Name: Advanced engineering mathematics
ISBN: 9780831134495

What Hacker News says

kingkongjaffaMar 2023

The best book, because it is full of worked examples and exercises, is K.A Stroud Engineering Mathematics, and the Advanced Engineering Mathematics book by the same author.

I used these books from First year to Masters level in Mechanical Engineering, it covers simple arithmetic to Laplace transforms and Fourier Analysis.

Warning they are Plug and Chug methods, you might also want to take a course on logic and proofs. But if you want to really nail the mechanics of solving typical problems you can't go wrong.

https://www.goodreads.com/book/show/2145638.Engineering_Math...

Here's a review I found:

This book represents a masterpiece in clear exposition. It takes the patient reader from quite basic mathematics through to that required by third year undergraduates in engineering and physical science courses in planned, frame-based, systematic and methodical steps. Each chapter has revision summaries, revision exercises and quizzes together with answers. Even mathematics undergraduates would probably benefit from it as part of their reading diet.

It's been the 'staple' diet for such courses for decades for a reason: it has few if any peers!

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kingkongjaffaMar 2023

The best place I found was The Best Textbooks on Every Subject by lukeprog

https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-best-t...

some updates here: https://www.lesswrong.com/posts/tJrEDkbS76xX96YDR/update-the...

It's quite old at this point, but most recommendations should be fairly evergreen.

For plug and chug mathematics from 0 to graduate level try, because it is full of worked examples and exercises, is K.A Stroud Engineering Mathematics, and the Advanced Engineering Mathematics book by the same author. Warning they are Plug and Chug methods, you might also want to take a course on logic and proofs. But if you want to really nail the mechanics of solving typical problems you can't go wrong.

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biofoxOct 2022

If you're not too concerned about proofs, I can highly recommend K. A. Stroud's 'Engineering Mathematics', and the follow-on text, 'Advanced Engineering Mathematics'.

It leads the reader from basic arithmetic all the way up to complex analysis, one exercise at a time.

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bargerJan 2019

While "all the high school math" is somewhat clear, the "all the college math" should be clarified a bit.

Are we talking about math for social studies majors, engineers, physicists, economists or mathematicians?

For example, there are books like [0] for engineers which serve as a boot camp of sorts. There are no theorems, proofs or deep math in it. There are many different kinds of engineers, so books like this don't include everything an engineer needs to know. For instance, there's no automata or group theory in [0]. It has a part at the beginning called Foundation Topics which could serve as "all the high school math one needs". In fact, this whole book could probably serve as "all the math an advanced high school student needs".

There are books like [1] for physicists. They are meant to introduce physics majors to a wide array of math topics in a relatively pain-free way. This book is much more rigorous and contains a LOT more material than [0]. Basically, a theoretical minimum for a physics major.

Economics majors also get somewhat rigorous math load where measure theory features a lot more prominently than it does in other majors (except mathematics proper).

List of subjects for math majors vary from place to place, but you'll have much easier time down the road if you master the (rigorous) rudiments of linear algebra (vector spaces), group theory, number theory and real analysis. Of course, knowing more math (say topology, complex analysis, category theory, combinatorics etc) is always good.

Before you get started with math for mathematicians, you'll want to learn their jive. A good intro is [2]. It's free and a really nice book. Another really nice book with non-existent pre-reqs is [3].

A pitfall that awaits a lot of people new to math is a concept of "multivariable calculus". This concept is a mess and means everything to everyone. Oftentimes it means surface level discussion of concepts in scalar fields (functions from R^n to R) and a little bit of talk about differential geometry of curves and surfaces (functions from reals and planes to R^n). The treatment is often not rigorous and n is limited to 2 and 3. After this laughable bullshit, one is thought ready to jump straight into the rigorous analysis of manifolds, granted they know a bit of real analysis. This is like jumping from 3rd grade straight to 9th grade. Along the way the most important thing missing is the rigorous treatment of vectors fields (say, at the level of Rudin). Some nice books here include [4]. Since diff geo (in particular, that of curves and surfaces) is its own thing entirely and there are a lot of really nice books for that like [5]. Also, note there's a nice new intro to "manifolds and stuff" [6] which is like what's calculus is to analysis.

Before I forget, most intro to stats books are written for science majors and are entirely inadequate for math majors, but there are elementary intro to stats books for math majors like [7].

Originally, I wanted to write a more fleshed out and huge comment, but I am running out of time.

Good Luck.

[0] Engineering Mathematics by Stroud/Booth

https://www.amazon.com/Engineering-Mathematics-K-Stroud/dp/0...

https://www.amazon.com/Advanced-Engineering-Mathematics-Kenn...

[1] A Course in Modern Mathematical Physics: Groups, Hilbert Space and Differential Geometry by Peter Szekers

https://www.amazon.com/Course-Modern-Mathematical-Physics-Di...

[2] Book of Proof by Richard Hammack

https://www.people.vcu.edu/~rhammack/BookOfProof/

[3] Linear Algebra: Step by Step by Kuldeep Singh

https://www.amazon.com/Linear-Algebra-Step-Kuldeep-Singh/dp/...

[4] An Introduction to Analysis by Wade