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.
Overview
Syllabus
- Ch0 The history of Newton and Leibniz
- Ch1 The applications of differential calculus
- 1.1 The applications of derivative：space traveler
- 1.2 The applications of chain rule：the clock
- 1.3 The applications of related rates：telescope
- 1.4 The application of differential: linear approximation
- 1.5 The applications of differential: Poiseuille's Law and Relative theory
- 1.6 The least squares
- 1.7 The cost, profit and revenue functions
- 1.8 The economic applications of derivative: the marginal idea
- 1.9 The applications of the Mean Value Theorem: velocity
- 1.10 Solving the equation: Newton's Method
- Ch2 The applications of optimazition
- 2.1 How to minimize the energy
- 2.2 The moving sofa problem
- 2.3 The fastest path of driving
- 2.4 The brachistochrone problem
- 2.5 The interesting cycloid
- Ch3 The applications of Integral calculus
- 3.1 The applications of definite integral: the area of a plane region
- 3.2 The applications of definite integral: the volume of solid of revolution
- 3.3 The volume of cross section: Mouhefanggai
- 3.4 The applications of definite integral: moments
- 3.5 continuous mass distribution
- 3.6 The applications of definite integral: expectation
- 3.7 Probability Density Function
- 3.8 Cumulative Distribution Function
- 3.9 The applications of definite integral-springs
- 3.10 The economic applications : present value and future value
- 3.11 The applications of improper integral-space capsule
- 3.12 The applications of improper integral-Torricelli’s trumpet
Taught by
Gao Xuefen, Dinghua, Jordan, Congming, Minhong, Jade, and Fenfen
