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?
Kristin –
I’ve worked with this textbook and its authors at UCLA and greatly appreciate it. So many national reports and groups (AAAS, etc.) have called for better integrating math into the undergraduate biology curriculum, and now it’s finally possible with this textbook. The authors cover the math actually used by biologists, from the basics of the derivative to linear algebra, using computer programming that is easy for students to understand. They also use lots of great biology examples and give lots of great problems.
Math Customer –
It is a good reading material for modeling. The contents are well organized and there are hundereds of graphics for demonstrations, especially the chapter on Chaos, good intro. Love it.
Kendall –
This textbook is the product of a few forward-thinking professors at UCLA who recognized the need for a fundamental change in the undergraduate instruction of mathematics. I completed both courses that use this textbook, and it was the best decision I have made in my time as a student at UCLA. The textbook is well-written and accessible to a wide range of students, which I (and many of my classmates) greatly appreciated as we worked our way through the courses. I especially enjoyed the relevance of the subject material: while it builds on the basic calculus skills that we learned in high school, it focuses not on intricate theories in calculus that have little to no biological relevance, but instead on basic calculus topics, such as the derivative, and explains the use of those fundamental calculus concepts as they relate to mathematical modeling in the field of biology. The textbook makes clear the fascinating connection between mathematics and biology as it leads students through the basics of population dynamics and modeling systems. The professors who wrote this textbook are now teaching the course series at UCLA, and it is evident from their writing that they are passionate and excited about sharing their expertise in this field with as many students as possible. I can’t say enough good things about this textbook and its authors – they have already influenced my undergraduate experience at UCLA and introduced me to a highly relevant area of study of which I was completely unaware before I arrived at UCLA. I would highly recommend this textbook to anyone who is interested in mathematics or biology as an interesting and engaging introduction to how intricately related the two fields actually are today. Great textbook!
Daniel –
Alan Garfinkel is my spirit animal.
Pamela T –
Great book, very detailed and informative
Ali Ersan –
Anyone leaving a 1 or 2 star review is a butt hurt math major/professor stuck in the 20th century. This is a phenomenal textbook that is made for students that are interested in biology who despise math. The content of the textbook will provide its readers with the tools required to understand and experiment with modern biology.
Anon –
This book is great! It is wayyy better than your traditional college calculus book because this book shows how calculus is applied in science and the real world. It shows that there is more to math than just memorizing formulas and plugging numbers in. The first half of the book reflects the LS30A course taught by the legend: Alan Garfinkel. Specifically, it talks about the concept of feedback in biological systems and how that is observed in mathematics through equilibrium points, bifurcation diagrams, and simple calculus concepts (derivatives, fundamental theorem of calculus, etc). The book ties all of this together in depth. This is the 21st century, it is time for students to be taught how mathematics actually works in real life instead of leaving them thinking “When will I ever need to solve for x?” Next time somebody asks me, “When will I ever need to know how to solve for x?” I will say, “To solve for equilibrium points in a differential equation, find their stability, and use that to plot, and find, the behavior of that system in state space.” Then I will shove this book in their face. Overall, the concepts and explanations in the book were simple and easy to follow. Anybody who hates on this book is a CLOWN stuck in the 20th century, period. MATH ISN’T ALL ABOUT FINDING PROOFS AND MEMORIZING FORMULAS! Dr. Garfinkel is really out here changing people’s perspective about math.Thank you Dr. Garfinkel for creating this book and for explaining how math can be applied in science. If it wasn’t for you people would still be programmed to think like a robot when it comes to solving math equations.
Math Customer –
This book is extremely helpful and well written with examples and questions meant to expand your understanding of the course materials. I would 100% recommend this book to any student taking LS 30A or LS 30B at UCLA or an equivalent class at other universities. Dr. Garfinkel and his co-authors put together a book that explains concepts well through the use of both understandable mathematical vocabulary and a plethora of diagrams. Garfinkel is an amazing professor who isn’t afraid to disprove the very basic underlying concepts of other classes unlike other professors who commented bad reviews of this textbook rather than focusing on their own course. Hope you enjoy your class and that this review helps!
Sergei G. –
The book is great, but there are a lot of practice questions there and no answers. So, it’s hard to check if you are correct.
EZ –
This is great book and highly recommended to those who research math models of life
Steve –
Great Textbook
Joey ooi –
What a great introduction to the subject. The guidance throughout the book is simply very crystal clear. On top of that there are videos on youtube by the author( search Alan Garfinkel ) makes a wonderful companion to this introductory text. Covers many areas including gene expression, heart arrhythmias , neuro excitations, etc and the list goes on…. the bio and the math are explained is with great clarity.
As a retired EE who has an ongoing interest in the subject of modeling “living systems” and complexity this text and the videos was all that I needed to get going. The biology explaination is high level enough for me as a non- life science person as not to get mired down into the depths of microbiology.
Although the math was simple ( author develops most concepts from ground up) enough for me the application was an eye-opener altogether.
As an intro text, the subject of spatial / partial diff equations applications are not covered here.
The topics of eigenvalues and eigenvectors are much better explained than any of the math and engineering books that I am familiar with !!
The only thing I wished the authors who have provided solutions to the exercises (many of them) to help check understanding.
Jorge Luis –
El libro es muy bueno, y te va enseñando gradualmente a modelar. Muchos ejemplos y ejercicios. Un buen libro.
Book Reader –
Taking calculus without understanding how it is to be applied can be torture.
With this book there are so many moments of this is so cool.
I want to learn more about math so that I can apply it and better understand biology.
With this book, calculus and linear algebra become a part of biology. (As opposed to math being a totally different unrelated subject.)
Roya –
It is highly recommended to biologist who entered the computational fields.
Rebecca N. –
I was a little hesitant to buy this because shipping was estimated to be ~2 weeks. The book arrived over a week early and was in perfect condition. It was described as very good but literally looks almost brand new. This was a reasonable price for a book I needed for my Mathematics for Life Sciences college class. Super happy with this purchase and would recommend!
Didier13 –
Livre arrivé avant la date prévue et avec un excellent état ( mieux que le descriptif)
Brandon B. –
This is the best book I’ve purchased over the past few years. This book asssumes nothing more than high school math and teaches not only some fascinating biological principles, but teaches you the foundational skills of differential equation modeling (which are mathematical models describing the behavior or dynamics of a system). You can take these skills and apply them to biology problems like this book does, but the same skills are useful in a wide array of contexts outside of biology, so this is just a great book to learn differential equations from even if you have no interest in biology. It’s absolutely outstanding. And there are some YouTube lectures that correspond to the book as well that make it even more approachable. This is a rare gem of an educational book.