Tenenbaum, Morris and Harry Pollard. 1985. Ordinary Differential Equations: An Elementary Textbook for Students in Mathematics, Engineering, and the Sciences. Dover Publications. 819 pp.
Republished in 1985. New York: Dover Publications. First published in 1963 by Harper & Row, Publishers, Inc. New York.
https://www.math.brown.edu/~mgulian/morris-tenenbaum-harry-pollard-ordinary-differential-equations-copy.pdf . Accessed 4 October 2016.
This is a monster book and all inclusive with rich examples, e.g., there is a whole chapter called “Problems leading to differential equations of first order.” It is 89 pages long and VERY rich in applications and models. These include geometric problems, dilution and accretion problems, interest problems, temperature problems, decomposition and growth, second order processes, problems of motion, pursuit models, and much more. There are also rich sets of comments interlaced in the narrative which provide reflection and motivation.
The opening essay of Lesson 1, "How Differential Equations Originated," indeed, the opening sentence of that essay says it all, "We live in a world of interrelated changing entitites."
There is also a section on “Problems giving rise to systems of equations, special types of second order linear and nonlinear equations solvable by reducing to systems” and it is 91 pages long.
As one might imagine in a text of this size there is rich coverage of the traditional differential equations topics including series solutions, Laplace Transforms, numerical methods, and existence and uniqueness proofs.
There are extensive exercises with many solutions offered and the examples in the text are worked out in great detail.
This is an encyclopedic work and could serve as a text book or resource book for a first course in differential equations.
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