/sci/ - Science & Math » Thread #12024158

23KiB, 453x600, calc3.jpg

View Same Google iqdb SauceNAO

Anonymous Wed 19 Aug 05:37:47 2020 No.12024158 View Reply Original Report

Quoted By: >>12024340 >>12024604 >>12024611 >>12024614

My calc 3 professor is having us use this. Is it good? Anything to note? It seems older but it's springer so it probably isn't too bad.

Anonymous

Anonymous Wed 19 Aug 2020 07:09:54 No.12024340 Report

Quoted By: >>12024367 >>12024604

>>12024158
>Weinstein
probably trash. weirdly enough though, I am yet to actually find a non-garbage multivariable calculus textbook. I would say it really depends on how your teacher likes to teach. If he is rigorous then you'll need a good theoretical text, but if he just brushes over proofs and only really cares about the general ideas and optimization problems, you will find the course very intuitive and easy. Ultimately though, you will benefit more from considering it from a rigorous standpoint. if you don't prove theorems and really think over these things, you'll just be left with a bunch of shit you barely remember let alone their derivation. I kinda like http://93.174.95.29/main/DED9DBFADA1C5BF4E92EA49630A79421 since it covers interesting things like Hessian matrices for linearization/stability which is imo the only interesting thing in a higher dimension than 1/2

Anonymous

Anonymous Wed 19 Aug 2020 07:20:53 No.12024367 Report

Quoted By: >>12024413

>>12024340
My calc 2 professor was literally a James Stewart Powerpoint, while my calc 1 professor was great still taught from that textbook. I'll be taking linear algebra from a similar non rigorous textbook alongside calc 3 from the same professor.

My plan is get through it like you said, but while I do it study how to prove things as well as do a rigorous review of calc 1 and 2.

Anonymous

View Same Google iqdb SauceNAO file.png, 118KiB, 319x217

Anonymous Wed 19 Aug 2020 07:38:26 No.12024413 Report

Quoted By: >>12024559

>>12024367
kek that's modern university man. I also had that shitty stewart for first three semesters of calc. While it's a fine book, it's too bulky and you'll be wasting your time reading that much instead of doing problems and studying. Now that I think about it, I don't think I really understood proofs when i was taking calc 3 (that comes in your first real analysis course). But if there is one thing I would tell my former self in your place, it would be to never take shit you are given at face value AND LEARN PROOFS. What I mean is this: You will come across a theorem called Clairout's lemma or wtv which goes as follows:
$\frac{\partial}{\partial x}\frac{\partial f}{\partial y} = \frac{\partial}{\partial y}\frac{\partial f}{\partial x}$ or in other words, partial derivatives commute (order is irrelevant) for "nice enough functions." You will simply be ordered to take this as fact but I would look into it and try to prove it- the worse that can happen is that you have no idea and you learn something knew from someone else's proof. I learned proofs from Tao's analysis and took inspiration from Rudin's clever proofs in his analysis book. Check them out :). Good luck anon, and most importantly have fun.

Anonymous

Anonymous Wed 19 Aug 2020 08:22:22 No.12024513 Report

Quoted By: >>12024559

It's 3 AM and I just emailed my linear algebra professor 10 different times on 3 different mediums asking for help on a problem about understanding what a vector is as a joke.

Anonymous

Anonymous Wed 19 Aug 2020 08:42:10 No.12024559 Report

Quoted By: >>12024572

>>12024413
>"nice enough functions."
This triggers me. I remember having to repeatedly ask professors what "nice enough functions" even means. In calc, it means that they have continuous partial derivatives; in ODEs, that their Wronskian isn't 0; in linear algebra, that they're linear, invertible and that the vector spaces over which the functions are defined is real or complex. This one time a TA literally told me to just "trust him." No, I fucking won't. I've been lied to by retards before. You're teaching math. If you want to use imprecise language, we have an entire social sciences building for that.

>>12024513
I really hope you get "an element of a vector space" as a reply.

Anonymous

Anonymous Wed 19 Aug 2020 08:46:56 No.12024572 Report

Quoted By:

>>12024559
The assignment is not even due until Monday but I worded each successive email as though I was become progressively more panicked.

Anonymous

Anonymous Wed 19 Aug 2020 09:02:55 No.12024604 Report

Quoted By:

>>12024158
>>12024340
Multivariable Mathematics, Shifrin
Vector Calculus, Linear Algebra, and Differential Forms, Hubbard and Hubbard
Introduction to Calculus and Analysis Vol II, Courant and John
Calculus, Vol II, Apostol
Advanced Calculus, Folland
Calculus on Manifolds, Spivak
Analysis on Manifolds, Munkres
Advanced Calculus, Loomis and Sternberg
Multidimensional Analysis I-II, Duistermaat and Kolk
Advanced Calculus, A Geometric View, Callahan

These are from what I can tell the best treatments of multivariable calc/analysis on manifolds/advanced calc/vector analysis that you can come by. All of them are on libgen.

Anonymous

Anonymous Wed 19 Aug 2020 09:08:54 No.12024611 Report

Quoted By:

>>12024158
IIRC Marsden has a very shitty Vector Calculus textbook so I wouldn’t be surprised if this was an earlier edition or something along the same lines. We used Hughes-Hallett which is essentially stewart tier engimonkey training wheels for idiots. I used a combination of the books in the previous post to supplement. I think Hubbard and Hubbard is actually very boring and badly typeset, and while Shifrin’s book is similarly formatted and typset horrendously his problems and especially his emphasis on integrating lin alg with multi as well as the level of detail he goes into with the linearizarion of nonlinear problems inherent in calc esp w/r/t extrema, the hessian, the multivariable taylor theorem, quadratic forms is unique.

Also, forgot to add in Advanced Calculus of Several Variables by CH Edwards. Its like a much more approachable version of Spivak’s book with far more of a good mixture of applied and pure problems. The proofs are thorough and tractable and I like the coverage of Lin Alg and Topology at the start and his treatment of the Implicit function theorem. There’s also a chapter on Calc of Variations at the end thrown in for fun.

Anonymous

Anonymous Wed 19 Aug 2020 09:11:38 No.12024614 Report

Quoted By:

>>12024158
Also, I would strongly recommend you pick one detailed proof-based treatment of Multi and something more applied. A good combination would be Apostol Vol II and Spivak or Courant Vol II and Edwards or Munkres depending on how comfortable you are with abstract lin alg and analysis.

Capcode	All Only User Posts Only Moderator Posts Only Admin Posts Only Developer Posts
Show Posts	All Only With Images Only Without Images
Deleted Posts	All Only Deleted Posts Only Non-Deleted Posts
Ghost Posts	All Only Ghost Posts Only Non-Ghost Posts
Post Type	All Only Sticky Threads Only Opening Posts Only Reply Posts
Results	All Grouped By Threads
Order	Latest Posts First Oldest Posts First

Your latest searches