I'm reading spivak's 3rd edition of calculus, and I'm wondering how many of the practice problems do you guys do...

I just started it, and while it is fun, I just want a good understanding of calculus, as I'm an engineer major.

It's completely up to the depth of understanding you want. is completely justified in using it to learn to apply calculus to real problems. However, there is definitely nothing wrong with doing every problem in a textbook if you're looking for building intuition and preparing yourself for more formal math.

Oh, you've never done calculus before? I'm doing it to get a better grasp of the rigor behind every minute detail. Don't worry, I started a few days ago, and I'm almost just done with the first chapter.

Apostol volume one and two covers basically an entire undergrad engineering mathematics education. Spivak is just calculus one and two over here in the states. It depends what you want out of a book

you'll go through material way slower than you need to if you do every problem.

there's often like 25 questions on the same few pages of material, isn't there? and from what I looked at , not all of them provide very much illumination and often consecutive problems are just variants on each other.

you'll get 97% of the educational value just from doing half or 1/3 of teh questions. just take every second or every 3'd question or 40% of the questions evenly spaced over the ordering.

I mean what do you want to get out of maths, do you want to be one of the best people at introductory analysis or do you want to be able to solve real problems using control theory or optmal control theory or pde or fourier analysis ?

I think you'll get good enough strength at intro analysis by doing just a selection of the uestions in spivak.

To get the foundation of rigor, strengthen my grasp of calc, and gain the problem-solving abilities/ tenacity of an actual mathematician

No I have done it, I just wanted to delve deeper, so I have a better intuitive understanding of calculus and how/why it works.

Aye then I guess just do what others are recommending. Good luck man, and remember, done dwell too much on the time it takes you to learn it, as long as you're constantly learning.

don't dwell*

apostol's book covers single and multivariable calculus, spivak only single variable calculus
apostol's book also has introductory diff eq, probability, and linear algebra

The only thing there I would need is multivariable calculus, maybe probability but I can learn that later, not my current intrest. I'm doing "Ordinary Differential Equations" by Morris Tenenbaum et al. and "A course in Linear Algebra" by Damiano et al. Not the hardest books or most rigorous, but it's more to learn as well as a rest from Spivak. Not OP btw, but do you think my approach is flawed? If someone puts problems in a textbook, he wants you to do them.

I'm the one who wrote that guide for you.

Way back when I went halfway through Apostol, then restarted with Spivak online because my book got trashed. Both the books are very good, and actual content is almost identical. However, Apostol is not only slightly longer, the second volume is not as good as the first volume due to a clumsy introduction to linear algebra and horrendous typesetting on the free online versions. Your knowledge of analysis on manifolds (multivariable calculus) will be easily secured by reading Loomis and Sternberg's Advanced Calculus following your completion of Spivak (you will perhaps be put at ease to know that this book, which was the text supplied to the students of Harvard's Math 55 in the 1960's, states in the preface that Spivak's Calculus is a book that will adequately prepare you to read it.)

Also, do all the questions.

>8153030
i posted this but i don't remember saying the word "desu"... wtf

Thanks man, but I didn't follow any guide for the books I chose minus Spivak, you have me confused with someone else friend. I'll write down that book and author.

Also, thanks for the affirmation.

welcome newfag enjoy your stay

really? what a bizarre coincidence. you even post pepe images like him and he also was motivated to learn algebraic geometry

Not OP, ah, you confused me by not posting who you were replying to. Idk about OP, maybe he did? I'm and

you learn mathematics by doing mathematics, so i think solving problems is the best way to learn.
try to attempt each problem, if you can't solve something after an honest attempt then maybe look for a small hint, or just move on and come back to it later

that man is an imposter, I'm the real OP, but yeah I just started reading spivak today, and I'm going to follow through on the rest of the books too, this stuff is exhausting my brain though.

t-t-t-thanks desu

You will obviously come out with a better understanding if you do every single question, but it seems tedious and unnecessary to me. Why waste time on the easy problems?
I usually just picked out a handful that seemed the most difficult, unusual, or interesting, and if I could get through those without trouble, I assumed that the other questions would be even easier.

Damn way to single me out even though I clarified. Anyways I know the feeling, fuck it sucks. Good luck at it, but I'm sure you've got it in you, you decided to face the task after all.

I read you reply after I saw the initial one. Anyways, summer started for me a month ago, so I don't really have anything better to do other than this.

Apostol is just fine for that, but spivak works too. Personally I like apostol for more of a reference text since it contains just about all of the material I need for undergrad. Spivak has some really slick problems in it that you should appreciate

>engineering
lol you won't use 10% of it once you graduate.

What's the opinion on Leithold?

More like 5%. It will improve his critical thinking though, but there are better ways to go about it in my opinion. Research, internships, independent study, etc.

My 2 cents.

Past undergrad doing pactice problems is an extreme investment that I only do when I want to get really good in a specific field of research.

It's the difference between understanding something and being good at it. Do you have time to be good in X field, or do you just need to understand it (along with the shitton of other fields you need) and bring in professionals as coauthors when you need difficult proofs?

unless you go into controls, dsp, cfd you will not really need math. the courses you will use are numerical methods and probability/statistics

I was planning on going into microsystems or robotics as my specialty.

Spend some time learning programming like ROS and doing small robotics projects. That will be worth your time in my opinion. Try to find some research in that area too.

Knowing calculus in-depth is great, but you're better off in my opinion doing projects is more beneficial.

>Get the international edition or just pirate it.

lol the first result on google for "apostol calculus" is the 600 page pdf

Exactly. It's only expensive if you buy it on amazon.

If you need the book because you prefer paper like me, either buy the poo in loo edition for like 10 bucks or borrow from a library.

I don't have a linux or mac platform

Dual boot Ubuntu, it's free.

Every math textbook worth its salt does that.

...you don't know calculus and you want to learn algebraic geometry? What the fuck is wrong with you? Do you know what algebraic geometry even is?

this

gen.lib.rus.ec/

Not OP, but I think that it's completely reasonable to want to learn AG before calculus. I'm a pre-law major, and even though I stopped taking math after Calc I, I've managed to learn most of modern scheme theory at an intuitive level. Even though I can't write formal proofs, I probably have a much deeper understanding of the subject than your average STEM symbol-pusher.

>I've managed to learn most of modern scheme theory at an intuitive level

>scheme theory
>intuitive level
pick one

The theory is very simple and beautiful once you strip away all of the confusing and irrelevant technicalities. I figured you STEM-fags would be butthurt that even after studying abstract math for years you still haven't reached my level of comprehension.

You say this as if mathematicians don't build an extensive intuition for everything they do. This is what doing exercises buys you.

While I'm at it, do you know how much of scheme theory is motivated by complex analysis and differential geometry? I get that you want to learn shit OP, but you don't even know what's out there yet. Learn things as you go and learn things well, and you'll know what you want to study as you get a little further.

there's no way this is true for a), right?

I add 2+(m^2 / n^2) to both sides and the inequality should be completely wrong.

I dont quite understand what you mean. No way what is true for (a).?

That the inequality was false, I got it now, but I'm just going to delete that post.

Just as a heads up, the book's problems are basically bullet proof. If you are having a problem with it, take it slow reading it and make sure you arent missing some kind of concept. Now admitably the answer book has an assortment of small errors but its right where it counts.

ITT: baby manchildren who whine about challenge talk shit on a good book.

If you go through Spivak and actually answer the hard questions, you'll come out understanding a fuckload more than the meme tier understanding of most undergrads.

>engineering

Have fun being a meme forever

>I can't write proofs, but I understand it

Topper meme lad, wew