Maxima 在微积分上之应用 - 屏东大学应用数学系.PDF

Maxima 在微積分上之應用 偏微分 國立屏東教育大學 應用數學系 研究助理 徐偉玲 weilinghsu@mail.npue.edu.tw 日期：2009/11/30 除另有說明外 ，本文件採用創用CC 「姓名標示、非商業性」 2.5 台灣條款 11.1 Surfaces Example 1. Sketch the portion of the cylinder x 2 + y 2 = 1 where 1≤ z ≤ 2 (Figure 11.1.12) Solution ：(%i1) load(draw); 因為Maxima 內沒有直接畫圓柱體的指令，因此， 要畫出圓柱體需要讀取模組draw ，用模組draw 內建的指令去畫圖 //讀取模組 draw (%i2) draw3d(cylindrical(1,z,1,2,az,0,2*%pi)); 畫圓柱體的指令 ： draw3d(cylindrical(半徑 ，z 座標 ，最小z 值，最大z 值，azi ，最小azi 值，最大 azi 值)) ，在此(z ，azi) 代表圓柱體的座標 //此題半徑為 1 ，z 軸的範圍為 1~2 Step 1 ： Draw the curve x 2 + y 2 = 1 in the (x , y ) plane. The curve is a circle of radius one. Step 2 ： Draw the three coordinate axes and the horizontal planes z =1, z = 2 . Step 3 ： Draw the circles x 2 + y 2 = 1 where the surface intersects the two planes z =1, z = 2 . Step 4 ： Complete the sketch by drawing heavy lines for all edges which would be visible on an “opaque” model of the given surface. This surface is called a circular cylinder. Example 2. Sketch the part of the cylinder z = x 2 where 0 ≤ y ≤2,0 ≤ z ≤ 1 . This is a parabolic cylinder parallel to the y -axis, because y does not appear in the equation. The four steps are shown in Figure 11.1.13. Solution ：(%i1) plot3d(x^2,[x,0,2],[z,0,1],[grid,30,30]); 畫3d 圖形的指令 ： plot3d(函數式 ，x 軸的範圍 ，y 軸的範圍 ，z 軸的範圍 ，其他繪圖選項) //函數式 為z = x 2 ，x 軸的範圍為 1~2 ，z 軸的範圍為0~1 ，網格劃分為30×30 For sketching the graph of a function z = f (x , y ) , a topographic map, or contour map, can often be used as a first step. It is a method of representing a surface which is often found in atlases. In a topographic map, the curves f (x , y ) = z 0 are sketched in the (x , y ) plane for several different constant z 0 , and each curve is labeled (Figure 11.1.1