一阶线性微分方程组探究

一阶线性微分方程组探究
几何画板及绘图内容加载中,请稍等……
2016-04-09 22:21
本范例演示了如何使用 GeoGebra 探究一阶线性微分方程组的解及其系数和初始位置的影响。涉及的核心数学概念包括微分方程、导数和数值积分。作图要点包括使用 NSolveODE 命令求解微分方程,Length 命令计算长度,PolyLine 命令绘制线条,以及对象如 Start, AB, y1', CD, y2', numericalIntegral1, numericalIntegral2, c, y1, x1, A1, B1, A2, B2, A3, B3, A4, B4, A5, B5, A6, B6, A7, B7, A8, B8, A9, B9, A10, B10, A11, B11, A12, B12, A13, B13, A14, B14, A15, B15 的应用。适合高中及以上学生学习和理解微分方程的应用。

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解,展示系数和初始位置的影响。使用数值积分方法求解微分方程,计算积分路径的长度,并用多段线连接积分路径上的点,形成连续曲线。通过这些曲线,观察微分方程的解随时间的变化,以及系数对解的影响。
以上提示语为根据原始绘图命令整理而来,仅供参考。