Lecture Notes in Differential Equations - Bruce E. Shapiro

418 BIBLIOGRAPHY
1950’s. Take at least an undergraduate class in analysis before you
attempt to read this.
[7] Courant, Richard and John, Fritz. Introduction to Calculus and Analysis
(Two volumes). Wiley (1974). (Reprint of an earlier edition). This
is a standard advanced text on calculus and its included here because it
has a good description (including proofs) of many of the basic theorems
mentioned here. Includes a good description of the implicit function
theorem that is usually left out of introductory calculus texts.
[8] Driver, Rodney D. Introduction to Ordinary Differential Equations.
Harper and Row (1978). Introductory text on differential equations.
Has understandable descriptions of the existence and uniqueness theorems.
[9] Edwards, C. Henry and Penney, David E. Elementary Differential
Equations. Sixth Edition. Prentice Hall (2007). One of the standard
introductory texts, like [2] and [12]. Also has a longer version that
includes boundary value problems.
[10] Gray, Alfred, Mezzino, Michael, and Pinsky, Mark A. Introduction
to Ordinary Differential Equations with Mathematica. An Integrated
Multimedia Approach. Springer. (1997) Another excellent introduction
to differential equations at the same level as [2], integrated with an
introduction to Mathematica. Problem is, Mathematica has moved on
to a higher version. Oh well, you just can’t keep up with technology.
Should’ve written the book in Python, I guess.
[11] Hurewitz, Witold. Lectures on Ordinary Differential Equations. Dover
Books. (1990) Reprint of MIT Press 1958 Edition. Very thin paperback
introducing the theory of differential equations. For advanced undergraduates;
a bit more difficult than [5]. A lot of value for the buck.
[12] Zill, Dennis G. A First Course in Differential Equations With Modeling
Applications. 9th Edition. Brooks/Cole. (2009) Another multi-edition
over-priced standard text. Comes in many different versions and formats
and has been updated several times. Same level as [2] and [9]. The
publisher also recognizes that it stopped getting any better after the
5th Edition and still sells a version called ‘The Classic Fifth Edition.
There’s also a version (co-authored with Michael Cullen) that includes
chapters on Boundary Value Problems.