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.
Best Answer
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:
"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.