I am looking for a text that gives a good exposition of power series solutions to second order equations with variable coefficients. My course I'm guessing focuses mainly on this section. My knowledge of power series and Taylor series is not great. But I'm in the process of rectifying this. In the meantime I need a text that puts emphasis on this section. Most of what I've come across focuses on systems of equations. Any help would be appreciated. This here is my entire syllabus.

Differential Equations II (30L, 2C)

Syllabus:Ordinary differential equations: Linear equations of the second order where the coefficients are functions of the independent variable; Ordinary points; Singular points; Regular singular points;Solution in series: Stability of the solutions; Solution of Laplace’s equation; Revision of Euler’s homogeneous form of the second order ordinary differential equations; Legendre’s equation; Legendre’s polynomials – their linear independence and recurrence relations; Bessel’s function.Introduction to Difference equations: Complementary functions and particular solutions. Assessment: End of semester examination.

  • $\begingroup$ @Amzoti: Exam focuses mainly on the applications. But I would prefer a text which covers theory well too. Would appreciate any recommendation actually. I'll check them out. $\endgroup$ – Ishfaaq Mar 20 '14 at 0:38

Here are some inexpensive books that you can peruse online:

  • Theory and problems: Ordinary Differential Equations, M. Tenenbaum, H. Pollard
  • Problems (Ch 15, excellent): 2500 Solved Problems in Differential Equations , R. Bronson
  • Problems: Golden Maths Series, Differential Equations, N.P. Bali

Some other helpful notes:

I would definitely search more of these out as they are free and can give you more problems.

You can also check out some of the online materials like at MIT Opencourseware and others like that.

Lastly, my best recommendation on these problems (given students typically have issues with these) is to do problems, problems, and more problems with practice, practice and then some more practice!

  • $\begingroup$ Thanks loads for the notes and the advice. I'll definitely check out the books too. $\endgroup$ – Ishfaaq Mar 20 '14 at 0:57
  • $\begingroup$ I forgot to mention that there are also books on this topic, like: Asymptotic Expansions for Ordinary Differential Equations By Wolfgang Wasow . Regards $\endgroup$ – Amzoti Mar 20 '14 at 1:01

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