微積分(二)
Calculus II
學期
106-2
學分
2
學分
當期課號
A705
永久課號
A5188
開課單位
生命科學系暨基因體科學研究所
授課教師
王禹超
校區
陽明
類別
必修
上課時間表
| 節 | 週二 |
|---|---|
3 10:10–11:00 | 微積分(二) YX501 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
週次計畫
| 週次 | 主題 |
|---|---|
| 第 2 週 | Course introduction Applications of integrals: area |
| 第 3 週 | Applications of integrals: average, volume Improper integrals - The comparison test |
| 第 4 週 | Review of differential equations Solving autonomous differential equations: separation of variable Solving nonautonomous differential equations: separation of variable |
| 第 5 週 | Quiz 1 Analysis of autonomous differential equations: equilibria Stability theorem for autonomous differential equations Biological examples for autonomous differential equations - Exponential population growth - Logistic population growth |
| 第 6 週 | Systems of autonomous differential equations Predator-prey model Euler’s method to systems of autonomous differential equations Equilibria of systems of autonomous differential equations Phase plane Nullclines |
| 第 7 週 | Phase plane trajectory Direction arrows The dynamics of competition between two species |
| 第 8 週 | Quiz 2 Limits and continuity of multivariable functions Partial derivatives Double integrals over rectangles Double integral in polar coordinates |
| 第 9 週 | Midterm exam |
| 第 10 週 | Deterministic vs. stochastic Sample space and events Set theory Classical definition of probability Probability axioms Conditional probability |
| 第 11 週 | Special cases for conditional probability The law of total probability Baye’s theorem Independence Random variables |
| 第 12 週 | Probability mass function (pmf) Cumulative distribution function (cdf) Expectations of discrete random variables Variance of discrete random variables Bernoulli random variable |
| 第 13 週 | Quiz 3 Binomial random variable Geometric random variable |
| 第 14 週 | Poisson random variable |
| 第 15 週 | Continuous random variable Probability density function (pdf) Cumulative distribution function (cdf) Probability density function of a function of a random variable Expectations of continuous random variables Variance of continuous random variables |
| 第 16 週 | Quiz 4 Uniform random variable Exponential random variable |
| 第 17 週 | Normal (Gaussian) random variable |
| 第 18 週 | Final exam |