Mathematical methods for physics and engineering-Reviews/Suggestions

In summary, the conversation is about a person asking for recommendations on a comprehensive book on mathematics that they can use from the beginning of their undergraduate physics studies until the end. They also ask for suggestions on other texts that could help with understanding physics concepts. The other person suggests looking at a textbook authored by Orodruin and mentions that it may be more geared towards upper-division studies. They also recommend looking at the Riley book, but mention that it may be too broad and not as intuitive or physical as the Orodruin textbook. The person also suggests checking out other classic texts for more advanced topics.
  • #1
warhammer
151
31
Hi,

I was told by someone to go for the above mentioned book (authored by Riley and a couple of other authors). I need a definitive tour de mathematica- something that I could use for the beginning of my Physics UG until the end of it (or even further if such a book exists!). Also, something that would help me explain nagging concepts in a great manner. Therefore, I would like to seek out your reviews/opinions/suggestions about the quality of the book and is it worth investing in (if not, then please feel free to suggest any other texts even if it doesn't explicitly match my criteria and could be used for the solid mathematical foundation necessary for a great understanding of Physics).
 
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  • #2
warhammer said:
I need a definitive tour de mathematica- something that I could use for the beginning of my Physics UG until the end of it (or even further if such a book exists!). Also, something that would help me explain nagging concepts in a great manner.
That's probably too broad of a range of your studies to try to find one book that will cover it all, IMO. You might be able to cover it with 2-3 books as adjuncts to your university texts, but I'm not sure.

I'll suggest that you look at this very useful textbook by our own @Orodruin -- I like it a lot, but it is geared more toward upper-division and beyond:

https://www.physicsforums.com/insights/the-birth-of-a-textbook/
https://www.amazon.com/dp/1138056901/?tag=pfamazon01-20

1567458602856.png
 
  • #3
berkeman said:
That's probably too broad of a range of your studies to try to find one book that will cover it all, IMO. You might be able to cover it with 2-3 books as adjuncts to your university texts, but I'm not sure.

I'll suggest that you look at this very useful textbook by our own @Orodruin -- I like it a lot, but it is geared more toward upper-division and beyond:

https://www.physicsforums.com/insights/the-birth-of-a-textbook/
https://www.amazon.com/dp/1138056901/?tag=pfamazon01-20

View attachment 249038
Thanks for your response. I will definitely check out this book. What is your opinion however about the book I mentioned if you have used it?
 
  • #4
BTW, the good thing about the textbook that I suggested is that it is something that you can grow into, and it will provide motivation for you as you are studying in your math classes at university. You can tell by looking ahead in the book what you will be learning in the next couple of years, and that should help to motivate you to want to learn those subjects.

I've mentioned here before on the PF how I always enjoyed buying my textbooks for the new semester at school -- I would stand in the bookstore and flip through the textbooks in my pile, and get very excited about the math and physics and engineering that I would be learning (and understanding) in the coming months.

Enjoy the ride! :smile:
 
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  • #5
warhammer said:
What is your opinion however about the book I mentioned if you have used it?

I have not used the Riley book. I did have one other book that I used after undergrad and for review for my work after I finished graduate school, but found it to be a bit more non-intuitive and non-physical than I preferred (I don't remember the author).

By using the Amazon "Look Inside" feature and looking through the Table of Contents of the Riley text, it looks pretty basic but it does look like it bridges into upper division undergraduate subjects fairly well. The important thing for me would be whether it uses practical real-world problems to illustrate all of the important concepts. That's what I like so much about the Blennow textbook. Have you looked through the Riley text at your university library yet?

https://www.amazon.com/dp/0521679710/?tag=pfamazon01-20

1567459774523.png
 
  • #6
The three standard broad-coverage texts are those by Boas, Riley and Arfken. (I used Arfken in grad school so it might be more advanced.) Each has admirers and detractors, so you can go to your university library and compare them to see which suits your tastes. Note that these strive to cover "all" of the methods of mathematical physics, so they tend to be terse and summary rather than offering derivations and deep explanations. For more advanced treatments (since you asked about "beyond"), classics include Courant and Hilbert, Whittaker and Watson, and the two-volume set by Morse and Feshbach.

To supplement one of the general texts above for a more pedantic approach to a specific topic, Dover has inexpensive texts on virtually every mathematical topic. As one example: Lebedev's Special Functions gives a comprehensive treatment of orthogonal functions and expansions with physics examples.
 
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  • #7
berkeman said:
I have not used the Riley book. I did have one other book that I used after undergrad and for review for my work after I finished graduate school, but found it to be a bit more non-intuitive and non-physical than I preferred (I don't remember the author).

By using the Amazon "Look Inside" feature and looking through the Table of Contents of the Riley text, it looks pretty basic but it does look like it bridges into upper division undergraduate subjects fairly well. The important thing for me would be whether it uses practical real-world problems to illustrate all of the important concepts. That's what I like so much about the Blennow textbook. Have you looked through the Riley text at your university library yet?

https://www.amazon.com/dp/0521679710/?tag=pfamazon01-20

View attachment 249041
No, I haven't yet checked it out for my uni library is pretty average. To be honest, I found Prof. Blennow's book really great after viewing a sample on Amazon but the book is way way beyond the budget of a middle class student in India (e-book costs about 5000 INR while the paperback is around 5500 INR). This why I was asking if the Riley one had been used by you so that you could provide me a picture of how good or bad the book is. Do you have any other recommendations?
 

Related to Mathematical methods for physics and engineering-Reviews/Suggestions

1. What are the main mathematical methods used in physics and engineering?

The main mathematical methods used in physics and engineering include calculus, linear algebra, differential equations, and complex analysis. These methods are used to model and solve problems in various areas such as mechanics, electromagnetism, thermodynamics, and quantum mechanics.

2. How important is a strong foundation in mathematics for studying physics and engineering?

A strong foundation in mathematics is essential for studying physics and engineering. These fields rely heavily on mathematical concepts and equations to describe and understand the physical world. Without a solid understanding of mathematical methods, it can be difficult to fully grasp the principles and theories in physics and engineering.

3. Are there any specific mathematical methods that are more useful for certain areas of physics and engineering?

Yes, certain mathematical methods may be more useful for specific areas of physics and engineering. For example, differential equations are commonly used in mechanics and electromagnetism, while complex analysis is often used in quantum mechanics. It is important to have a broad understanding of various mathematical methods to effectively apply them to different areas of study.

4. How can I improve my mathematical skills for physics and engineering?

Practicing regularly and seeking help from resources such as textbooks, online tutorials, and study groups can help improve mathematical skills for physics and engineering. It is also important to have a solid understanding of basic mathematical concepts and to continuously review and reinforce them.

5. Are there any recommended resources for learning mathematical methods for physics and engineering?

There are many resources available for learning mathematical methods for physics and engineering, including textbooks, online courses, and video lectures. Some popular textbooks include "Mathematical Methods in the Physical Sciences" by Mary L. Boas and "Mathematical Methods for Physics and Engineering" by K.F. Riley, M.P. Hobson, and S.J. Bence. Online resources such as Khan Academy and MIT OpenCourseWare also offer free courses and tutorials on mathematical methods for physics and engineering.

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