Название: Mathematical Models in the Biosciences I
Автор: Michael Frame
Издательство: Yale University Press
Год: 2021
Страниц: 542
Язык: английский
Формат: pdf (true)
Размер: 14.3 MB

An award-winning professor’s introduction to essential concepts of calculus and mathematical modeling for students in the biosciences.

This is the first of a two-part series exploring essential concepts of calculus in the context of biological systems. Michael Frame covers essential ideas and theories of basic calculus and probability while providing examples of how they apply to subjects like chemotherapy and tumor growth, chemical diffusion, allometric scaling, predator-prey relations, and nerve impulses. Based on the author’s calculus class at Yale University, the book makes concepts of calculus more relatable for science majors and premedical students.

So far as we can tell, mathematics is universal. The substitution rule for integration works the same in physics, biology, chemistry, economics, and literature. This universality is a deep feature of mathematics, in some part responsible for Eugene Wigner’s writing on “The unreasonable effectiveness of mathematics in the natural sciences.” It leads to obvious economies: one calculus course can, and often does, serve students who intend to major in fields other than math. This book and its companion volume began as notes for two courses, second and third semester calculus - integration, infinite series, and vector calculus - for biosciences students.

This book grew out of the first of two math for biosciences courses I developed at Yale. Along the way we develop some other mathematics useful in biosciences but not often seen in calculus classes. Many of these phenomena can be modeled, at least in broad strokes, with differential equations. Some of these, called pure-time equations, can be solved by integration.