then will give a feel for the properties of the scalar function.We show such a contour map in the xy-plane atz=0 for Eq.(1.2.2),namely, 1 1/3 (x,y,0)= (1.2.3) Vx2+y+d2Vx2+y-d0月 Various contour levels are shown in Figure 1.2.4,for d=1,labeled by the value of the function at that level. -2 0 Figure 1.2.4 A contour map in the xy-plane of the scalar field given by Eq.(1.2.3). 2.Color-Coding Another way we can represent the values of the scalar field is by color-coding in two dimensions for a fixed value of the third.This was the scheme used for illustrating the temperature fields in Figures 1.2.1 and 1.2.2.In Figure 1.2.5 a similar map is shown for the scalar field (x,y,0).Different values of (x,y,0)are characterized by different colors in the map. 0 2 0 21 Figure 1.2.5 A color-coded map in the xy-plane of the scalar field given by Eq.(1.2.3). 1-61-6 then will give a feel for the properties of the scalar function. We show such a contour map in the xy-plane at z = 0 for Eq. (1.2.2), namely, ( ) ( ) 2 2 2 2 1 1/3 ( , ,0) x y x yd x yd φ = − ++ +− (1.2.3) Various contour levels are shown in Figure 1.2.4, for d =1, labeled by the value of the function at that level. Figure 1.2.4 A contour map in the xy-plane of the scalar field given by Eq. (1.2.3). 2. Color-Coding Another way we can represent the values of the scalar field is by color-coding in two dimensions for a fixed value of the third. This was the scheme used for illustrating the temperature fields in Figures 1.2.1 and 1.2.2. In Figure 1.2.5 a similar map is shown for the scalar field ( , ,0) φ x y . Different values of ( , ,0) φ x y are characterized by different colors in the map. Figure 1.2.5 A color-coded map in the xy-plane of the scalar field given by Eq. (1.2.3)