This text places the basic ideas of real analysis and numerical
analysis together in an applied setting that is both accessible and
motivational to young students. The essentials of real analysis are
presented in the context of a fundamental problem of applied
mathematics, which is to approximate the solution of a physical
model. The framework of existence, uniqueness, and methods to
approximate solutions of model equations is sufficiently broad to
introduce and motivate all the basic ideas of real analysis. The
book includes background and review material, numerous examples,
visualizations and alternate explanations of some key ideas, and a
variety of exercises ranging from simple computations to analysis
and estimates to computations on a computer.
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