Calculus Books on waves, ODE, PDE and calculus

[chiraganand]

Hi,

I am looking for good books with somewhat of an intuitive explanation on waves physics (acoustic waves), elastic waves, on ODEs, PDEs, and calculus? Also some good ones on DSP

Thanks in advance

Chirag

 

[micromass]

1) DSP?
2) What is your current background? High school student, college physics student? Retired veteran?
3) What is your current knowledge in math? Please be detailed and make a comprehensive list.
4) Have you tried calculus before? Did you struggle?
5) What are your future plans? Engineering? Math? Starting a rock band?

 

[The Bill]

1) DSP?

In this context, I think DSP stands for digital signal processing.

 

[Ssnow]

For the basic on the wave equation I suggest: " Partial Differential Equations '', Evans, AMS 19

 

[Frimus]

The Physics of Waves by Howard Georgi. It's a free downloadable textbook

 

[chiraganand]

1) DSP?
2) What is your current background? High school student, college physics student? Retired veteran?
3) What is your current knowledge in math? Please be detailed and make a comprehensive list.
4) Have you tried calculus before? Did you struggle?
5) What are your future plans? Engineering? Math? Starting a rock band?

1) digital Signal Processing
2) Engineering graduate
3) Basically need books to brush up my math skills in calculus, differential equations and linear algebra. I have worked with all of these before but more in a sense of working out problems in textbooks. Want to delve deeper into these. Need these math skills to understand the maths underlying acoustical imaging, wave propagagation and digital signal processing
4) Have tried calculus before. Struggled a little bit but find it tough when vectors and differential equations are combined together.
5) Background is engineering but now moving to a hybrid of engineering, physics and math

 

[The Bill]

I recommend you look at Fourier Analysis by T. W. Körner. It's a very well written and reasonably thorough book on the basics of the maths behind all of those topics.

 

[micromass]

Hi,

I am looking for good books with somewhat of an intuitive explanation on waves physics (acoustic waves), elastic waves, on ODEs, PDEs, and calculus? Also some good ones on DSP

Thanks in advance

Chirag

I'm still not quite sure what you want. You're an engineering grad, right? So that should mean you know calculus. So what is it you want?

Is it that you forgot most of calculus and want to refresh everything you know?

Or is it that you have learned calculus already but not very indepth/rigorously?

 

[chiraganand]

I have learned calculus but want a little more depth..

 

[The Bill]

I have learned calculus but want a little more depth..

There are three different ways I could interpret this, and they'd each lead to different recommendations.

You could mean that you want to see the tools of calculus applied in more ways, with more explanation and expansion on applications than in a first course. A mathematical methods text like Riley, Hobson, and Bence should serve you well for that.

You could mean that you want a fuller explanation of the concepts of calculus with a focus on intuition and why each tool is used when it is used. Morris Kline's text or Kalid Azad's website and textbook Calculus Better Explained might help here.

You could mean that you want a more rigorous approach to calculus which justifies all the details of the definitions and proofs. For that, I'd recommend Spivak's Calculus or an undergraduate real analysis text like Hoffman's Analysis in Euclidean Space.

David Metzler's YouTube video series on analysis would probably be a good idea to watch and work through no matter which of the above apply to you:

 

[chiraganand]

Thank you all for your suggestions... I have started reading kline. I basically want to build up so that I can understand better theorems such as green's theorem, green's functions etc. In learning about elastic waves and wave propagation, acoustical imaging etc, i come across a lot of PDE's regarding vectors, stress- strain tensors etc and sometimes i am unable to understand the derivations or how the solution for the PDE was found out etc. So I assumed that if i started from the basics again, I would be better posed to understand these derivations

 

[deskswirl]

After you get through the basics and you are still interested pickup the book Green's Functions with Applications by Duffy. I've got a copy before me on my desk, the clearest explanation of Green's functions and how to find them I've seen.

 

[chiraganand]

Ok.. so I am starting of with Calculus by Morris Kline.. any ideas on how should i progress further? next would be ODEs and PDEs right?

 

[Mondayman]

Kline's book is alright, but it lacks exercises. Try to use another book for an extra source of practice problems if you can.