a = 0; b = 10; ContourPlot[{y + 3 ArcTan[y/(x - a)]}/20, {x, -b,
  b}, {y, -b, b}, Exclusions -> {x == a}, PlotPoints -> 50,
ContourStyle -> {Red}, Frame -> True, Axes -> True,
ContourShading -> None, PlotLegends -> {"\[Psi](x,y)"}]

a = 0;
Limit[y + 3 ArcTan[y/(x - a)], x -> 0, Direction -> #] & /@ {-1, 1}
(* {y + (3 \[Pi] Sqrt[y^2])/(2 y), y - (3 \[Pi] Sqrt[y^2])/(2 y)} *)

a = 0; b = 10;
ContourPlot[{y + 3 Arg[(x - a) + I y]}/20, {x, -b, b}, {y, -b, b},
  ContourStyle -> Red, Frame -> True, Axes -> True,
  ContourShading -> None] /.
Graphics[a__] :>
  Legended[Graphics[a],
   Placed[LineLegend[{Red}, {"\[Psi](x,y)"}], After]]

2Â¥: Originally posted by xzczd at 2015-01-07 22:28:07
ºÜÒź¶£¬Èç¹ûÄã¼á³ÖÒªÓÃÕâ¸ö·½³Ì£¬ÄÇôÕâ¾ÍÊǸö²»¿ÉÄܵÄÈÎÎñ£¬ÒòΪContourPlotÖÒʵµØ»­³öÁËÄãÊäÈëµÄ¶«Î÷£º

a = 0;
Limit & /@ {-1, 1}
(* {y + (3 \ Sqrt)/(2 y), y - (3 \ Sqrt)/(2 y)} *)


ÈçÄãËù¼û ...

2Â¥: Originally posted by xzczd at 2015-01-07 22:28:07
ºÜÒź¶£¬Èç¹ûÄã¼á³ÖÒªÓÃÕâ¸ö·½³Ì£¬ÄÇôÕâ¾ÍÊǸö²»¿ÉÄܵÄÈÎÎñ£¬ÒòΪContourPlotÖÒʵµØ»­³öÁËÄãÊäÈëµÄ¶«Î÷£º

a = 0;
Limit & /@ {-1, 1}
(* {y + (3 \ Sqrt)/(2 y), y - (3 \ Sqrt)/(2 y)} *)


ÈçÄãËù¼û ...

z1 = -(0.5*Log[x^2 + y^2] - Arg[x + y I])/(2 Pi);
ContourPlot[{z1}/300, {x, -10, 10}, {y, -10, 10},
ContourStyle -> {Red}, Frame -> True, Axes -> False,
ContourShading -> None,
Exclusions -> {x == 0, y == 0}, PlotPoints -> 50]

3Â¥: Originally posted by kabaisun at 2015-01-07 23:00:15
´íλ¾ÀÕýÁË£¬»¹ÓÐÒ»¸öÒÉÎÊ£ºArcTanÇó½Ç¶ÈºÍArgÇóµÄ²»Ò»ÑùÂð£¿...

4Â¥: Originally posted by kabaisun at 2015-01-07 23:31:20
Èç¹û·½³ÌÖв»Ö¹Õâ¸ö·ù½Çº¯ÊýÓмä¶Ïµã£¬»¹ÓжÔÊýº¯Êý£¬ÈçÏÂÃæ´úÂëÖеķ½³Ì£¬Õâ¸ö´íλ¿ÉÒÔµ÷ÕûÂð£¿
z1 = -(0.5*Log - Arg)/(2 Pi);
ContourPlot

ƽÃæÎÞÐýÁ÷µþ¼Óͼ.png
...

6Â¥: Originally posted by xzczd at 2015-01-08 10:26:41
¡­¡­¸úLogû¹Øϵ£¬ÕâÊǼ«¶ËÌõ¼þϵÄÊýÖµÎó²î¡££¨Â¥Ö÷ÄãºÜÓвÅÄÜ°¡£¬Õâô¶Ìʱ¼äÄÚÄܲȳöÕâô¶àÀס££©àÅ£¬ÓÐÒâ˼£¬WorkingPrecisionÑ¡Ïî¶ÔÕâÖÖÇé¿öËƺõÎÞЧ¡£¶ÔÓÚÄãÕâ¸öÎÊÌ⣬×î¼òµ¥µÄ·½·¨£¬¾ÍÊDZð³ýÄǸö300¡£³ý²»³ý ...

5Â¥: Originally posted by xzczd at 2015-01-08 09:42:49
Äã×Ðϸ»ØÒäÒ»ÏÂArcTanµÄÊýѧ¶¨Ò塣ʵÔڼDz»ÇåµÄ»°¾Í»­¸öͼ¿´¿´¡£...

8Â¥: Originally posted by kabaisun at 2015-01-08 13:49:46
²î±ð¿ÉÄÜÖ»ÔÚÔ­µã´¦£¬arctan(0)ÊǼä¶Ïµã£¬¶øarg²»ÊÇ¡£...

(* ×¢ÒâÖµÓò *)
Plot3D[ArcTan[y/x], {x, -10, 10}, {y, -10, 10}]

(* ×¢ÒâÖµÓò *)
Plot3D[Arg[x + I y], {x, -10, 10}, {y, -10, 10}]

9Â¥: Originally posted by xzczd at 2015-01-08 14:05:16
¡­¡­²»£¬ArcTanÖµÓòÊÇ-Pi/2µ½Pi/2£¬ËùÒÔÄãתÁË°ëȦ¾ÍÓÖÑ­»·»ØÈ¥ÁË£¬µ¼ÖÂͼÏñ´íλ¡£Arg²»Ò»Ñù£¬¿ÉÒÔת¹»Ò»È¦¡£ËùÒÔ˵Äã»­ÏÂͼ¾Í¶¼Ã÷°×ÁË£º



(* ×¢ÒâÖµÓò *)
Plot3D

(* ×¢ÒâÖµÓò *)
Plot3D
...