微积分应用（Applications of Calculus I ）

Overview

Calculus is one of the greatest achievements of human thought, explaining everything from relative theory to the optimal profits. This course covers the applications of core ideas of single variable Calculus and historical motivation for calculus. The course is ideal for students beginning in the engineering, computer science, business administration and so on.

课程围绕微积分的核心概念，重点讲授一元微积分的应用，共含有40余个应用案例。教学兼顾直观性、应用性、历史性，注重讲述微积分的源与流。视频中具有丰富的动画、实物教具等，其课程安排顺序与一般微积分课程的顺序一致，既可以作为一个独立的课程，也可以作为一般的高等数学课的辅助课程或混合式课程。视频采用英文讲授配以中英文字幕，适合中外高中生、大学生及社会人士学习。

Syllabus

Ch0 The history of Newton and Leibniz 从牛顿和莱布尼茨谈起

Ch1 The applications of differential calculus 微分学应用

1.1 The applications of derivative：space traveler 导数的应用：太空漫步问题
1.2 The applications of chain rule：the clock 链式法则的应用：时针与分针问题
1.3 The applications of related rates：telescope 相关变化率的应用：望远镜问题
1.4 The application of differential: linear approximation 微分的应用：线性近似
1.5 The applications of differential: Poiseuille's Law and Relative theory 微分的应用：泊肃叶定律、相对论
1.6 The least squares 最小二乘法
1.7 The cost, profit and revenue functions 成本、利润和收入函数
1.8 The economic applications of derivative: the marginal idea-导数的经济应用：边际
1.9 The applications of the Mean Value Theorem: velocity 中值定理的应用：速度
1.10 Solving the equation: Newton's Method 利用牛顿法解方程

Ch2 The applications of optimazition

2.1 How to minimize the energy 如何节约能量
2.2 The moving sofa problem 移动沙发问题
2.3 The fastest path of driving 最快行驶路线
2.4 The brachistochrone problem 最速降线
2.5 The interesting cycloid 有趣的摆线

Ch3 The applications of Integral calculus 积分学的应用

3.1 The applications of definite integral: the area of a plane region-平面图形的面积
3.2 The applications of definite integral: the volume of solid of revolution 旋转体的体积
3.3 The volume of Mouhefanggai 牟合方盖
3.4 The applications of definite integral: moments 力矩
3.5 continuous mass distribution 连续质量分布
3.6 The applications of definite integral: expectation 期望
3.7 Probability Density Function 概率密度函数
3.8 Cumulative Distribution Function 概率分布函数
3.9 The applications of definite integral-springs 功：弹簧
3.10 The economic applications : present value and future value 现值与将来值
3.11 The applications of improper integral-space capsule 反常积分：宇宙飞船
3.12 The applications of improper integral-Torricelli’s trumpet 反常积分：托里拆利小号