 5}];

-4

-2

0

2

4

-4 -2

0 2

4 -2

0 2

-4

-2

0

2

4

p0=Plot3D[-Sin[x]/Sqrt[1.0001-Cos[x]^2]

ArcSin[Sin[y]],{x,-5,5},{y,-5,5}];

-4

-2

0

2

4

-4 -2

0 2

4 -1

0 1

-4

-2

0

2

4

(7)

p0=Plot3D[ Sin[x] Cos[y],{x,-5,5},{y,-5,5}];

-4 -2

0

2

4

-4 -2

0 2

4 -1

-0.5 0 0.5

1

-4 -2

0

2

4

p0=Plot3D[ Sin[x]+Cos[y],{x,-5,5},{y,-5,5}];

-4

-2

0

2

4

-4 -2

0 2

4 -2

-1 0 1 2

-4

-2

0

2

4

(8)

p1 = Plot3D @ x ^ 2 + y ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

0 2 4 6 8

-2

-1

0

1

p2 = Plot3D @ x y, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-4 -2

0 2 4

-2

-1

0

1

(9)

p3 = Plot3D @ 0, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-1 -0.5

0 0.5

1

-2

-1

0

1

Show @ p2, p3 D ;

-2

-1

0

1

2 -2 -1

0 1

2 -1

0 1

-2

-1

0

1

? PlotPoints

PlotPoints is an option for plotting functions that

specifies how many initial sample points to use. Mehr…

(10)

p4 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 < , PlotRange ® 8 -5, 5 < , PlotPoints ® 50 D ;

-2

-1

0

1

2 -2 -1

0 1

2

-4 -2

0 2 4

-2

-1

0

1

p4 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.2, 0.2 < , 8 y, -0.2, 0.2 < , PlotRange ® 8 -1, 1 < , PlotPoints ® 50 D ;

-0.2

-0.1

0

0.1

0.2 -0.2 -0.1

0 0.1

0.2

-1 -0.5

0 0.5

1

-0.2

-0.1

0

0.1

(11)

p4 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.02, 0.02 < , 8 y, -0.02, 0.02 < , PlotRange ® 8 -15000, 15000 < , PlotPoints ® 50 D ;

-0.02

-0.01

0

0.01

0.02 -0.02 -0.01

0 0.01

0.02 -10000

0 10000

-0.02

-0.01

0

0.01

ContourPlot @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.02, 0.02 < , 8 y, -0.02, 0.02 < , PlotRange ® 8 -15000, 15000 < , PlotPoints ® 50 D ;

-0.02 -0.01 0 0.01 0.02

-0.02

-0.01

0

0.01

0.02

(12)

p5 = Plot3D @ 50 • H 10 + 3 H x - 1 L ^ 2 + 5 H y + 1 L ^ 2 L +

70 • H 10 + 2 H x + 1 L ^ 2 + 10 H y - 2 L ^ 2 L , 8 x, -5, 5 < , 8 y, -5, 5 < , PlotPoints ® 50 D ;

-4

-2

0

2

4

-4 -2

0 2

4 0

2 4 6

-4

-2

0

2

4

ContourPlot @ 50 • H 10 + 3 H x - 1 L ^ 2 + 5 H y + 1 L ^ 2 L +

70 • H 10 + 2 H x + 1 L ^ 2 + 10 H y - 2 L ^ 2 L , 8 x, -5, 5 < , 8 y, -5, 5 < , PlotPoints ® 50 D ;

-4 -2 0 2 4

-4

-2

0

2

4

(13)

Animate! (Die Bilder werden hier nicht wiedergegeben - nur als Film sinnvoll...)

Table[Plot3D[(1+Sin[k Pi/20]) 50/(10+3(x-1)^2+5(y+1)^2)+ (1+Cos[k Pi/20]) 70/(10+2(x+1)^2+10(y-2)^2),{x,-5,5},{y,-5,5},PlotPoints®

50,PlotRange->{0,20},Boxed->False,Axes->None],{k,0,40}];

Landschaft

f @ x_, y_ D := 1 • E ^ x ^ 2 Cos @ x • 5 D H 1 - y ^ 2 • 5 L

Plot @ f @ x, 0 D , 8 x, -5, 5 < , PlotRange ® 8 0, 1 <D ;

-4 -2 2 4

0.2

0.4

0.6

0.8

1

(14)

Remove @ f D ;

f @ x_, y_ D := 1 • E ^ x ^ 2 Cos @ x • 5 D H 2 - H y - 3 L ^ 2 • 2 L ; g @ x_, y_ D := 1 - 1 • E ^ H x ^ 2 L Cos @ x • 5 D ;

Plot3D @ -f @ x, 0 D H 1 + Cos @ x + y DL H Cos @ y D + f @ y • 2, 0 DL + 4 g @H x - 0.3 L , 0 D + H x • 4 L ^ 2, 8 x, -5, 5 < , 8 y, -5, 5 < , PlotRange ® 8 6, -6 <D ;

-4 -2

0

2

4

-4 -2

0 2

4 -5

-2.5 0 2.5

5

-4 -2

0

2

4

Uebungen

Plot3D @ x ^ 2 + y ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

0 2 4 6 8

-2

-1

0

1

(15)

ContourPlot @ x ^ 2 + y ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2 -1 0 1 2

-2 -1 0 1 2

Plot3D @ x y, 8 x, -2, 2 < , 8 y, -2, 2 < , AspectRatio ® 2 D ;

-2 -1

0 1

2 -2 -1

0 1

2

-4 -2 0 2 4

-2 -1

0

1

(16)

ContourPlot @ x y, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2 -1 0 1 2

-2 -1 0 1 2

Plot3D @ x y, 8 x, -2, 2 < , 8 y, -2, 2 < , AspectRatio ® 2, ViewPoint -> 8 1.606, -2.976, -0.120 <D ;

-2 -1 0 1 2 -2

-1 0

1 2

-4

-2

0

2

4

(17)

Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 < , PlotPoints ® 50, PlotRange ® 8 -5, 5 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-4 -2

0 2 4

-2

-1

0

1

ContourPlot @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2 -1 0 1 2

-2

-1

0

1

2

(18)

Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 < , PlotPoints ® 50, PlotRange ® 8 -5, 5 < , AspectRatio ® 2,

ViewPoint -> 8 1.606, -2.976, -0.120 <D ;

-2 -1 0 1 2 -2

-1 0

1 2

-4 -2 0 2 4

Plot3D @ Sin @ x y D , 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-1 -0.5

0 0.5

1

-2

-1

0

1

(19)

ContourPlot @ Sin @ x y D , 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2 -1 0 1 2

-2 -1 0 1 2

Plot3D @ Sin @ x + y D , 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-1 -0.5

0 0.5

1

-2

-1

0

1

(20)

Plot3D @ Sin @ x y ^ 2 - 1 • H x ^ 2 + 1 LD , 8 x, -5, 5 < , 8 y, -5, 5 < , PlotPoints ® 200 D ;

-4 -2

0

2

4

-4 -2

0 2

4 -1

-0.5 0 0.5

1

-4 -2

0

2

4

p2 = Plot3D @ x y, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-4 -2

0 2 4

-2

-1

0

1

(21)

p3 = Plot3D @ 0, 8 x, -2, 2 < , 8 y, -2, 2 <D ;

-2

-1

0

1

2 -2 -1

0 1

2

-1 -0.5

0 0.5

1

-2

-1

0

1

Show @ p2, p3 D ;

-2

-1

0

1

2 -2 -1

0 1

2 -1

0 1

-2

-1

0

1

? PlotPoints

PlotPoints is an option for plotting functions that

specifies how many initial sample points to use. Mehr…

(22)

p3 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -2, 2 < , 8 y, -2, 2 < , PlotRange ® 8 -5, 5 < , PlotPoints ® 50 D ;

-2

-1

0

1

2 -2 -1

0 1

2

-4 -2

0 2 4

-2

-1

0

1

p3 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.2, 0.2 < , 8 y, -0.2, 0.2 < , PlotRange ® 8 -1, 1 < , PlotPoints ® 50 D ;

-0.2

-0.1

0

0.1

0.2 -0.2 -0.1

0 0.1

0.2

-1 -0.5

0 0.5

1

-0.2

-0.1

0

0.1

(23)

p3 = Plot3D @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.02, 0.02 < , 8 y, -0.02, 0.02 < , PlotRange ® 8 -15000, 15000 < , PlotPoints ® 50 D ;

-0.02

-0.01

0

0.01

0.02 -0.02 -0.01

0 0.01

0.02 -10000

0 10000

-0.02

-0.01

0

0.01

ContourPlot @ x y • H x ^ 2 + y ^ 2 L ^ 2, 8 x, -0.02, 0.02 < , 8 y, -0.02, 0.02 < , PlotRange ® 8 -15000, 15000 < , PlotPoints ® 50 D ;

-0.02 -0.01 0 0.01 0.02

-0.02

-0.01

0

0.01

0.02

(24)

50 • H 10 + 3 H x - 1 L ^ 2 + 5 H y + 1 L ^ 2 L + 70 • H 10 + 2 H x + 1 L ^ 2 + 10 H y - 2 L ^ 2 L

€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ 70 €€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€

10 + 2 H 1 + x L

2

+ 10 H - 2 + y L

2

+ 50

€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€ €€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€€

10 + 3 H -1 + x L

2

+ 5 H 1 + y L

2

p3 = Plot3D @ 50 • H 10 + 3 H x - 1 L ^ 2 + 5 H y + 1 L ^ 2 L +

70 • H 10 + 2 H x + 1 L ^ 2 + 10 H y - 2 L ^ 2 L , 8 x, -5, 5 < , 8 y, -5, 5 < , PlotPoints ® 50 D ;

-4

-2

0

2

4

-4 -2

0 2

4 0

2 4 6

-4

-2

0

2

4

(25)

ContourPlot @ 50 • H 10 + 3 H x - 1 L ^ 2 + 5 H y + 1 L ^ 2 L +

70 • H 10 + 2 H x + 1 L ^ 2 + 10 H y - 2 L ^ 2 L , 8 x, -5, 5 < , 8 y, -5, 5 < , PlotPoints ® 50 D ;

-4 -2 0 2 4

-4 -2 0 2 4

p4 = Plot3D[Floor[x]+Floor[y],{x,-3,3},{y,-3,3}];

-2

0

2

-2 0

2 -5

0 5

-2

0

2

(26)

p5 = Plot3D[Floor[x]-Floor[y],{x,-3,3},{y,-3,3}];

-2

0

2

-2 0

2 -5

0 5

-2

0

2

p6 = Plot3D[Floor[x] Floor[y],{x,-3,3},{y,-3,3}];

-2

0

2

-2 0

2 -5

0 5

-2

0

2

(27)

p7 = Plot3D[Floor[x] Floor[y]^2,{x,-3,3},{y,-3,3}];

-2

0

2

-2 0

2 -20

0 20

-2

0

2

p8 = Plot3D[Floor[5 Sin[x] Sin[y]],{x,-3,3},{y,-3,3}];

-2

0

2

-2 0

2 -4

-2 0 2 4

-2

0

2

ParametricPlots

Remove @ "Global`*" D

(28)

v @ t_ D := 8 t, 1 - 0.25 t ^ 2 < ;

ParametricPlot @ v @ t D , 8 t, -2, 2 < , AspectRatio ® Automatic D ;

-2 -1 1 2

0.2 0.4 0.6 0.8 1

v @ t_ D := 8 2 Sin @ t D • H 1 + Cos @ t DL , 2 Cos @ t D • H 1 + Cos @ t DL< ;

ParametricPlot @ v @ t D , 8 t, -Pi • 2, Pi • 2 < , AspectRatio ® Automatic D ;

-2 -1 1 2

0.2 0.4 0.6 0.8 1

? PlotRange

PlotRange is an option for graphics functions

that specifies what points to include in a plot. Mehr…

v @ t_ D := 8 2 t - 3 t ^ 2 + t ^ 3, 1 - t ^ 2 + 3 t ^ 3 - 3.25 t ^ 4 + 1.5 t ^ 5 - 0.25 t ^ 6 < ; ParametricPlot @ v @ t D , 8 t, -0.52138, 2.52138 < , AspectRatio ® Automatic,

PlotRange ® 8 0, 1 <D ;

-1 -0.5 0.5 1

0.2

0.4

0.6

0.8

1

(29)

v @ t_ D := 8 Sin @ t D , Cos @ t D , t < ;

ParametricPlot3D @ v @ t D , 8 t, 0, 2 Pi < , ViewPoint -> 8 0.891, -1.387, 1.773 <D ;

-1 -0.5 0 0.5

1 -1

-0.5 0 0.5

1

0 2

4 6 -0.5

0 0.5

1

0 2

4

(30)

v @ t_ D := 8 Sin @ t D , Cos @ t D< ;

ParametricPlot @ v @ t D , 8 t, 0, 2 Pi < , AspectRatio ® Automatic D ;

-1 -0.5 0.5 1

-1 -0.5 0.5 1

v @ t_ D := 8 Sin @ t D , t < ;

ParametricPlot @ v @ t D , 8 t, 0, 10 Pi <D ;

-1 -0.5 0.5 1

5

10

15

20

25

30

(31)

v @ t_ D := 8 Sin @ t D , Cos @ t D , t < ;

ParametricPlot3D @ v @ t D , 8 t, 0, 4 Pi < , AspectRatio ® Automatic D ;

-1 -0.5 0 0.5 1

-1 -0.5 0 0.5 1 0

5 10

v @ t_ D := 8 t Sin @ t D , Cos @ t D , Sin @ t D< ; ParametricPlot3D @ v @ t D , 8 t, 0, 5 Pi <D ;

-10

0

10

-1 -0.5 00.5 1 -1 -0.5 0 0.5 1 -10

0

10

(32)

v @ t_ D := 8 t Sin @ t D , Cos @ t D , Sin @ t D< ; ParametricPlot3D @ v @ t D , 8 t, 0, 2 Pi <D ;

-4

-2

0

-1 -0.5

0 0.5

1 -1 -0.5

0 0.5

1

-4

-2

0

-1 -0.5

0

v @ t_ D := 8 t Sin @ t D , Cos @ t D , Sin @ t D< ; ParametricPlot3D @ v @ t D , 8 t, 0, 20 Pi <D ;

-50

-25

0

25

50 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -50

-25

0

25

50

(33)

v @ t_ D := 5 8 Sin @ t D , Cos @ t D< ;

par1 = ParametricPlot @ v @ t D , 8 t, 0, 2 Pi < , AspectRatio ® Automatic D ;

-4 -2 2 4

-4 -2 2 4

v @ t_ D := 5 8 Sin @ t D , Cos @ t D< + 8 Sin @ 10 t D , Cos @ 10 t D< ;

par2 = ParametricPlot @ v @ t D , 8 t, 0, 2 Pi < , AspectRatio ® Automatic D ;

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

(34)

Show @ par1, par2 D

-6 -4 -2 2 4 6

-6 -4 -2 2 4 6

… Graphics …

(35)

v @ t_ D := 5 8 Sin @ t D , Cos @ t D< + 8 Sin @ E t D , Cos @ E t D< ;

par2 = ParametricPlot @ v @ t D , 8 t, 0, 200 Pi < , AspectRatio ® Automatic D ;

-6 -4 -2 2 4 6

-6

-4

-2

2

4

6

(36)

v @ t_ D := 5 8 Sin @ t D , Cos @ t D< + 8 Sin @ E t D , Cos @ E t D< ;

par2 = ParametricPlot @ v @ t D , 8 t, 0, 4000 Pi < , AspectRatio ® Automatic, PlotPoints ® 400 D ;

-6 -4 -2 2 4 6

-6 -4 -2 2 4 6

v @ t_, u_ D := 8 t Sin @ t D , Cos @ t D , Sin @ u D< ;

ParametricPlot3D @ v @ t, u D , 8 t, 0, 4 Pi < , 8 u, 0, 4 Pi <D ;

-10

-5

0

5

-1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 -10

-5

0

5

(37)

v @ t_, u_ D := 8 Sin @ t D , Cos @ t D , Sin @ u D< ;

ParametricPlot3D @ v @ t, u D , 8 t, 0, 4 Pi < , 8 u, 0, 4 Pi <D ;

-1 -0.5

0

0.5

1 -1

-0.5 0

0.5 1

-1 -0.5

0 0.5

1

-1 -0.5

0

0.5 -1

-0.5 0

0.5

v @ t_, u_ D := 8 Sin @ t D , Cos @ 2 t D , Sin @ u D< ;

ParametricPlot3D @ v @ t, u D , 8 t, 0, 4 Pi < , 8 u, 0, 4 Pi <D ;

-1 -0.5

0

0.5

1 -1

-0.5 0

0.5 1

-1 -0.5

0 0.5

1

-1 -0.5

0

0.5 -1

-0.5 0

0.5

(38)

v[t_,u_]:={Sin[t],Cos[u+t],Sin[u]};

ParametricPlot3D[v[t,u],{t,0,4Pi},{u,0,4Pi},PlotPoints®15];

-1 -0.5

0

0.5

1 -0.5

0 0.5

1

-1 -0.5

0 0.5

1

-1 -0.5

0

0.5 -0.5

0 0.5

vec[u_,v_]:={Sin[u] Cos[v],Sin[u] Sin[v],Cos[u]};

ParametricPlot3D[vec[u,v],{u,0,2Pi},{v,0,Pi}];

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0

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(39)

Zeit! Time! Temps!

Remove["Global`*"]

v @ t_, u_ D := 8 Sin @ t D , Cos @ u + t D , Sin @ u D< ;

ParametricPlot3D @ v @ t, u D , 8 t, 0, 4 Pi < , 8 u, 0, 4 Pi < , PlotPoints ® 20 D ;

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Referenzen

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