This chapter focuses on dynamical systems, wherein the simplest nonlinear mathematical models could give rise to incredibly complex behaviour. It mentions scientists studying biological and physical processes of nature that were in the forefront of the revolution in mathematics for discovering dynamical systems. It also introduces some basic concepts of complexity theory: equilibria and stability, bifurcations, and chaos. The chapter begins with a brief snapshot of the birth of chaos theory, particularly theories of pattern formation and ecological implications. It cites the truncation error, which is another source of error in numerical methods that happens by approximating the true function by a Taylor series that is truncated after the first two or three terms.
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Extension: dynamical systems
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The respiratory system
This chapter details the principal role of the respiratory system, which is to provide an exchange of gases between the body and the environment. It outlines the functions of the respiratory system, such as its contribution to the maintenance of plasma pH and the production of sound. It also explains how the respiratory system ensures that adequate amounts of oxygen are delivered to tissues and carbon dioxide is efficiently removed when exchanging gases in a variety of environmental challenges. The chapter talks about the paired lungs that sit inside the thorax, which are formed from a series of bifurcations of a single trachea. It details how air enters the lung by a suction pump, wherein inspiration results in an increase in volume and a decrease in pressure inside the lungs.
