微積分(二)
Calculus II
學期
114-2
學分
2
學分
當期課號
114400
永久課號
GEKY10005
開課單位
基礎科學微積分小組
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) YX406 2 節連堂 |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
有別於傳統微積分課程強調嚴謹的數學證明及計算，本課程強調微積分的基本概念及其在生物醫學領域的應用。本課程將延續上學期微積分一的內容，講述微分方程式及多變量微積分，此外，機率及隨機變數也將在本課程中介紹。由於本課程的對象多為生醫領域相關學生，因此課程中的主題將利用生醫相關範例來講解，希望學生可以從課程中學到數學及生醫科學的關聯性。
先修科目
微積分一
教學方式
讓學生了解微積分及機率的基本觀念並認識數學模型在生物醫學領域的角色，以培養生醫領域的量化分析能力，此外亦培養學生的邏輯推理能力，建立學生進一步從事生醫領域研究之數學基礎。
評分方式
作業25%，小考15%，期中考30%，期末考30%
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction Improper integrals |
| 第 2 週 | Review of differential equations Euler's method: a numerical method to solve differential equations Solving autonomous differential equations: separation of variable Euler's method to solve autonomous differential equations Solving nonautonomous differential equations: separation of variable |
| 第 3 週 | Analysis of autonomous differential equations: equilibria - Stability theorem for autonomous differential equations Biological examples for autonomous differential equations - Exponential population growth - Logistic population growth Systems of autonomous differential equations - Predator-prey model - Euler's method to solve systems of autonomous differential equations |
| 第 4 週 | Quiz 1 Equilibria Phase plane Nullclines Phase plane trajectory Direction arrows |
| 第 5 週 | The dynamics of competition between two species Multivariable calculus - Multiple-variable function - Limits - Continuity - Partial derivatives |
| 第 6 週 | Multivariable calculus - Second partial derivatives - Partial differential equations - Double integrals over rectangles - Double integrals in polar coordinates |
| 第 7 週 | Midterm exam |
| 第 8 週 | Deterministic vs. stochastic Sample space and events Set theory Classical definition of probability Axioms of probability Conditional probability |
| 第 9 週 | The law of total probability Bayes' theorem Independence Random variables |
| 第 10 週 | Probability mass function (pmf) Cumulative distribution function (cdf) Expectations and variances of discrete random variables Bernoulli random variable |
| 第 11 週 | Quiz 2 Binomial random variable Geometric random variable |
| 第 12 週 | Poisson random variable Continuous random variable Probability density function (pdf) |
| 第 13 週 | Cumulative distribution function (cdf) Probability density function of a function of a random variable Expectations and variances of continuous random variables |
| 第 14 週 | Quiz 3 Uniform random variable Exponential random variable |
| 第 15 週 | Normal (Gaussian) random variable |
| 第 16 週 | Final exam |
教科書
參考書： 1. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, 3rd edition, Frederick R. Adler, Cengage Learning, 2012. 2. Calculus for Biology and Medicine, 3rd edition, Claudia Neuhauser, Pearson, 2010. 3. Biocalculus: Calculus, Probability, and Statistics for the Life Sciences, James Stewart and Troy Day, Brooks Cole, 2015.
Office Hours
- 地點
- 守仁樓R307
- 時間
- By appointment
- 聯絡方式
- yuchao@nycu.edu.tw