I've seen questions on what are some good differential equations textbook and people generally points to Ordinary Differential Equations by Morris Tenenbaum and Harry Pollard and so on

I was wondering if there are any free (GNU free documentation license, CC, or alike) textbooks on the subject. A good example, but not for differential equations, is http://joshua.smcvt.edu/linearalgebra/

Disclaimer: I'm a student currently taking a course (and our textbook is quite frankly.. very badly written) on the subject and actually need to cover the following topics:

  • First order equations
  • Second order equations
  • Linear systems. Homogeneous linear systems
  • Sequences, series and convergence.
  • Fourier series

But it looks like I'm gonna have to do a majority of this on my own.


I think a number of people have been in a very similar situation to you, in a course on differential equations or otherwise, and have looked for an alternate source for the material. I myself am very familiar with the problem.

There are a number of excellent textbooks on the subject that sell for less that $15, my personal favorite of which is Tenenbaum/Pollard, but this opinion is obviously not objective and you, along with a number of other answeres seem to find significant faults with their development of the subject.

I will list some other possible inexpensive or free resources that I am at least mildly familiar with:

  • Agnew's Differential Equations is an old book that treats the subject very classically in a way similar to Tenenbaum/Pollard. One of the greatest aspecsts of this book is its index, which is quite extensive. It relies heavily on physical applications. And you can get it for less than \$5 from Amazon including shipping. This is not a particularly famous choice, as I purchased a copy at a local used bookstore for \$1 but it is nonetheless excellent.
  • MIT OCW 18.03 course, as others have pointed out, is a complete set of lectures, notes, and problem sets that would basically make up a course if you were to take from a spectacular lecturer. I would not reccommend buying the textbook suggested on the syllabus page, however. The supplemental notes from what I remember are excellent.
  • Paul's Math Notes have a set of lecture notes on differential equations that cover all of the topics you are asking for. I have never read these, although I've seen them refrenced quite frequently and they are considered excellent from what I have seen.
  • Google site:.edu filetype:.pdf. Google is an incredible tool, and is far more extensive that most people imagine. They have a number of operators that refine your search, and their engine is so powerful that there is an entire area of computer security devoted to using google to hack websites. By using the operators site:edu and filetype:pdf we restrict our search to .pdf files from academic institutions. By selecting a query such as "Bernoulli equations" with the operators described (i.e., type "Bernoulli equations" site:edu filetype:pdf into the google search bar) you will recieve a plethora of lecture notes and descriptions of whatever topic you are looking for. Read one, read 5, read 1000. By reading the lecture notes of many different lecturers you can grasp a topic from a number of different viewpoints and methods of development simultaneously, and this provides an excellent supplement to your course and or any of the resources I described above.

I wish you luck with your course. Have fun learning.

  • $\begingroup$ Accepted as the most comprehensive post here. However it is a shame that there is not GNU FDL books on differential equations. $\endgroup$ – Pwnna Jan 31 '13 at 1:31

I like Martin Braun's book Differential Equations and Their Applications: An Introduction to Applied Mathematics. There are several editions of this book, and you can find one of them used for 1-2 bucks on amazon (plus shipping). This textbook is a very standard course in ODE with a lot of applications. The author takes his time to explain many important concepts and gives plenty of examples. All the topics from the first ODE course are covered. The book is self-contained and provides all the information from Linear Algebra you would need.


This is not a textbook, but (maybe better) a video lecture series from MIT about Differential Equations: http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/

It's about First-order differential equations, Second-order linear equations, Fourier series, First order systems

Enjoy :-)


Take a look a Trillia's list of online math resources, they list several. Check MIT's open courseware, they have hundreds of courses online, many with complete lecture notes and plenty of old exams and homework. Coursera seems to have nothing right now, but I'd check back later.

Get some computer algebra program (I like maxima, but there are many others; Wolfram Alpha can be used through the web). They know more of analytical solutions than you'll ever learn, and that helps in checking your work.


You might look at some old course notes of mine: http://www.math.ubc.ca/~israel/m215/m215s02.html


I actually don't like Tenenbaum & Pollard. The subject may be classic, but the book is showing its age.

  1. Goes from 1st order directly to nth order. Most modern books (correctly) emphasize the 2nd order equations much more.

  2. The Laplace transform section does not cover discontinuous and impulsive sources, which are some of the primary reasons to use the Laplace transform. (Well, it seems you don't need the Laplace transform at all.)

  3. Is very long and interspersed with tangentially related material. Its practical use requires skipping of sections or parts of sections (hence, knowing what can be skipped).

Although not free, McOwen's book sells for $10. I like its modern approach to the subject and the concise style of writing (although I can imagine that being a drawback for self-study). It does not cover series and Fourier series in particular.

But since what you really need is a supplement to the course that already has a textbook, MIT videos may be just the right kind of resource.

  • $\begingroup$ The wording of the book I'm suppose to have is terribly in concise and convoluted (looks to be self published). That's why I'm looking for a more professional and reviewed one. $\endgroup$ – Pwnna Jan 16 '13 at 16:06

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