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当学员按自己的认识和推理与课本及教师的讲述不一致或得不到满足时,就会产生疑惑。现举例说明如何解惑。一、全微分的几何解释,可微函数z=f(x,y)的全微分dzf_x~(?)dx+f_y~(?)dy是两个偏微分之和,几何解释应是两线段之和,偏微分f_x~(?)dx是在y=y_0平面上,曲线z=f(x,y),y=y_0的切线纵坐标z的增量d_1,f_y~(?)dy是在x=x_0平面上,曲线z=f(x,y),x=x_0的切线纵坐标z的增量d_2,d_z如是两切线决定的平面,即z=f(x,y)在点的切平面,竖坐际Z的增量d_0在图上易证d=d_1+d_2。二、曲线积分的几何解释。微积分的每一定义都有几何解释,但课本上没有曲线积分的几何解释。引起学员的
When the students are inconsistent or unsatisfied with the textbooks and the teacher’s statements according to their own understanding and reasoning, doubts will arise. Here is an example of how to solve doubts. First, the full differential interpretation of the geometry, differentiable function z = f (x, y) of the full differential dzf_x ~ (?) dx + f_y ~ (?) dy is the sum of two partial differentials, geometric interpretation should be two lines of the And, the partial differential f_x~(?)dx is on the y=y_0 plane, the curve z=f(x,y), and y=y_0 is the tangent y of the y-axis, d_1, where f_y~(?)dy is at x In the plane of =x_0, the curve z=f(x,y), the increment d_2 of the tangent ordinate z of x=x_0, d_z is the plane determined by the two tangents, that is, z=f(x,y) at the point , the incremental d_0 of the vertical squat Z is easily proved on the map d=d_1+d_2. Second, the geometric interpretation of the curve integral. Each definition of calculus has a geometric interpretation, but there is no geometric explanation of the curve integral in the textbook. Cause students