This text serves as the companion text to Introductory Engineering Mathematics, which introduces common mathematical concepts we see in engineering, including trigonometry, calculus, and functions. This text assumes a level of mathematics of a high school senior, plus some elements from the introductory text. Additional concepts we see in engineering are also introduced: specifically, matrices, differential equations, and some introduction to series. The concepts are introduced by examples rather than strict mathematical derivation. As a result, this text likely will not be an effective substitute for a differential equations course, but by illustrating the implementation of differential equations, it can be a companion to such a course. We primarily use historical events as examples (including failures) to illustrate the use of mathematics in engineering and the intersection of the disciplines. We hope you develop an appreciation for how to apply these concepts, and find a new lens through which to view engineering successes (and failures).

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Ohio Northern University

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