Modeling Life: The Mathematics of Biological Systems
暫譯: 生命建模：生物系統的數學
Garfinkel, Alan, Shevtsov, Jane, Guo, Yina
- 出版商: Springer
- 出版日期: 2018-08-14
- 售價: $2,490
- 貴賓價: 9.5 折 $2,366
- 語言: 英文
- 頁數: 445
- 裝訂: Quality Paper - also called trade paper
- ISBN: 3319866893
- ISBN-13: 9783319866895
海外代購書籍(需單獨結帳)
相關主題
商品描述
This book develops the mathematical tools essential for students in the life sciences to describe interacting systems and predict their behavior. From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions.
Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler's method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking.
Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?
商品描述(中文翻譯)
這本書發展了生命科學學生所需的數學工具，以描述互動系統並預測其行為。從生態系統中的捕食者與獵物族群，到體內的荷爾蒙調節，自然界充滿了深刻影響我們的動態系統。複雜的反饋關係和反直覺的反應在自然界中很常見；這本書發展了探索這些互動所需的定量技能。
微分方程是量化變化的自然數學工具，也是本書的主要驅動力。使用歐拉法（Euler's method）使非線性範例變得可處理且易於接觸，適合廣泛的初學者，因此提供了一種實用的替代方案，取代傳統微積分課程的程序性方法。本書在眾多相關範例中發展工具，強調數學模型的構建、評估和解釋。在具體情境中接觸這些概念，學生不僅學習定量技術，還學會如何在生物學和數學思維之間架起橋樑。
範例範圍廣泛，探索神經元和免疫系統的動態，直到族群動態和 Google PageRank 演算法。每個情境僅依賴於對自然界的興趣；不假設學生或講師具備生物學專業知識。本書以預備微積分（Precalculus）為唯一前提，適合一、二年級本科生的兩學期課程，並滿足醫學院入學的數學要求。後面的材料為數學和生命科學的高年級學生提供了在豐富的現實框架中重新審視理論知識的機會。在所有情況下，重點都很明確：數學如何幫助我們理解科學？
作者簡介
Alan Garfinkel received his undergraduate degree from Cornell in Mathematics and Philosophy, and a PhD from Harvard in Philosophy and Mathematics. After some years of practicing philosophy of science, Garfinkel transitioned to medical research, applying qualitative dynamics to phenomena in medicine and physiology. Along with James Weiss and Zhilin Qu, he studies cardiac arrhythmias from the point of view of nonlinear dynamics.
Jane Shevtsov earned her BS in Ecology, Behavior and Evolution from UCLA, and her PhD in Ecology from the University of Georgia. Her main research interests lie in mathematical models of food webs and ecosystems.
Yina Guo received her PhD from Nankai University in Control Engineering. Her PhD thesis used partial differential equations to explain the branching structure of the lung. Her computer simulations of branching processes were featured on the cover of the Journal of Physiology. She is particularly interested in the use of graphics and visualization techniques in both research and teaching.
作者簡介(中文翻譯)
艾倫·加芬克爾（Alan Garfinkel）在康奈爾大學獲得數學和哲學的學士學位，並在哈佛大學獲得哲學和數學的博士學位。在從事科學哲學的幾年後，加芬克爾轉向醫學研究，將定性動力學應用於醫學和生理學現象。與詹姆斯·韋斯（James Weiss）和曲志林（Zhilin Qu）一起，他從非線性動力學的角度研究心臟心律不整。
簡·謝夫佐夫（Jane Shevtsov）在加州大學洛杉磯分校（UCLA）獲得生態學、行為學和進化論的學士學位，並在喬治亞大學獲得生態學的博士學位。她的主要研究興趣在於食物網和生態系統的數學模型。
郭怡娜（Yina Guo）在南開大學獲得控制工程的博士學位。她的博士論文使用偏微分方程解釋肺部的分支結構。她對分支過程的計算機模擬曾登上《生理學雜誌》的封面。她特別對在研究和教學中使用圖形和可視化技術感興趣。
