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Volume Two of an award-winning professor's introduction to essential concepts of calculus and mathematical modelling for students in the biosciences
This is the second of a two-part series exploring essential concepts of calculus in the context of biological systems. Building on the essential ideas and theories of basic calculus taught in Mathematical Models in the Biosciences I, this book focuses on epidemiological models, mathematical foundations of virus and antiviral dynamics, ion channel models and cardiac arrhythmias, vector calculus and applications, and evolutionary models of disease. It also develops differential equations and stochastic models of many biomedical processes, as well as virus dynamics, the Clancy-Rudy model to determine the genetic basis of cardiac arrhythmias, and a sketch of some systems biology. Based on the author's calculus class at Yale, the book makes concepts of calculus less abstract and more relatable for science majors and premedical students.
Michael Frame retired in 2016 as an adjunct professor of mathematics at Yale University. For more than twenty years Frame taught courses on fractal geometry and calculus, based on applications in biology and medicine. Amelia Urry and he are the coauthors of Fractal Worlds: Grown, Built, and Imagined.
"Clear, enthusiastic, and communicating a love of maths, this is a useful, engaging and well-written text."
– Becca Asquith, Professor of Mathematical Immunology, Imperial College London
"This is a wonderful book, wise and witty. It would have taught me most of the math I needed for my career in research – if I did all the problems."
– Stephen Stearns, author of The Evolution of Life Histories and Evolutionary Medicine
"This well-written book covers multivariate calculus and dynamical systems within the context of the biological sciences, providing well-chosen, up-to-date biomedical examples. The Markov chain, along with its many interesting applications, is also introduced."
– Hongyu He, Professor of Mathematics, Louisiana State University
