Book recommendation on a variety of topics

In summary, Jason is looking for books that will help him learn physics concepts in a way that he can understand, and that will also provide applications to problems. He recommends the book "Students Guide to Vectors and Tensors" and the book "Nonlinear Dynamics and Chaos" by Strogatz.
  • #1
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
 
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  • #2
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
 
  • #3
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.
 
  • #4
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
 
  • #5
for your request for book recommendations. I understand the importance of finding resources that help us truly understand and apply concepts, rather than just memorizing them. I have a few recommendations that may fit your criteria.

For matrices and their applications, I would suggest "Linear Algebra and Its Applications" by David C. Lay. This book provides a good balance between theory and applications, with many real-world examples and exercises to help you understand and apply the concepts. It also includes helpful visuals and step-by-step explanations.

For ODE and PDE, I would recommend "Differential Equations with Applications and Historical Notes" by George F. Simmons. This book not only covers the theory of differential equations, but also provides historical context and real-world applications. It also includes many exercises and examples to help you understand the concepts.

Another resource that may be helpful for you is the "For Dummies" series. They have books on various topics, including matrices and differential equations, that are written in a more approachable and easy-to-understand manner.

I hope these recommendations help you in your quest to truly understand these topics. Remember, practice and application are key to truly mastering any subject. Good luck!
 

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