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Mathematical Mechanics: From Particle to Muscle

Ellis D. Cooper
World Scientific
Publication Date: 
Number of Pages: 
World Scientific Series on Nonlinear Science, Series A 77
[Reviewed by
Tom Schulte
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On its back cover, this work purports to “offer all the details of the mathematical mechanics underlying modern modeling of skeletal muscle contraction. The aim is to provide an integrated vision of mathematics, physics, chemistry and biology for this one understanding.” This is quite an ambitious goal for under five hundred pages in an octavo-sized book. Still, while not delivering quite the grand synthesis it promises, this book has charm and scope.

The book’s breadth comes from skimming over category theory, calculus, vectors and more before dealing with applications such as particle mechanics, chemistry, and a few dozen pages of a timeline of muscle contraction research. With this applied material and in the appendices is “timing machinery”, the author’s model for stochastic nonlinear systems, which he has implemented in Matlab.

The author is a retired high school teacher and Mathematical Mechanics is aimed at AP-level high school calculus students and their teachers. The author also hopes to reach undergraduates researchers. It cannot be said that the author succeeds entirely in reaching such a wide audience while covering such a constellation of topics. But Cooper writes in a personal, wandering forward fashion that brings to mind a notebook, something like a scientific memoir. Asides, favorite quotations and improvements to proofs and theorems give the text that flavor and make it something that can be dipped into by the enthusiast at any point.

Tom Schulte ushers minds from high school to university at Oakland Community College in Michigan.

  • Introduction
  • Ground & Foundation of Mathematics
  • Calculus as an Algebra of Infinitesimals
  • Algebra of Vectors
  • Particle Universe
  • Introduction to Timing Machinery
  • Stochastic Timing Machinery
  • Algebraic Thermodynamics
  • Clausius, Gibbs & Duhem
  • Experiments & Measurements
  • Chemical Reaction
  • Muscle Contraction