The discussion revolves around the preparation for a Differential Equations course, particularly focusing on the foundational knowledge of series from Calculus 2. Participants express concerns about their understanding of series and its application in solving ordinary differential equations (ODEs), while seeking advice on what material to prioritize and supplemental resources to consider.
Participants do not reach a consensus on the relative importance of series versus integration techniques in the context of ODEs. There are competing views on the necessity of linear algebra knowledge, and some participants express uncertainty about the course content and its focus.
Limitations include varying levels of preparedness among participants and differing experiences with ODEs, particularly regarding the use of power series and the types of coefficients encountered in their courses.
Students preparing for Differential Equations courses, particularly those with a weak foundation in series or integration techniques, may find this discussion relevant.
PhotonSSBM said:My series foundation is really weak, and this spring I'll be taking Differential Equations. I know series plays a big role in solving some ODEs, so I'll be re-learning the material from Calc 2 to make sure I'm up to par for the class. I'll be working through Stewart's chapter on series but was wondering what I should prioritize and if maybe I could leave some stuff out. Any supplemental material suggestions would be appreciated.
What do you mean to be non-linear? The ODE or the series? And in the latter case, what do you mean by that?Remixex said:ODEs that solve with power series (which are non-linear, i believe) are not something of interest in many Differential Equations courses.
"God made the integers, all else is the work of man." (L. Kronecker)Remixex said:god damn differential equation
Exactly, we only saw constant coefficients, so i wouldn't know about that (the only non-constant coefficient I've seen is an Euler equation)Krylov said:Power series solutions for linear ODE with non-constant coefficients
Thanks for the useful post. My integration skills are sharp from doing complicated double and triple integrals all semester. So I should be fine there.MidgetDwarf said:Hmm, my understanding of ODE intro courses, is that they are recipe courses in general.
You will have to know how to add Summations, whether or not the series converges, radius and interval of converges ,and taylor series expansion about x=0 (McLaurian Series) of the basic functions.
They where all covered in my ODE textbook. However, depending on the rigor of the problems, you may need to review a Calculus 2 book (writing the terms of a series in summation notation).
What i would focus on more is on integration techniques. I would recommend and older edition of Zill. It is a very cook-book, however you can supplement it with say, Coddington. I purchased an older edition for 5 bucks. I swear, that my 8th ed with modeling functions is the same as the newer 8th ed with boundary problems. The difference in price was 120 dollars.
The class doesn't require it as a prerequisite. But on the off chance it comes up what areas of LA will be important?micromass said:Depending on the class, you might want to review some linear algebra too. Maybe the class won't require it though.
PhotonSSBM said:The class doesn't require it as a prerequisite. But on the off chance it comes up what areas of LA will be important?
Cool. I'm good on all those fronts so even if it comes up I'll be ok. Thanks :Dmicromass said:It really depends on the course. But LA will be important if you study linear systems of linear equations, and linear equations of higher order. What is important there are determinant, linear dependence, vector spaces, subspaces. Those will get you pretty far. But if LA is not a requirement, then this will probably not be covered.