线性一阶微分方程组演示

线性一阶微分方程组演示
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2016-04-09 22:21
①本范例演示了两个线性一阶微分方程组的数值解及其积分曲线;②涉及的核心数学概念包括微分方程、数值解法(NSolveODE)、积分曲线、解析几何等;③作图要点使用了GeoGebra的NSolveODE命令求解微分方程,Length命令计算长度,PolyLine命令绘制曲线,以及Start, AB, CD, y1', y2', numericalIntegral1, numericalIntegral2, c, y1, x1, A1-B15等对象进行参数设置和图形绘制;④适合高中及以上学生学习和理解微分方程的数值解法和图形表示,可用于教学演示和探究性学习。

GeoGebra 命令及参数

  1. NSolveODE({y1', y2'}, 0, {x(Start), y(Start)}, 50) → numericalIntegral1, numericalIntegral2
  2. Length(numericalIntegral1) → len
  3. PolyLine({I_8, J_8, K_8, L_8, M_8, N_8, O_8, P_8, Q_8, R_8, S_8, T_8, U_8, V_8, W_8, Z_8, A_9, B_9, C_9, D_9, E_9, F_9, G_9, H_9, I_9, J_9, K_9, L_9, M_9, N_9, O_9, P_9, Q_9, R_9, S_9, T_9, U_9, V_9, W_9, Z_9, A_{10}, B_{10}, C_{10}, D_{10}, E_{10}, F_{10}, G_{10}, H_{10}, I_{10}, J_{10}, K_{10}, L_{10}, M_{10}, N_{10}, O_{10}, P_{10}, Q_{10}, R_{10}, S_{10}, T_{10}, U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}, C_{11}, D_{11}, E_{11}, F_{11}, G_{11}, H_{11}, I_{11}, J_{11}, K_{11}, L_{11}, M_{11}, N_{11}, O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}, U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}, C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}, I_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}, O_{12}, P_{12}, Q_{12}, R_{12}, S_{12}, T_{12}, U_{12}, V_{12}, W_{12}, Z_{12}, A_{13}, B_{13}, C_{13}, D_{13}, E_{13}, F_{13}, G_{13}, H_{13}, I_{13}, J_{13}, K_{13}, L_{13}, M_{13}, N_{13}, O_{13}, P_{13}, Q_{13}, R_{13}, S_{13}, T_{13}, U_{13}, V_{13}, W_{13}, Z_{13}, A_{14}, B_{14}, C_{14}, D_{14}, E_{14}, F_{14}, G_{14}, H_{14}, I_{14}, J_{14}, K_{14}, L_{14}, M_{14}, N_{14}, O_{14}, P_{14}, Q_{14}, R_{14}, S_{14}, T_{14}, U_{14}, V_{14}, W_{14}, Z_{14}, A_{15}, B_{15}, C_{15}, D_{15}, E_{15}, F_{15}, G_{15}, H_{15}, I_{15}, J_{15}, K_{15}, L_{15}, M_{15}, N_{15}, O_{15}, P_{15}, Q_{15}, R_{15}, S_{15}, T_{15}, U_{15}, V_{15}, W_{15}, Z_{15}, A_{16}, B_{16}, C_{16}, D_{16}, E_{16}, F_{16}, G_{16}, H_{16}, I_{16}, J_{16}, K_{16}, L_{16}, M_{16}, N_{16}, O_{16}, P_{16}}) → a

AI 绘图提示语参考

绘制一组线性一阶微分方程的数值解和积分曲线,展示微分方程的数值解方法,用不同颜色的曲线表示至少两条积分曲线,曲线从起点开始,经过多个点,最后到达终点,曲线长度用不同颜色或粗细区分,整体呈现数学分析中的几何表示效果。
以上提示语为根据原始绘图命令整理而来,仅供参考。