A clear, practical refresher of core engineering mathematics.
Chapter 1
Preliminaries
1.1 Number Systems: The Integers, Rationals and Reals
Calculus is a part of the mathematics of the real numbers. You
will probably be used to the idea of real numbers, as numbers on
a “line” and working with graphs of real functions in the product
of two lines, i.e. a plane. To define rigorously what real numbers
are is not a trivial matter. Here we will mention two important
• Refresh key techniques in algebra, functions, and calculus quickly
• Gain clarity on topics often seen as difficult, like differentiation
• Build essential linear algebra tools for multivariate work
• Learn core methods for integration, series, ODEs, and complex functions
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