CHAPTER 8
Multivariable Extensions
8.3 Eigenvalues and Eigenvectors
Figure 8.1 During a SARS outbreak in China in 2002–2003, children wore face masks to protect themselves. In Section 8.5, we will study models of disease outbreaks, like SARS.
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“For the things of this world cannot be made known without a knowledge of mathematics.”
Roger Bacon, Philosopher and Franciscan friar, 1214–1294. Opus Majus part 4 Distinctia Prima cap 1, 1267.
The exquisite tapestry that is our biological world arises as a result of interacting populations—whether molecules, cells, complex organisms, or groups of organisms. These interactions often create complex patterns of the kind and numbers of individuals that vary over time and space. To gain insight into these patterns that depend on more than one variable requires mathematical concepts that go well beyond what is typically covered in a first course on calculus. The analysis of multivariable models draws upon theories of general linear algebra (also known as matrix theory) and ordinary differential equations, both of which require a term of study to understand these theories in a comprehensive way. It is possible, however, to introduce these topics without invoking many results from advanced ...
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