微積分(一)
Calculus I
| 節 | 週三 |
|---|---|
1 08:00–08:50 | 微積分(一) YX406（陽明） 2 節連堂 |
2 09:00–09:50 |
* 根據陽明交大上課時間表所列
課程概述: 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。本課程將由指數、對數、三角函數的介紹開始,帶入離散動態系統、微分、積分及微分方程式等概念,此外,機率、隨機變數等主題也將在下學期微積分二中介紹。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。 教學目標: 讓學生了解微積分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。
高中數學
無備註
E3數位課程平台 https://e3.nycu.edu.tw/
作業25%、小考15%、期中考30%、期末考30%
教師未提供此項資料
| 週次 | 主題 |
|---|---|
| 第 1 週 | Course introduction Review of high school math Introduction to mathematical modeling 2024-09-04(三) 時數：[2024-09-04]王禹超(2.00) |
| 第 2 週 | Functions Inverse functions Exponential functions and logarithmic functions Trigonometric functions and inverse trigonometric functions 2024-09-11(三) 時數：[2024-09-11]王禹超(2.00) |
| 第 3 週 | Discrete-time dynamical systems Cobwebbing: a graphical solution technique for discrete-time dynamical systems Equilibria of discrete-time dynamical systems Average/instantaneous rate of change Limits of functions 2024-09-18(三) 時數：[2024-09-18]王禹超(2.00) |
| 第 4 週 | Quiz 1 The squeeze theorem Continuity Derivatives 2024-09-25(三) 時數：[2024-09-25]王禹超(2.00) |
| 第 5 週 | Computing derivatives - Power rule - Sum rule, constant product rule, product rule, quotient rule - Chain rule Derivative of trigonometric functions Derivative of exponential functions 2024-10-02(三) 時數：[2024-10-02]王禹超(2.00) |
| 第 6 週 | Implicit differentiation Derivative of inverse trigonometric functions Derivative of inverse functions Derivative of logarithmic functions 2024-10-09(三) 時數：[2024-10-09]王禹超(2.00) |
| 第 7 週 | Quiz 2 Higher derivatives Increasing / decreasing functions Maximum / minimum Concavity 2024-10-16(三) 時數：[2024-10-16]王禹超(2.00) |
| 第 8 週 | Midterm exam 2024-10-23(三) 時數：[2024-10-23]王禹超(2.00) |
| 第 9 週 | Curve sketching Useful theorems for continuous/differentiable functions - Intermediate value theorem - Extreme value theorem - Rolle's theorem - Mean value theorem Limits at infinity - L'Hopital's rule 2024-10-30(三) 時數：[2024-10-30]王禹超(2.00) |
| 第 10 週 | Approximating functions Newton's method: a numerical method to solve an equation Introduction to differential equations Euler's method: a numerical method to solve differential equations Antiderivatives 2024-11-06(三) 時數：[2024-11-06]王禹超(2.00) |
| 第 11 週 | The definite integral The fundamental theorem of calculus 2024-11-13(三) 時數：[2024-11-13]王禹超(2.00) |
| 第 12 週 | 全校運動會(停課) 2024-11-20(三) 時數：[2024-11-20]王禹超(2.00) |
| 第 13 週 | Quiz 3 Mean value theorem for definite integrals Integration by substitution 2024-11-27(三) 時數：[2024-11-27]王禹超(2.00) |
| 第 14 週 | Integration by parts Integration by partial fractions 2024-12-04(三) 時數：[2024-12-04]王禹超(2.00) |
| 第 15 週 | Applications of integrals - Average - Area - Volume 2024-12-11(三) 時數：[2024-12-11]王禹超(2.00) |
| 第 16 週 | Final exam 2024-12-18(三) 時數：[2024-12-18]王禹超(2.00) |
參考書: 1. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists, 3rd edition, Frederick R. Adler, Cengage Learning, 2012. 2. Biocalculus: Calculus, Probability, and Statistics for the Life Sciences, Stewart and Day, Brooks Cole, 2015. 3. Calculus for Biology and Medicine, 3rd edition, Claudia Neuhauser, Pearson, 2010.
- 地點
- 教師未提供此項資料
- 時間
- By appointment
- 聯絡方式
- E-mail: yuchao@nycu.edu.tw