Introducing myself to calculus

[DanM]

This fall I will be enrolled in courses on calculus and calculus based physics at my school. Over summer I plan to introduce myself to the topic. I know almost nothing about it other than that it is the study of change and the definition of "derivative," along with some historical context.

Which books, websites and other media would you recommend?

 

[Quick_Nick]

Honestly, just wiki.
I don't think a head-start is necessary for those classes.
I took AP Calculus BC last year (jumped in in "middle" of the year) was surprised by how much I knew. All I learned was little bits of stuff on my own, much of which I didn't understand at the time, and I had to take a minute and be reminded how to do derivatives.

---------- Post added at 08:03 PM ---------- Previous post was at 08:03 PM ----------

More after dinner xD

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I was familiar with concepts. I knew the basics of derivatives, integrals, reimann sums, and some names and theories.
I mostly just pursued calculus in my spare time so I could understand more about orbital mechanics, and I had thought I totally failed. I didn't know I picked up much more than I would need. You don't even begin to use integrals until the second semester of BC.
I would have taken Physics C if my school didn't enjoy inhibiting my education. But I know the class very well. Physics C really uses like 0.1% of what you'll learn in calculus.
So if you're concerned about being prepared, don't worry. With a reasonable aptitude for math and science and/or determination, you'll do just fine starting from scratch. And, by the way, you will probably not use anything you learned from "pre-cal". :lol: (maybe never again!)

 

[Cras]

Is there anything more worthless than Pre-cal?

 

[Scav]

I discovered recently that in order to even begin to qualify to start to pursue my BS in Computer Science at the University, I need to have an existent Calculus background.

Calculus for computers? :huh:

 

[DanM]

I discovered recently that in order to even begin to qualify to start to pursue my BS in Computer Science at the University, I need to have an existent Calculus background.

Calculus for computers? :huh:

Calculus seems to be in everything. :shrug:

 

[Cras]

and it is a BS. You need math for a BS. And you will use calculus in computer science, I guarantee it.

 

[Scav]

and it is a BS. You need math for a BS. And you will use calculus in computer science, I guarantee it.

You hear that sizzling sound? Yeah. That's coming from my brainpan. :uhh:

 

[RGClark]

Is there anything more worthless than Pre-cal?

I'm puzzled. What do you and Quick_Nick think is discussed in Pre-Calculus that is never used in Calculus?


Bob Clark

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I discovered recently that in order to even begin to qualify to start to pursue my BS in Computer Science at the University, I need to have an existent Calculus background.
Calculus for computers? :huh:

Most universities allow you take to take them at the same time.

Bob Clark

 

[Quick_Nick]

It's generally just elements of algebra and trigonometry that you rarely use, combined with stuff so simple that you should already know it from previous classes or in general given that you're taking calculus.
I didn't take pre-cal, but I've seen the work. Basically none of it applies to calculus except algebraic approximations. You don't need to know trigonometric identities or even the functions really for calculus. You have a calculator if you need the sine of an angle. Very little memorization is needed. I think my only notes were over series tests for convergence.

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The phrase "boolean calculus" makes my brain twitch.

 

[RGClark]

It's generally just elements of algebra and trigonometry that you rarely use, combined with stuff so simple that you should already know it from previous classes or in general given that you're taking calculus.
I didn't take pre-cal, but I've seen the work. Basically none of it applies to calculus except algebraic approximations. You don't need to know trigonometric identities or even the functions really for calculus. You have a calculator if you need the sine of an angle. Very little memorization is needed. I think my only notes were over series tests for convergence.

I don't agree with this. Perhaps you are saying this because you didn't have to take algebra because it was too easy for you. However, I think it is reasonable to suppose that if someone has questions about the difficulty of a following course then the previous course was not easy for them.
After teaching both calculus and algebra it is my opinion that the biggest problem students have with calculus is that they don't have a good grounding in algebra. There are alot of basic calculations you have to do with powers of variables and with polynomials that if you don't have a firm foundation with them then you will have great difficulty with them in calculus.
I really must say I don't agree with what you said about memorization either. Again some students find calculus easy and they don't have to do much work, such as memorization, to do well in it. But that is not true for many students.
Prior to taking calculus the best single advice I can give is that you are strong in doing calculations with powers and polynomials. How do you add them. What are like terms. How do you multiply polynomials. How do you divide them. When adding fractions of numbers or of polynomials how do you find the common denominator.
Also extremely important is knowing how to do compositions of functions, i.e, functions of functions.




Bob Clark

 

[Notebook]

Have to agree, I found Calculus very difficult, mostly because my Algebra was poor. Did a lot of work on that, and sort of understand it eventualy. Still go back to Algebra when things get tough.

N.

 

[Quick_Nick]

I don't agree with this. Perhaps you are saying this because you didn't have to take algebra because it was too easy for you. However, I think it is reasonable to suppose that if someone has questions about the difficulty of a following course then the previous course was not easy for them.
After teaching both calculus and algebra it is my opinion that the biggest problem students have with calculus is that they don't have a good grounding in algebra. There are alot of basic calculations you have to do with powers of variables and with polynomials that if you don't have a firm foundation with them then you will have great difficulty with them in calculus.
I really must say I don't agree with what you said about memorization either. Again some students find calculus easy and they don't have to do much work, such as memorization, to do well in it. But that is not true for many students.
Prior to taking calculus the best single advice I can give is that you are strong in doing calculations with powers and polynomials. How do you add them. What are like terms. How do you multiply polynomials. How do you divide them. When adding fractions of numbers or of polynomials how do you find the common denominator.
Also extremely important is knowing how to do compositions of functions, i.e, functions of functions.




Bob Clark

You're right. There are a number of students who have trouble with algebra.
I was going on the belief that DanM specifically has an aptitude for math like I do. The algebra parts of pre-cal are covered in Algebra I and II. It's just a matter of retaining information which many students don't do if that's not their best subject. I don't see many students keeping the useful bits of pre-cal over the summer unless they were one of those students that didn't really need the review in the first place. And then you 'need' some sort of drive to even begin calculus. At least here it's not a required class and you have to have started highschool math a year early to get it into your schedule anyways.
I still hold the belief that there are many elements of pre-cal that one is highly unlikely to use regularly though, especially in calculus.

 

[PhantomCruiser]

I'm not a math wiz in any sense of the word. I can do it, but it's not my favorite subject. I always though trig was under-rated, algebra is kind of fundamental, but trigonometry is a very versital and useful (much more than people realize). Just my $0.02.

Anyway, am I the only one here who thought about helping with the introduction?
DanM, meet calculus - Calculus, meet DanM

 

[jimblah]

Calculus Level Algebra and Trig is essential

My personal experience is that a Pre-Calculus course of study prepares you for a level of Algebra and Trigonometry above and beyond the level at what you were taught those subjects initially. Not only do you review, but you will grasp the topics more firmly. You need to graph and translate functions with your mind without relying on clumsy graphic calculators. On exams I've seen too many students fail to complete it in the time alloted because they couldn't input the equations fast enough or correctly. The only calculator I need now or in the future is a scientific multifunction calculator. If I need more my laptop with Maple, Mathematica, (Orbiter), and a host of other tools are close by. A professor isn't going to give you an exam question that necessitates any one of those tools. Your first semester of Calculus will not be difficult, but don't be surprised if a line of Calculus involves a page and a half of algebra and trig; especially if you are expected to rigorously show your work.

 

[RisingFury]

Honestly, just wiki.

NO, NO, JUST NO!

Yes, it has to be in caps. If you wanna learn Calculus and Physics, stay away from Wiki and find good books.

 

[Quick_Nick]

NO, NO, JUST NO!

Yes, it has to be in caps. If you wanna learn Calculus and Physics, stay away from Wiki and find good books.

I'm not saying learn it that way. I'm just saying it has the maximum amount of information you could "need" entering a calculus class. Every bit of it and much more will be taught (probably well) from scratch.
I just really mean to emphasize not to stress over getting into calculus.

 

[Scav]

I just really mean to emphasize not to stress over getting into calculus.

That's right - clear the mind of any anxiety and prepare it like a sponge. That's what I'm trying to do before I retake Algebra. I'm -going- to get this stuff...

 

[SandroSalgueiro]

This is how I learned it:

 

[Gerdih]

Calculus I and II on my university follow some lines of Larson, Calculus, 8e book wich I think is one of the best books I've seen about calculus. I've it and it helps me a lot when I need it. Also I dont know what you mean with calculus because I differentiate calculus from algebra. With calculus I understand the areas of limits, derivates, integrals, series,... I think you have to learn first what is a derivate what is a limit and what is an integral. Then you have to learn to calculate easy limits integrals and learn to derivate. Also I think is important knowing a lot of things about functions and his characteristics. Also you have to learn trigonometrics. And then you can start with the book I have said.

 

[george7378]

I didn't know what calculus meant until about 1.5 years ago, and now it's pretty much all I do in maths, and it shows up in physics too. I didn't need any introduction to it before I started - I think it comes quite naturally to most people.

I suppose it shows up a lot in university physics - I will find out soon I hope