I’m studying differential equations (specifically Laplace Transforms) right now with my college assigned ‘Differential Equations with Application and Historical Notes’-George F Simmons. While I like the text, I’m not a big fan of the fact that there are not many solved examples and a solution manual isn’t available.
Can you guys suggest a decent book with a good range of questions (easy as well as difficult) which most importantly, has a solution manual available to refer to, after I’ve dwelled on a question for hours and still haven’t figured it out.
For a text with a solution manual: See P. Blanchard, R. L. Devaney, G. R. Hall, Differential Equations, 4th Ed., 2011.
Another, less expensive choice (“cheap” compared to most textbooks), is Ordinary Differential Equations, from Dover Books on Mathematics collection. The book has received great reviews, and includes solutions to most of the exercises.
For another “cheap” reference, see Schaum’s Outline of Differential Equations, 3Ed. The link will take you to Amazon.com where you can “preview” the book, it’s table of contents, etc..
The following are not “text books” in the usual sense of the term, but
Paul’s Online Notes may help elucidate some of the concepts you’re struggling with, and includes many worked examples, with solutions.
See also Khan Academy: Differential Equations, where you can access tutorials, and accompanying exercises with solutions.
Another book is Elementary Differential Equations @ http://www.amazon.com/Elementary-Differential-Equations-William-Boyce/dp/0470458321/ref=dp_ob_title_bk/177-7352718-7974048. It has a student’s solution manual and an instructor’s solution manual.