欧拉法可视化

几何画板及绘图内容加载中，请稍等……

2018-07-05 18:16

①本范例演示了如何使用欧拉法对一阶微分方程dy/dx=f(x,y)进行数值求解并可视化；②涉及的核心数学概念包括微分方程、数值方法、方向场和近似解；③作图要点——使用了SlopeField（方向场）、PolyLine（折线）、Textfield（文本）、TableText（表格文本）和SolveODE（求解常微分方程）等GeoGebra命令；④适合高阶数学课程或需要理解微分方程数值解法的学员学习。

GeoGebra 命令及参数

SlopeField(f, 20) → slopefield1
PolyLine({B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, Z_1, A_2, B_2, C_2}) → a_1
Textfield(f) → InputBox1
TableText({{A1, B1, C1, D1}, {A2, B2, C2, D2}, {A3, B3, C3, D3}, {A4, B4, C4, D4}, {A5, B5, C5, D5}, {A6, B6, C6, D6}, {A7, B7, C7, D7}, {A8, B8, C8, D8}, {A9, B9, C9, D9}, {A10, B10, C10, D10}, {A11, B11, C11, D11}, {A12, B12, C12, D12}, {A13, B13, C13, D13}, {A14, B14, C14, D14}, {A15, B15, C15, D15}, {A16, B16, C16, D16}, {A17, B17, C17, D17}, {A18, B18, C18, D18}, {A19, B19, C19, D19}, {A20, B20, C20, D20}, {A21, B21, C21, D21}, {A22, B22, C22, D22}, {A23, B23, C23, D23}, {A24, B24, C24, D24}, {A25, B25, C25, D25}, {A26, B26, C26, D26}, {A27, B27, C27, D27}, {A28, B28, C28, D28}, {A29, B29, C29, D29}, {A30, B30, C30, D30}, {A31, B31, C31, D31}, {A32, B32, C32, D32}, {A33, B33, C33, D33}, {A34, B34, C34, D34}, {A35, B35, C35, D35}, {A36, B36, C36, D36}, {A37, B37, C37, D37}, {A38, B38, C38, D38}, {A39, B39, C39, D39}, {A40, B40, C40, D40}, {A41, B41, C41, D41}, {A42, B42, C42, D42}, {A43, B43, C43, D43}, {A44, B44, C44, D44}, {A45, B45, C45, D45}, {A46, B46, C46, D46}, {A47, B47, C47, D47}, {A48, B48, C48, D48}, {A49, B49, C49, D49}, {A50, B50, C50, D50}, {A51, B51, C51, D51}}, "|_") → text1
SolveODE(f(x, y), A) → g

AI 绘图提示语参考

绘制一阶微分方程的数值解和可视化，首先展示斜率场，然后在该基础上绘制使用欧拉方法得到的近似解曲线，并标注方程式和表格数据，最后求解微分方程得到精确解曲线进行对比。

以上提示语为根据原始绘图命令整理而来，仅供参考。