EAN: 9783319597300

MODELING LIFE - ALAN GARFINKEL JANE SHEVTSOV YI...

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?

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