American """education"""

>>8780198
>Stewart
Fuck this book

>>8780198
Stewart was Canadian tho u dumb yuropoor

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Do you have a name for everyone of these?

>>8780250
>>8780255
wait until you get to the Integral Sum Rule and the Integral Difference rule (This is probably in the "calculus 2" section though, very advanced)

>>8780250
>>8780255
>being this autistic
Is what you posted not true? Kill yourselves

>>8780198
Stewart is okay, just actually try reading the examples.

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>>8780275
> studying math, without being able to handle the smallest amount of abstraction
you first.

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>>8780275
>Is what you posted not true? Kill yourselves
A good book makes clever definitions so that theorems follow effortlessly.
Good luck proving anything with the definitions provided in Stewart.
My high school book was far better than this.

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>>8780322
>>8780324
It's true what they say, math majors are fucking autists

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In Rudin you have theorem [math]5.3[/math] dealing with the "product rule".
The proof says that it is clear from theorem [math]4.4[/math].
In [math]4.4[/math]'s proof is stated that you can prove it from [math]4.2[/math] and [math]3.3[/math] with minimal brainwork.

You cannot do this using the definitions provided in Stewart's book.
Everything has to be shown separately.

>>8780334
but I have an engineering degree.

>>8780359
So a gay autist then

>>8780334
>It's true what they say, math majors are fucking autists
Is the first time I see anything like that and I've gone through a lot of Analysis textbooks.
Again, not even high school textbooks do this.
You don't need to define the limits for metric spaces like Rudin does.
Just give a useful (something you can work with) simplified definition for functions [math]f:\mathbb{R}\rightarrow \mathbb{R}[/math] like Spivak in Calculus on Manifold does.

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Oh no, Stewart calls it "the sum rule" instead of "5.3a" like it is in Rudin.

>>8780394
You missed the point.
>>8780394
>You cannot do this using the definitions provided in Stewart's book.
>Everything has to be shown separately.
That's why you have to suck up two "proofs" for "sum and difference rule".
After you have finished this book you still are not able to prove things.
I understand now the existence of books devoted to showing how to prove something.

>>8780394
I saw this in late high-school and the teacher just said, here are some generals rule about "derivatives" :

(u + v)' = u' + v'
(uv) = u'v + uv'
(u^n)' = u'(u^n-1)
...

And so on. We didn't prove them, but we did saw the definition of a derivative and the teacher told us "you can try to prove them if you want, it's not too hard."

Same with limits, he just called it "arithmetic of limits."

>>8780356
This is retarded too. Whenever a textbook say "This exercise is trivial", they shouldn't have said it at all.

>>8780428
>This is retarded too. Whenever a textbook say "This exercise is trivial", they shouldn't have said it at all.
He says
>it is clear by
>these assertions follow immediately from
which is true.
If you cannot prove it/rearrange it by yourself you're not really understanding what you're doing.
You build skills by reading the book.
But then, what if an exercise is really easy?
By saying that it's trivial the author is giving you a hint.
If the reader is a total beginner, that's not his fault.

>>8780498
To me, (yes I'm a little snowflake), it feels condescending. Yes, most of the time those exercises are way easier than those around them, but it could be phrased differently.

>It can be shown with blabla than
>We can show it using theorem x.y

It might be pointless semantic, but it would also makes the academia appears less arrogant.

>>8780428
Those proofs aren't trivial for an introductory calculus course. Assuming the epsilon delta definition of a limit has been established,

Let lim x->a f(x) = L1, lim x->a g(x) = L2 . Let h(x) = f(x) + g(x) , let the domain of h be defined as the intersection of the domains of f and g.

lim h(x) x->a = L1 + L2 <-> lim x->a [ f(x) + g(x) ] = lim x->a f(x) + lim x->a g(x)

remark:: given epsilon > 0 , one must find delta > 0 such that: 0 < | x - a | < delta -> 0 < | ( f(x) + g(x) ) - (L1 + L2) | < epsilon

| ( f(x) + g(x) ) - (L1 + L2) | =
| ( f(x) - L1) + (g(x) - L2) | <=
| f(x) - L1 | + | g(x) - L2 |

remark:: both absolute values of f(x) - L1 and g(x) - L2 can be set to be arbitrarily close to zero by choice of delta1 and delta2 respectively, therefor:

| f(x) - L1 | <= epsilon / 2
| g(x) - L2 | <= epsilon / 2
| f(x) - L1 | + | g(x) - L2 | <= epsilon
| ( f(x) + g(x) ) - (L1 + L2) | <= epsilon <-> lim x->a [ f(x) + g(x) ] = lim x->a f(x) + lim x->a g(x)

or informally, the limit of a sum is the sum of the limits in the case of 2 functions.

>>8780516
When used correctly, the word "trivially" can be used to convey that a theorem, solution, or proof is simple or immediately evident. The difference between it and

>it can be shown

is the explicit ease of the exercise. In these cases, the solutions should come quickly and naturally, and if you get stuck on one of them you should ask your teacher or peers for clarification. It is one way of gauging the comprehension of material and can be immensely useful for the success of education for the course.

The professor or writer is not arrogant nor appears arrogant by using the word this way and you shouldn't feel condescended by its use. If a professor is condescending while using the word, that is a problem with the professor and not the language of the material.

>>8780198

Wrong at jump street; nice try though.

"James Drewry Stewart (March 29, 1941 – December 3, 2014) was a Canadian mathematician..."

>>8780324

The only reason you might need this in a book is to demonstrate how mathematicians articulate that notation.

The "sum rule" and other bullshit don't need that, as its no more complicated than the addition of two specific derivatives.

>>8780906
ur rite

>>8780885
>using epsilon-delta fuckery for something like that
Is it really worth the hassle ?

>>8780198
lmao fuck this book i'm so glad i'm done w calc for 2 quarters

I am reading this book cover to cover, its not that bad.

All I care about is the multi variable parts.

>>8782146
>All I care about is the multi variable parts.
Spivak from page 1 to 74.
http://www.ime.unicamp.br/~marcio/ps2009/spivak

>>8780324
I don't why wouldn't use epsilon-delta definition from beginning, Stewards is just that but reworded to be more obscure and harder to grasp and use.

Epsilon is your greatest tool and friend in analysis, you will have to learn it somepoint.

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Why do Americans think calculus is advanced math?

>pic semi-related

>>8781135
I would have to say yes. There are many problems in high school math which need the definition of limits to be able to solve them

>>8780198
Not only is this book good, it's the best calc book for non-mathematicians

>>8780198
Should I start with Baby Rudin or Spivak's Calculus? Or is Baby Rudin the same just with more content? As a European I don't know the difference between Calculus and Analysis.

>>8780334
I'm starting graduate school in math this fall, and everyone I know plus I think Stewart is okay. Only a fucking brainlet cares about what's going on in calculus books.

>>8782719
You'll most definitely not understand what's going on in Rudin. Spivak is autistically slow.

>>8782621
>Why do Americans think calculus is advanced math?
Because you only learn very simple algebra in highschool.
Then if you go to college for a 2 year degree, or non-S.T.E.M. 4 year degree you learn the rest of algebra (college algebra).

If you go for an advanced S.T.E.M. degree you have learn calculus. So calculus = advanced math.

>>8782231

All the foundations I need to understand that is in Stewart. I dont have a good grasp on parametric equations, vector spaces, or partial derivatives.

Theres no possible way I can understand what you linked yet.

>>8782746
In my country everyone has to learn Calculus to graduate high school.

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>>8783607
In America we have the No Child Left Behind act.
We have a standardized test, how well the school does on the test decided how much money the school gets for the year. As a result anything not on the test is not taught. So you don't learn algebra, you just learn the parts of algebra that are on the test.

Schools keep pushing for lower and lower standards so you get fewer and fewer parts of algebra showing up on the test.

>>8783770
>fewer and fewer parts of algebra showing up on the test
and more and more nonsensical English questions with completely arbitrary answers

just kill me

I just finished self teaching myself precalc and ordered this book

it better be good and not just a meme

>>8784140
/sci/ likes to hate it but it's got a shitload of practice problems in it and you'll be able to learn, just watch videos on youtube of people that can explain the logic behind what you're doing better than the book itself does

>>8784140
I just looked at the first chapter, its got great casual filter.
>You should be able to solve all of this before you start to learn calculus.

>>8780198
Stay mad, fag.

>>8782728
I already heard an Analysis course but want to repeat everything since I don't think I grasped all content. What do I formally need to read to understand Rudin?

>>8784140
its a good book for learning the computational mechanics of calculus and applying it
it is not very good at developing the theoretical aspects of calculus, but thats arguable for an analysis course anyway

>>8780198
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>>8780250
this is how they introduce babby's first linear operator over infinite dimensional vector space.

its called pedagogy.

im sorry youre too smart for this world, i dont know how you have survived so long without killing yourself

>>8783501
>All the foundations I need to understand that is in Stewart. I dont have a good grasp on parametric equations, vector spaces, or partial derivatives.
What?
>Typical moronic student who uses Stewart.

>>8784281
>Stay mad, fag.
Did you buy it for $ 284.95 or rented for $ 17.87?

>>8784311
>What do I formally need to read to understand Rudin?
Already have gone though Analysis so you have a good intuition of what you're doing.
Some things you won't understand, you have to get used to them.
Then you need to be able to prove things yourself.

>>8784705
Do you really need to have subtraction rule?
Give me a break.