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所在平台: Udemy |
课程主页: https://www.udemy.com/course/calculus-1-limits-and-continuity/
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Coursera 课程“微积分 1 - 极限与连续”涵盖了高中生和大学一年级学生学习微积分入门所必需的核心概念。 该课程的核心主题是**极限**，并通过多种方法进行讲解： * **数据表格法**：通过观察数据趋近某个值时的函数值变化来估算极限。 * **直接代入法**：当函数在某点有定义时，直接代入点的值来计算极限。 * **三角函数极限**：重点讲解三角函数的极限求解。 * **极限的运算法则**：包括乘法和除法法则。 * **因式分解法**：通过提取公因式、平方差公式、立方和（差）公式以及分组分解等方法求解极限。 * **含平方根的极限**：处理涉及到平方根和根式的极限计算。 * **有理函数极限**：包括一般的得分函数以及包含平方根的有理函数。 * **特殊三角函数极限**：聚焦于正弦、余弦和正切函数的特殊极限。 * **夹逼定理**：利用夹逼定理来求解复杂函数或特定函数的极限。 * **图像法**：通过分析函数的图像来理解和确定极限。 * **分段函数极限**：处理定义在不同区间上的分段函数的极限。 本课程强调**极限与导数**之间的紧密联系。学习极限是理解导数的基础，因为导数可以被看作是函数在某一点的瞬时斜率，而利用极限和平均变化率公式可以计算这一瞬时斜率。因此，极限是导数概念的关键铺垫。 总而言之，本课程是学习微分学的第一门关键课程，为理解更深层的微积分概念打下坚实基础。
This course is designed for high school and college students taking their first semester of calculus and who are learning limits and continuity. Here is a list of topics covered in this video.1. Evaluating Limits Using a Data Table2. Evaluating Limits Analytically Using Direct Substitution3. Finding The Limit of Trigonometric Functions4. Properties of Limits - Multiplication and Division5. Evaluating Limits By Factoring - GCF, Difference of Perfect Squares & Sum of Cubes, & Factoring By Grouping6. Limits With Square Roots and Radicals7. Limits of Rational Functions and Fractions8. Limits of Rational Functions With Square Roots9. Limits of Special Trigonometric Functions - Sine, Cosine, and Tangent - Trigonometry10. The Squeeze Theorem 11. Evaluating Limits Graphically 12. Limits and Piecewise FunctionsThis section covers the main topics that you will typically encounter on your first major calculus exam. Learning limits is important because it ties in nicely with the second major topic taught in calculus which is Derivatives. The derivative is a function that can tell you the instantaneous slope of a function at any x value. You can also calculate the instantaneous slope of any function at any x value using limits and the average rate of change formula. In this way, limits and derivatives are related.
