MYMathApps微积分:枫图

Philip Yasskin
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引用次数: 0

摘要

我正在写一个叫做MYMathApps微积分的在线微积分教材。您可以在https://mymathapps.com/mymacalc-sample/The上看到一个示例,文本具有高度交互性和可视性。几乎所有的图形都是用Maple制作的,包括2D和3D,静态和动画。使用图形和动画图形帮助学生理解一些概念,如导数的定义是割线斜率的极限,积分的定义是黎曼和的极限,偏导数的定义是轨迹的斜率,曲率和扭转,切向和法向加速度,散度和旋度,多重积分,曲线坐标和雅可比矩阵。三角不等式的证明,中值定理和积分应用的公式。绘图函数,极坐标曲线,参数曲线和曲面。解决涉及线性近似、相关速率、最大/最小、面积、弧长、表面积、切片体积、旋转体积、功、混合问题、几何级数、泰勒级数、方向导数、拉格朗日乘子、展开和循环等应用问题。如何使用格林定理,斯托克斯定理和高斯定理中的右手定则。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
MYMathApps Calculus: Maple Plots
I am writing an online Calculus text called MYMathApps Calculus. You can see a sample at           https://mymathapps.com/mymacalc-sample/The text is highly interactive and visual. Nearly all of the graphics have been made with Maple, both 2D and 3D, static and animated. The use of plots and animated plots helps students understand concepts such as the definitions of a derivative as the limit of slopes of secant lines, an integral as limits of Riemann sums, partial derivatives as slopes of traces, curvature and torsion, tangential and normal acceleration, divergence and curl, multiple integrals, curvilinear coordinates and Jacobians. the proofs of the triangle inequality, the mean value theorem and formulas for applications of integrals. plotting functions, polar curves, and parametric curves and surfaces. solving applied problems involving linear approximation, related rates, max/min, area, arc length, surface area, volumes by slicing, volumes of revolution, work, mixing problems, geometric series, Taylor series, directional derivatives, Lagrange multipliers, expansion and circulation. how to use the right hand rule in Green’s, Stokes’ and Gauss’ theorems.
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