Book recommendation on a variety of topics

[Steve Drake]

Hi Guys,

I am after recommendations of books that teach in a specific way. Basically I have come out of a 3 year physics degree with just doing the work but not really understanding the material (the mathematics) that well.

I want to re-learn a bunch of topics in a way so I will actually understand them. The kind of books I am after are like the Students guide to vectors and tensors. It literally breaks the topics down and holds your hand every step of the way. This is the only way I can learn. I have learned more about vectors in 10 pages of this book than my entire undergrad maths course.

I also need a lot of applications of things being taught. I can't just read something as it is and understand the point unless I see it applied to a problem. Basically most books start with a proof or the definition and that stuff just blows over me. I am more after the physical Meaning of what these functions / operations / do.

That being said, does anyone have any books they've come across that teach in such a way? I am mainly after topics such as matrices and their uses to real problems. Formulating problems into matrix algebra and solving them. And books on ODE and PDE.

Thanks

 

[jasonRF]

I am not familiar with the book you cite so I am not sure if I am on the right track, but for a nice application-oriented presentation of linear algebra, I really like:
https://www.amazon.com/dp/0155510053/?tag=pfamazon01-20
It is a standard book used by engineers, and include lots of applications to help motivate why you should care. Cheap used editions are available; I am only familiar with the 3rd edition.

The same author also has an "introduction to linear algebra" book (that is perhaps more popular than the one I listed) that goes along with lectures you can find on ocw.mit.edu, but I am not familiar with it.

The easiest book on PDEs is the book by Farlow. period.
https://www.amazon.com/dp/048667620X/?tag=pfamazon01-20

I don't really know any ODE books that have any hope of fitting the bill - I cannot think of any that aren't uninspiring. But I am no expert. One really FUN book that you might like as a physicist is "nonlinear dynamics and chaos" by Strogatz.

Don't forget free books. The math methods book by Nearing looks good to me:
http://www.physics.miami.edu/~nearing/mathmethods/



jason

 

[Daverz]

I recommend the math methods book by Boas. Used copies of the 2nd edition go for reasonable prices:

https://www.amazon.com/dp/0471044091/?tag=pfamazon01-20

Otherwise, working through a good QM or EM book can exercise your mathematical skills pretty well.

 

[Steve Drake]

Hi Guys,

Thanks a lot for your responses. I will see if my Uni library has these books and have a flip through them. I can detect pretty quickly weather I will learn anything from a book, but these look good. That PDE book looks like a gem also. The key of 'what does it mean physically' really allows me to fully grasp a theory.

Random side note but I am working through a PhD and couldn't for the life of me grasp a certain concept. I found a book that had a simple graphical illustration of what it means, and it instantly made me understand it. I hope some of these books have that 'eureka' moment.

Thanks again