While this book has limitations, I think engineers and scientists sorely need books like this. Engineers and scientists could learn most applied math easier if they had certain foundations that are more common in mathematicians. I was toying with an idea for such a book if I could return to academia. But my formal training stopped at a math BS, and one of my mentors shot that idea down. He exposed me to many areas of math not common in math methods books. I wouldn't be as good as I am if it wasn't for him. I can hold my own in math, but I feel there are specific nuances that elude me because I think I have not delved deeper into things like functional analysis. Near the end of my postdoc, I finally started getting to inverse problems. I am low-key obsessed with them.
An analogous book, both amazing and on the cheap side, but geared exclusively to physicists is "Mathematics of Classic and Quantum Physics" by Byron and Fuller. I'm not a physicist but the glorious users reviews and the low cost made me curious, and I gave it a try. Back in the day, it was the first book that helped me clearly visualize for the first time how sine and cosine are mutually orthogonal, and therefore they form an orthonormal basis that make Fourier integrals possible to work. A momentous moment indeed for me "Mathematics of Classic and Quantum Physics" is not recent but still widely used, I saw it at the least in the bookshelf of two physicists friends of mine. Its strength is that it's constantly illuminating the connections between (apparently very far from each other) mathematical ideas and how their relate to the physics. For example, this is an excerpt, that it got me so excited, that I wrote it immediately to other friends about it: "The eigenvalue λ is numerically equal in value and meaning to the Lagrange multiplier λ, in the context that the operator A is linear and self-adjoint: Ax=λx; and its inner product is I=(x, Ax)" I told my friends "Fuller calls it notable...I call it jaw-dropping"...my friend were very impressed as well. No other books make the time to illuminate those things for you, except the books of Cornelius Lanczos, perhaps Fuller and Byron don't mention explicitly real and complex analysis, functional analysis measure and operator theory. But a book that has a full chapter on Integral Equations, with Banach spaces as a sub-item, for sure expects you have some understanding of real analysis. They kind of built it for you throughout the book, without saying it explicitly, but stay away from formal definitions of it. For example there is no explicit treatment of deltas of epsilon, or Heine-Borel theorem, etc Another book, similar to the book of this video, and dearly recommended by the RUclipsr "Andrew Dotson" is "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence
I've had that book for a while now, actually, and never gave it a shot. That definitely is jaw-dropping. I didn't know that! Great stuff again, I appreciate you pointing this book out to me. I'll get back at your email soon. Thanks again!
Don't forget to like, comment, subscribe, share and use our affiliate links! Shoutout to Yann and Adam. I consulted with them briefly on this book. Yann has a PhD in Cosmology and can be found here: twitter.com/Yann_Le_Du Adam is a PhD student in Solid State Physics and can be found here: twitter.com/Fermion_Adam Yann mentioned that the book was a good overview, but needed more exercises. Adam mentioned that the book was missing quite a few topics needed at the research and PhD level such as group/representation theory for physics and Sobolev spaces for engineering. He mentioned that it was sufficient at the master's level. Thank the both of you very much.
While this book has limitations, I think engineers and scientists sorely need books like this. Engineers and scientists could learn most applied math easier if they had certain foundations that are more common in mathematicians. I was toying with an idea for such a book if I could return to academia. But my formal training stopped at a math BS, and one of my mentors shot that idea down. He exposed me to many areas of math not common in math methods books. I wouldn't be as good as I am if it wasn't for him. I can hold my own in math, but I feel there are specific nuances that elude me because I think I have not delved deeper into things like functional analysis. Near the end of my postdoc, I finally started getting to inverse problems. I am low-key obsessed with them.
I couldn't agree more! Do you know of any other books similar to this one?
Thanks for sharing.
I agree... It's not a deep dive, but enough for quick intro. There are other Springer books that go way deeper in individual subjects.
An analogous book, both amazing and on the cheap side, but geared exclusively to physicists is "Mathematics of Classic and Quantum Physics" by Byron and Fuller. I'm not a physicist but the glorious users reviews and the low cost made me curious, and I gave it a try. Back in the day, it was the first book that helped me clearly visualize for the first time how sine and cosine are mutually orthogonal, and therefore they form an orthonormal basis that make Fourier integrals possible to work. A momentous moment indeed for me
"Mathematics of Classic and Quantum Physics" is not recent but still widely used, I saw it at the least in the bookshelf of two physicists friends of mine. Its strength is that it's constantly illuminating the connections between (apparently very far from each other) mathematical ideas and how their relate to the physics. For example, this is an excerpt, that it got me so excited, that I wrote it immediately to other friends about it:
"The eigenvalue λ is numerically equal in value and meaning to the Lagrange multiplier λ, in the context that the operator A is linear and self-adjoint: Ax=λx; and its inner product is I=(x, Ax)" I told my friends "Fuller calls it notable...I call it jaw-dropping"...my friend were very impressed as well.
No other books make the time to illuminate those things for you, except the books of Cornelius Lanczos, perhaps
Fuller and Byron don't mention explicitly real and complex analysis, functional analysis measure and operator theory. But a book that has a full chapter on Integral Equations, with Banach spaces as a sub-item, for sure expects you have some understanding of real analysis. They kind of built it for you throughout the book, without saying it explicitly, but stay away from formal definitions of it. For example there is no explicit treatment of deltas of epsilon, or Heine-Borel theorem, etc
Another book, similar to the book of this video, and dearly recommended by the RUclipsr "Andrew Dotson" is "Mathematical Methods for Physics and Engineering" by Riley, Hobson and Bence
I've had that book for a while now, actually, and never gave it a shot. That definitely is jaw-dropping. I didn't know that!
Great stuff again, I appreciate you pointing this book out to me. I'll get back at your email soon.
Thanks again!
Don't forget to like, comment, subscribe, share and use our affiliate links!
Shoutout to Yann and Adam. I consulted with them briefly on this book.
Yann has a PhD in Cosmology and can be found here: twitter.com/Yann_Le_Du
Adam is a PhD student in Solid State Physics and can be found here: twitter.com/Fermion_Adam
Yann mentioned that the book was a good overview, but needed more exercises.
Adam mentioned that the book was missing quite a few topics needed at the research and PhD level such as group/representation theory for physics and Sobolev spaces for engineering. He mentioned that it was sufficient at the master's level.
Thank the both of you very much.
Do you know if this book is available only in softcover ? Thanks.
It's actually available in hardback. I didn't know that. Cool! Here's a direct link to SpringerLink:
link.springer.com/book/10.1007/b138494
I really like this book.
2k Subs LETSSS GOOOO
This looks good. A Stepup of Kreyszig I think ???🤔🤔
Yes! Thanks for commenting!