Tracy, Craig A. 2016. Lectures on Differential Equations.
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Author: Tracy, Craig A.
Title: Lectures on Differential Equations.
Date of Publication: 2016
Location: https://www.math.ucdavis.edu/~tracy/courses/math22B/22BBook.pdf
Accessed 16 August 2016.
Craig A. Tracy, Distinguished Professor of Mathematics, University of California Davis, has produced a beautiful book with theory and very instructive derivations of physical models with differential equations, both classical and modern.
The complete 173 page pdf download can be found at PROF Tracy’s course page: https://www.math.ucdavis.edu/~tracy/courses/math22B/math22B.html. Once there click on Lectures on Differential Equations .
This is a set of lecture notes which could serve as a text book in a differential equations course, certainly as a good resource on specific coverages. The text is interlaced with Mathematica and MatLab code for modest command activities. After a topic is introduced almost immediately an application is introduced, e.g., interest accounts after integrating factors. This is followed by conservative system approach to mechanics and Total Energy conservation. The exercise sets are rich applications of the differential equations under study and will pull students further into the use of methods to solve interesting problems.
Difference equations are used to model physical phenomena such as a weighted string to produce the wave equation and the heat equation, while rich and deep detail is offered in quantum harmonic oscillator study.
Along the way many basic fundamental identities are established and used to support theory and furtherance of the applications.
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