I am studying a book titled "Microscale Acoustofluidics" so that I could understand more about my thesis on the formation of ultrasonic standing waves that causes acoustophoresis.
I am in need of advice; this book has a lot of equations and a lot of mathematical terms. I sometimes understand the equation, but some are just too complex. In the end, even if I do understand the equation, I do not know how to imply it in real life.
How do you understand a book that is full of equations and complex mathematical terms like one rank tensors, two rank tensors? I only think of one way for me to fully understand this book and that is to study what each terms means like what is pressure density, tensor, viscous friction and such and then imagine their existences within the fluid domain and such. Isn't there any 'shortcuts' for me to understand this book?
The equations of mathematical physics are indeed quite complex. If you really need to be able to understand them - in order to derive similar, for example - you have to go through that. However, there are different types of books. Mathematical authors sometimes put excess complexity, while some physicists try to put some intuition behind them. If you want to understand how it works and know physical principles - it might be better to start from some physical lectures on this topic. They might have less equations, but more discussion about the meaning of different terms.
Tensor of rank 2 is just like matrix. Sometimes physical equations are more complex - with tensors of rank 3 or 4. To understand matrix algebra is very important, and differential equations as well. Did not you have good calculus class to come through that? Maybe you can go to wikipedia or similar source and put unclear term to get what does it mean and where is applied.
To stud a book full of equations and understand it you have no choice to go through each of the equation include in the book and identify where an specific equation come from, why it has been used and try to understand the connection between the specific equation and others, and what is the importance of the equation, among others.
To study through this type of book you should have a solid mathematical background and a deep knowledge of the main subject of the book. Otherwise you will be block many times during the study of the content of the book.
If you have somebody that is an expert on the subject, then ask for his/her advise.
I am not sure how familiar you are with this complex field that comprises acoustics and fluid mechanics together. As Yuri and Jorge have already suggested, you need to first have a solid understanding of the background materials.
I think, sometimes, it is better to take a step back and brush up the fundamentals first which for your case would be any illustrative undergrad book on sound, basic fluid mechanics and engineering mathematics dealing with differential equations and matrix algebra.
I would not say, even you get these subjects right, immediately you would be able to finish that book at a single go, but probably you would be able to appreciate the topic better.
Like all have said you need to develop a deep understanding of the subject and mathematics. Revise engineering mathematics and its application. Mathematical topics can be mastered by having in depth understanding and practise.
Also every mathematical eqn has a physical interpretation, try to understand that physical view. It will help you understand and correlate eqn better.
This happens with everyone and only solution is better preparation.
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