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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?
Neuroprosthetics is a fast-growing area that brings together the
fields of biomedical engineering and neuroscience as a means to
interface the neural system directly to prostheses. Advancing
research and applications in this field can assist in successfully
restoring motor, sensory, and cognitive functions. Emerging Theory
and Practice in Neuroprosthetics brings together the most
up-to-date research surrounding neuroprosthetics advances and
applications. Presenting several new results, concepts, and further
developments in the area of neuroprosthetics, this book is an
essential publication for researchers, upper-level students,
engineers, and medical practitioners.
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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