Calculus...difficult for a newbie?

Telekinesis said:

I have never been exposed to calculus at all. Should I take pre-cal first or jump right into it with regular Calculus?

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I have never taken pre calculus in my life and jumped right away into calculus and got an A. They give you preview of precalculus at the start of calculus course any ways to refresh your memory so don't worry and don't waste your time with pre calculus. But that's if you are good in math though so you decide.

In my opinion, pre calculus is a lot harder than calculus.

Here's my take on it:

Some people say they if you dont have any background, take a pre calc course. Most courses cover a small portion on limits and spend a big chunk on trig.

However, Calc couldn't be any more different than pre calc. Pre Calc was more like advanced algebra II mixed with trig stuff. The only thing i was able to take away from Pre Calc was knowing trig values and identities like the back of my hand. This does help later in some calc.

Bottom line:

If you think it'll make you feel more comfortable in calc, take pre calc, but i wouldnt say it is absolutely necessary.

Telekinesis said:

I have never been exposed to calculus at all. Should I take pre-cal first or jump right into it with regular Calculus?

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Here are some pre-calc topics you should make sure you know before Calculus. If you are really unfamiliar with these, you might want to review or take pre-calc.

-Graphing basic algebraic functions; shapes of graphs (parabolic, hyperbolic, square, cube etc.); basic components of graphs (x- & y-intercept, slope, points of inflection, asymptotes)
-Solving basic quadratics, determinants
-Basic aspects of functions (roots/degrees of polynomials, odd/even)
-Logarithms (what they are, changing bases, natural logs, graphs of exponential & natural log fxn)
-Polar/spherical coordinates
-Complex numbers, conjugates, plane; imaginary numbers
-Vectors (cross/dot products, normal vectors, algebra of vectors)
-Rational/irrational numbers
-Trigonometry
-Sequences & series

ponyo said:

Here are some pre-calc topics you should make sure you know before Calculus. If you are really unfamiliar with these, you might want to review or take pre-calc.

-Graphing basic algebraic functions; shapes of graphs (parabolic, hyperbolic, square, cube etc.); basic components of graphs (x- & y-intercept, slope, points of inflection, asymptotes)
-Solving basic quadratics, determinants
-Basic aspects of functions (roots/degrees of polynomials, odd/even)
-Logarithms (what they are, changing bases, natural logs, graphs of exponential & natural log fxn)
-Polar/spherical coordinates
-Complex numbers, conjugates, plane; imaginary numbers
-Vectors (cross/dot products, normal vectors, algebra of vectors)
-Rational/irrational numbers
-Trigonometry
-Sequences & series

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Good list. Wish I thought of it

Just some thoughts: As far as Vectors and Sequences and series goes,
depending on the Calc course you wont need it/they teach it to you there for the first time.

BMEN said:

Good list. Wish I thought of it

Just some thoughts: As far as Vectors and Sequences and series goes,
depending on the Calc course you wont need it/they teach it to you there for the first time.

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This was true at my school for vectors. For series we were taught specific series for the first time (Taylor/Maclaurin) but we were supposed to already have a good idea of what they are and the relevant notations (e.g. Sigma notation; arithmetic vs geometric; infinite vs finite; convergent vs divergent)

I'm pretty sure everything you need to know about sequences/series prior to calc is on Sparknotes: http://www.sparknotes.com/math/precalc/sequencesandseries

Calculus is way easier than Pre-calculus in my opinion. The concepts are really straight forward-- well at least differential calculus (calc I) is. Calc II on the other hand is just memorizing formulas and techniques of integration which isn't hard but tedious.

I would say the best way to prepare for Calc I is just know the basic stuff like simple algebra, the drawing and transformations of graphs, some basic trig, stuff like that. Youtube and other video sites are tremendous resources as well.

www.centerofmath.org has full lectures on each subject for free. I would recommend using this site. Good luck.

I think if you have time to spare and after taking precalculus, will go into calculus right afterward, then take precalculus. It might not be the most relevant for calculus but understanding all the trig stuff well enough will be a huge benefit later on.

But if you'd rather take calculus straight away and are decent at math, then it shouldn't be a problem like others said.

Telekinesis said:

Some of this stuff I don't even remember. I was an algebra tutor so maybe I know more than I think I know.

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I don't think you need precalc if you understand what Ponyo has listed. If you have time before enrolling I would check out what is recommended to know at the Khan academy, as well as what others have recommended.

http://www.khanacademy.org/#precalculus

This guy will help out quite a bit.
http://justmathtutoring.com/

Iirc, pre-calc only helped in introducing all of the topics briefly. You might be able to skip pre-calc if you feel confident enough in your math skills. Also noticed that you're from Texas, if you're attending UT, this guy will really pay off since he tutors UT students if I remember right. Either way, still helpful.

Calc 1 is pretty easy, it's 5% new concepts and 95% algebra.

ponyo said:

-Graphing basic algebraic functions; shapes of graphs (parabolic, hyperbolic, square, cube etc.); basic components of graphs (x- & y-intercept, slope, points of inflection, asymptotes)
-Solving basic quadratics, determinants
-Basic aspects of functions (roots/degrees of polynomials, odd/even)
-Logarithms (what they are, changing bases, natural logs, graphs of exponential & natural log fxn)
-Polar/spherical coordinates
-Complex numbers, conjugates, plane; imaginary numbers
-Vectors (cross/dot products, normal vectors, algebra of vectors)
-Rational/irrational numbers
-Trigonometry EDIT: Make sure you know the basic trig. identities and basic trig. graphs!
-Sequences & series

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If you have understanding of all of these, you'll be in good shape for Calc I/II. Make sure that you can do them without using an idiot box (TI-whatever).

I would also recommend learning some basic physics (i.e. acceleration and velocity) if you've never had physics. Calculus was invented in part to create a mathematical system for modeling these physical concepts.

Like others suggest, khanacademy.org is a great resource for self study.

As far as books go, I really like the "Calculus Lifesaver" and "Calculus Made Easy" as supplements. Between those two and the Knanacademy, I taught myself Calc in about six months for fun a few years ago.

There was a REEEALLLLYY good book on calc that I used when I was taking it, but I cannot remember the name. It was like a "for dummies" kind of book, but not from that series. It had a yellow cover and comic book style fonts and artwork. And it was actually pretty funny. If anyone knows the name of that book, buy it OP, and you will be fine jumping straight into calculus.

ponyo said:

Here are some pre-calc topics you should make sure you know before Calculus. If you are really unfamiliar with these, you might want to review or take pre-calc.

-Graphing basic algebraic functions; shapes of graphs (parabolic, hyperbolic, square, cube etc.); basic components of graphs (x- & y-intercept, slope, points of inflection, asymptotes)
-Solving basic quadratics, determinants
-Basic aspects of functions (roots/degrees of polynomials, odd/even)
-Logarithms (what they are, changing bases, natural logs, graphs of exponential & natural log fxn)
-Polar/spherical coordinates
-Complex numbers, conjugates, plane; imaginary numbers
-Vectors (cross/dot products, normal vectors, algebra of vectors)
-Rational/irrational numbers
-Trigonometry
-Sequences & series

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The bold topics are calculus II/III topics at my school.

Telekinesis said:

http://www.amazon.com/How-Ace-Rest-Calculus-Multi-Variable/dp/0716741741/ref=pd_sim_b_4

Was this it?

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YES!!!!! That book is incredible. I have some friends who are incompetent at math, and they aced calculus just by using that book. It is amazing. Incredible well-written, with awesome explanations of all the topics, and detailed step-by-step solutions for a lot of very common calc I midterm questions. Get on it!

And BTW, I found precalc to be harder than calc I. Not sure why, but I think its cuz of how disjointed the topics in precalc are compared to how integrated everything in calc I is. Everything you learn in calc I builds off the previous topics, so you get a very comprehensive understanding of stuff. Unlike precalc, where you just learn at a superficial level to perform on exams and homework.

If you go to A&M and sign up for i think Math 171 you dont need to know vector stuff. Or even series stuff. Polar might help but isnt needed. You just need to now some trig identities and values, basic functions, logs and exponents. You dont use complex numbers until like Diffy Q at A&M math. Polar doesnt get used till Calc 2/3 and only for integration

If you need help for Calc at TAMU there is the math help desk and SI sessions for calc I

Telekinesis said:

I'm taking Math 147-Calc bio majors.

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Alright. its the same thing then. Everything else still applies

You'll just be doing a lot of derivatives; they're pretty easy. I don't think that precalc is 100% necessary unless you consider yourself to be weak in math.

Paine said:

This is key. Be the kid who sits in your TA's/professor's office hours doing problem after problem and asking questions. It's the only way you learn math - by doing.

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Honestly, if you are decent at math, just doing the assigned HW problems should suffice. I agree though- doing math is the only way to learn it.

Telekinesis said:

Totally agree.

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this

do them ad naseum , concepts are fairly straightforward

every night after class i went over questions that he assigned for class best way

I have yet to take it either but what I believe Calc I pertains to is limits, derivatives, and integrals. Anyone care to elaborate further?

ponyo said:

Here are some pre-calc topics you should make sure you know before Calculus. If you are really unfamiliar with these, you might want to review or take pre-calc.

-Graphing basic algebraic functions; shapes of graphs (parabolic, hyperbolic, square, cube etc.); basic components of graphs (x- & y-intercept, slope, points of inflection, asymptotes)
-Solving basic quadratics, determinants
-Basic aspects of functions (roots/degrees of polynomials, odd/even)
-Logarithms (what they are, changing bases, natural logs, graphs of exponential & natural log fxn)
-Polar/spherical coordinates
-Complex numbers, conjugates, plane; imaginary numbers
-Vectors (cross/dot products, normal vectors, algebra of vectors)
-Rational/irrational numbers
-Trigonometry
-Sequences & series

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circulus vitios said:

The bold topics are calculus II/III topics at my school.

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Same. No one needs to know any of that for starting in Calculus I.

gettheleadout said:

Same. No one needs to know any of that for starting in Calculus I.

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Aside of determinates and vectors, we covered those bold topics in high school Calculus.

As to the OP, I though precalc was much more difficult than calculus. Calculus was very straightforward to me. You learn a few core subjects (derivatives/integrals/etc) and build off those the entire year. It is very self-referential, much like orgo. So if you are good with those types of classes, it shouldn't be too bad.

From my experience... I got an A+ in Precal, and did that help me in Cal I? Absolutely not. I got a B+ there. Very few things from Precal were introduced, and when they were, they were explained. In addition to that, the textbook we used (Stewart) had an appendix for prerequisite stuff you should know.

If you've decided not to take Precal, then I would suggest getting the book early if it has that appendix and going over it before classes begin. Calculus is just really different from Precal.

(Also, the only useful part from precal was trig. But, that shouldn't take more than a day to go over and learn).

cham90 said:

I don't think you need precalc if you understand what Ponyo has listed. If you have time before enrolling I would check out what is recommended to know at the Khan academy, as well as what others have recommended.

http://www.khanacademy.org/#precalculus

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This. Sal Khan is absolutely brilliant. He breaks down any subject and teaches you from the fundamentals. Then builds from the basics to more complex ideas. I would recommend him not only for calculus, but any other subject that he has posted. He is just so thorough that by the end of each video you will feel like you know this subject well. He has questions posted on his site so that you can reinforce all the material he goes over. So grab a piece of paper and a pen, and start watching the videos. DO NOT take pre-calc. it is glorified algebra, and it is a WASTE of your time.

Please please please don't take precalculus, if they make you take a placement test and you score underneath what it takes.. study the material and retake the placement test.

Precalculus is basically just learning trig functions and college algebra over again.

Calculus 1 isn't that difficult, the most difficult subject in it is optimization problems, but you know I did horrible in that area and still got an A in the class as it's just one subject out of many. Most of the subjects in calculus 1 are easy to learn. You start with limit problems which is basically just algebra problems. Then you start doing derivatives which is basically just memorization techniques + logical thought. You can do well in calculus assuming you have a solid algebra and graphical understanding.

Calculus 1 isn't hard. As long as you work, you'll be fine.

Truzzi said:

Aside of determinates and vectors, we covered those bold topics in high school Calculus.

As to the OP, I though precalc was much more difficult than calculus. Calculus was very straightforward to me. You learn a few core subjects (derivatives/integrals/etc) and build off those the entire year. It is very self-referential, much like orgo. So if you are good with those types of classes, it shouldn't be too bad.

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I wasn't talking about high school calculus. AP courses often have different schedules from their college equivalents. In my Calculus I class in college, we didn't cover any of that.

But yes, Precal has a ton of random useless junk that is needlessly difficult.

gettheleadout said:

I wasn't talking about high school calculus. AP courses often have different schedules from their college equivalents. In my Calculus I class in college, we didn't cover any of that.

But yes, Precal has a ton of random useless junk that is needlessly difficult.

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Good to hear. I was a little worried going into Calc without pre cal, but I've heard from others that pre cal in college is useless and that you can pick up on the essentials in the first few weeks (assuming you have a good to moderate algebra background.)

Don't do it unless you're confident in your skills in Algebra. It would definitely help if you're good at trigonometry and, of course, basic math.

Calculus is easy if you're allowed to use a calculator, though.

Pinoko said:

Don't do it unless you're confident in your skills in Algebra. It would definitely help if you're good at trigonometry and, of course, basic math.

Calculus is easy if you're allowed to use a calculator, though.

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If you have a solid Algebra, Trigonometry, and basic math foundation, Calculus 1 is easy (and, in some cases, faster) without a calculator, as well.

Hey, OP, since we go to the same school, I am gonna give u my advice.
And I did took Calc 2 at A&M, I will tell you that it is not for the weak-minded.
Personally, I took Calc BC in high school, took the credit for calc 1 and retake calc 2 at A&M, even though I took Calc 2 repeatedly for 2 consecutive semester technically, I had to put in considerable amout of work to make the A. This is the Calculus sclss for science major (math 171/172); I cant imagine what happen in the engineering math class (rumor had said that only 5% of the class get A).
In general, anything related to calculus at A&M is not recommended unless you have a strong foundation in math (which mean you take classes such as physics C, calc in high school). I took another calculus statistic class at the same semester and it is definitely the hardest class that I've ever taken. It is not hard because of the concepts, but it is the tests that is hard, they just give you problems that you've never seen before.
Edit: if you are talking about the math class for bio major (like 131 or something) then that class is super easy, dont worry about it.

Studying for calculus is like studying for ochem: do lots of practice problems.

Imma break down calculus for you.

Newton was a smart guy. He realized that you can use the old rise/run formula from algebra to find the slope of a function. He was tricky because he realized that using really small run values will allow you to find the slope at every point in the function. The rise/run formula, using really small run values at lots of different points in the function, becomes the new derivative formula. This derivative function will give you the slope at any point for a given starting function.

Similarly, Newton realized that you can construct a bunch of little squares under a curve to find the area under that curve. If you make the squares really small and over a range of values, you get an integral function.

Derivatives are useful for figuring out the behavior of an object, such as the classic projectile problems in physics--you can find out whether it's speeding up or slowing down. Integrals are useful because you can figure out how far the ball went over time.

You spend most of calculus 1 figuring out how Newton arrived at the simple method of differentiating functions and why differentiating works. The latter part of calc 1 is usually practicing and applying differentiation; you may start on integrating, which is the opposite of differentiating. Calc 2 focuses half on integrals and half on proving weird stuff related to series approximations, which don't make any sense until you apply them in engineering classes way down the road (I hated calc 2, ftr). Calc 3 uses more than one variable, diff EQ uses more than one derivative.

See? Calculus and calc-based physics are not that hard. Most math teachers just use difficult, obfuscating terminology to make it hard to digest. The good math teachers are the ones who explain things in simple words and more conceptually/applicably than just theoretically.