|
所在平台: Udemy |
课程主页: https://www.udemy.com/course/understanding-calculus-course-2/
课程评论：没有评论
**课程名称：** 理解微积分 - 第二部分 **课程概述：** 本课程是“理解微积分”系列课程的第二部分。完成本课程后，学生将能够完全掌握以下主题： 1. **微分的概念与形式化定义** 2. **导数的规则**：包括乘积法则、商法则、链式法则等。 3. **可微性与连续性的关系**：证明可微性蕴含连续性。 4. **基本函数的导数公式**：涉及多项式、三角函数、对数函数和指数函数。 5. **与微分相关的重要定理**：包括中值定理 (MVT)、一阶/二阶导数检验、增减函数及其与微分的关系、洛必达法则。 6. **导数在函数图像绘制上的应用** 本课程以严谨的数学推理为特点，深入细致地讲解了各种证明及其思路。同时，课程中辅以大量实例，帮助学生建立对所学知识的具象化理解。 **学完本课程，您将能够：** * 自信地运用导数规则和导数公式，计算由基本函数复合而成的函数的导数。 * 运用与微分相关的重要定理，通过洛必达法则计算不定形式的极限。
This course is the 2nd course of my "Understanding Calculus" course series. At the end of this course, students will completely understand the following topics:(1) Idea and formal definition of differentiation(2) Derivative rules: product rule, quotient rule, chain rule, etc.(3) Differentiability implies continuity.(4) Derivative formulas of elementary functions, including polynomials, trigonometric functions, logarithmic functions, and exponential functions(5) Important theorems related to differentiation: mean value theorem (MVT), 1st/2nd derivative tests, increasing/decreasing functions and their relation to differentiation, L'Hopital's rule(6) Application to function sketchingThis course is very mathematically rigorous in the sense that the proofs and their ideas are gone over and explained in details. Moreover, examples are also discussed, which build a concrete understanding of the topics that are introduced in the course. After completing this course, students will be able to confidently apply derivative rules and derivative formulas to compute the derivatives of functions that are composed of elementary functions. Also, students will be able to apply important theorems related to differentiation to compute limits in indeterminate forms using L'Hopital's rule.
