課程資訊
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課程基本資訊
| 項目 | 內容 |
| 課程名稱 | 生命科學數學 |
| 開課學期 | 114-2 |
| 授課對象 |
生命科學所 生命科學系 |
| 授課教師 | 柯柏如 |
| 課號 | LS 5073 |
| 課程辨識碼 | B21 U2170 |
| 班次 | |
| 學分 | 2 |
| 全/半年 | 半年 |
| 必/選修 | 選修 |
| 上課時間 | 星期一 8,9(15:30~17:20) |
| 上課地點 | 共202 |
| 備註 | 與郭鴻基、謝志豪、張俊偉合授 |
課程大綱
| 項目 | 內容 |
| 課程概述 | The course focuses on the development of mathematical models and the analysis of dynamic systems. Using simple mathematical models and key examples from life sciences, the course covers four main topics: (1) the formulation of governing equations, (2) analytical solutions and analyses, (3) numerical simulations, and (4) scientific interpretation. Model examples spans multiple scales, from enzyme kinetics to ecosystem processes, with a focus on common feedback mechanisms and stability issues in dynamic systems. Additionally, the course emphasizes fundamental mathematical concepts and introduces the application of dimensional and scaling analysis in scientific research. |
| 課程目標 | By the end of the course, students are would be familiar with the basic building blocks of dynamic systems, and would be able to formulate and analyze simple models of their own. The hands-on practice component should allow students to link their scientific intuition with the underlying mathematical model, helping them to better understand the primary literature of theoretical biology and ecology. |
| 課程要求 | Students are only expected to have basic understanding of calculus (e.g., freshman introductory course). It's OK if you're not familiar with calculus as we will review them during the first couple weeks and whenever we encounter them. We will also point you to relevant material online to review during the first week (i.e., the wonderful 3Blue1Brown channel by Grant Sanderson, you can check out their Calculus series). |
| 預期每週課前或/與課後學習時數 | The final grade consists of: assignment problem sets (80%), participation (10%), and attendance (10%). |
| 參考書目 | We will use a combination of textbooks of theoretical ecology and biology. The majority of the lecture is based on the lecturer’s PDF; textbook chapters and additional reading materials will be provided when necessary. 1. A Biologist’s Guide to Mathematical Modeling in Ecology and Evolution. Sarah Otto & Troy Day, 2011. 2. Nonlinear Dynamics and Choas. Steven Strogatz, 2000. 3. An Illustrative Guide to Theoretical Ecology. Ted Case, 2000. 4. Modeling the Dynamics of Life, Calculus and Probability for Life Scientists. Frederick Adler, 2012. 5. Modeling Differential Equations in Biology. Clifford Taubes, 2012. |
| 指定閱讀 |
課程進度
| 週次 | 日期 | 單元主題 |
| 第1週 | 2/23 | Course introduction and basic R [Ke] |
| 第2週 | 3/2 | R programming [Ke] |
| 第3週 | 3/9 | Matrix, calculus, and ODEs (I) [Kuo] |
| 第4週 | 3/16 | Matrix, calculus, and ODEs (II) [Kuo] |
| 第5週 | 3/23 | Matrix, calculus, and ODEs (III) [Kuo] |
| 第6週 | 3/30 | Numerical simulation of ODEs [Hsieh] |
| 第7週 | 4/6 | Holiday [no class] |
| 第8週 | 4/13 | Stability analysis of ODEs [Hsieh] |
| 第9週 | 4/20 | Discrete systems and chaos [Hsieh] |
| 第10週 | 4/27 | Matrix population models [Ke] |
| 第11週 | 5/4 | Bifurcation and alternative stable states [Ke] |
| 第12週 | 5/11 | Stochastic processes [Chang] |
| 第13週 | 5/18 | Networks [Chang] |
| 第14週 | 5/25 | Invited talk [Dr. 邱澗庚] |
| 第15週 | 6/1 | Invited talk [Dr. 林暐翔] |
| 第16週 | 6/8 | Invited talk [Dr. 陳昇宏] |
補課資訊
| 編號 | 補課日期 | 補課開始時間 | 補課結束時間 | 補課地點或方式 |
成績評量方式
| 編號 | 項目 | 百分比 | 說明 |
| 1 | Assignment | 80% | |
| 2 | Invited talk participation | 10% | |
| 3 | Attendance | 10% |
針對學生困難提供學生調整方式
| 調整方式 | |
| 上課形式 | 以錄影輔助 |
| 作業繳交形式 | 學生與授課老師協議改以其他形式呈現 |
| 考試形式 | |
| 其他 | 由師生雙方議定 |
面談時間
| 備註 | Please email corresponding professors to arrange office hours |