微積分(二)
Calculus II
學期
107-2
學分
2
學分
當期課號
A764
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 1 週 | Course introduction Applications of integrals: area, average |
| 第 2 週 | Applications of integrals: volume Improper integrals - The comparison testCourse introduction Applications of integrals: area |
| 第 3 週 | Review of differential equations Solving autonomous differential equations: separation of variable Solving nonautonomous differential equations: separation of variableApplications of integrals: average, volume Improper integrals - The comparison test |
| 第 4 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 growthReview of differential equations Solving autonomous differential equations: separation of variable Solving nonautonomous differential equations: separation of variable |
| 第 5 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 NullclinesQuiz 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 | Phase plane trajectory Direction arrows The dynamics of competition between two speciesSystems 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 | Quiz 2 Limits and continuity of multivariable functions Partial derivatives Double integrals over rectangles Double integral in polar coordinatesPhase plane trajectory Direction arrows The dynamics of competition between two species |
| 第 8 週 | Midterm examQuiz 2 Limits and continuity of multivariable functions Partial derivatives Double integrals over rectangles Double integral in polar coordinates |
| 第 9 週 | Deterministic vs. stochastic Sample space and events Set theory Classical definition of probability Axioms of probabilityMidterm exam |
| 第 10 週 | Conditional probability - Special cases for conditional probability The law of total probability Bayes’ theoremDeterministic vs. stochastic Sample space and events Set theory Classical definition of probability Probability axioms Conditional probability |
| 第 11 週 | Independence Random variables Probability mass function (pmf) Cumulative distribution function (cdf)Special cases for conditional probability The law of total probability Baye’s theorem Independence Random variables |
| 第 12 週 | Quiz 3 Expectations of discrete random variables Variances of discrete random variables Bernoulli random variableProbability mass function (pmf) Cumulative distribution function (cdf) Expectations of discrete random variables Variance of discrete random variables Bernoulli random variable |
| 第 13 週 | Binomial random variable Geometric random variableQuiz 3 Binomial random variable Geometric random variable |
| 第 14 週 | Poisson random variable Continuous random variable Probability density function (pdf) Cumulative distribution function (cdf)Poisson random variable |
| 第 15 週 | Quiz 4 Probability density function of a function of a random variable Expectations of continuous random variables Variances of continuous random variablesContinuous 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 | Uniform random variable Exponential random variableQuiz 4 Uniform random variable Exponential random variable |
| 第 17 週 | Normal (Gaussian) random variable |
| 第 18 週 | Final exam |