Can anyone recommend a good linear algebra/ODE book?

[Eclair_de_XII]

In particular, I would like a book that explains the theory of function spaces, linear transformations, to explain the ways one can interpret ODEs as linear transformations on function spaces. I need to read up on these for a project in my Intro to Differential Equations class. Any suggestions will be welcome. Thanks.

 

[StoneTemplePython]

You might want to take a look at:

https://math.byu.edu/~klkuttle/Linearalgebra.pdf

If you don't have some prior background in Linear Algebra it will probably be a bit much. I like that the text is free and covers a LOT of different stuff (including householder reflections and numerical / algorithmic concerns). Plus its free.

Note that on page 185 there is an exorcise that begins with "This and the following problems will present most of a differential equations course. Most of the explanations are given. You fill in any details needed..."

Also there is Appendix D (page 403) entitled "Differential Equations".

 

[Eclair_de_XII]

Thank you. The fact that it's free and in pdf form saves me much trouble, because I have all my textbooks ready on my e-reader, anyway.

 

[Supercool_ed]

I find Gilbert Strang's book to be invaluable. Still consult it from time to time, and the applications section is quite nice.

https://www.valorebooks.com/textbooks/introduction-to-linear-algebra-fourth-edition-4th-edition/9780980232714?utm_source=Froogle&utm_medium=referral&utm_campaign=Froogle&date=02/18/17

 

[bacte2013]

Hoffman/Kunze and Axler covers the basics of functional analysis and transformation in-depth. You might want to consult H/K.

 

[mpresic]

I learned linear algebra many years ago and have not been keeping up with the current books. Last week I took out Strang's book with Kai Borre, that covers linear algebra, geodesy and GPS. I found it great

 

[bacte2013]

Also by the way, you might be interested in George Simmon's book in the differential equations, which was published around 1980s or 1990s. The book has superb exposition of both ODE and PDE, both in theories and applications.

 

[mpresic]

I do not remember the edition of Simmons DE that I used. I liked it but I took it from the Simmons textbook in 1976. I really liked Simmons including the Historical Notes.

 

[bacte2013]

I do not remember the edition of Simmons DE that I used. I liked it but I took it from the Simmons textbook in 1976. I really liked Simmons including the Historical Notes.

I believe that is a correct edition. It seems that newer edition came out on the last year with more topics. He is extremely good writer (Calculus, Topology and Modern Analysis, and Precal.).

 

[Eclair_de_XII]

These are all good suggestions. So are there any books that go into detail about how differential equations can be interpreted as a linear transformation of a function space? I'm not finding anything specific about it in most of the books listed.

 

[Eclair_de_XII]

I mean I have an idea of what function spaces are, but I need some elaboration and clarification. Basically, what I'm thinking is that for example, $B=${$x^2,xe^x,x^2e^x$} forms a basis for a function space that consist of linear combinations of those three elements. Then using the differential operator $D$, I can perform a change of basis to $B'=${$2x,e^x+xe^x,2xe^x+x^2e^x$} and I guess that will be my linear transformation? So I use that operator again to form $B''=${$2,2e^x+xe^x,2e^x+4xe^x+x^2e^x$}. In conjunction, putting these three vectors in a 3-by-3 matrix will form my function space, I think? I suppose I should review my linear algebra.