Calculus 1 Advice for Kaos: What to Look Out For

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I'm taking calculus 1 and I'm a bit nervous because I forgot some of the Algebra formulas and trig. unit circles. I know I can review them all with no worries, but I had a feeling of doubt(or cold feet).

Can I have some advice in this math course and what I should watch out for.
thanks.

-Kaos-
 
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Make sure you are comfortable with algebra and trig.
 
Be afraid. Be very afraid. You may not be able to fall asleep after the first time you see an integral.
 
kaos86 said:
I'm taking calculus 1 and I'm a bit nervous because I forgot some of the Algebra formulas and trig. unit circles. I know I can review them all with no worries, but I had a feeling of doubt(or cold feet).

Can I have some advice in this math course and what I should watch out for.
thanks.

-Kaos-

Definetly know all the important values of sin cos and tan of the unit circle including their graphs, periods, and such; and obviously csc sec and cot. In my opinion, trig comes in more to calculus than algebra, but you will need some basic reminders of factorization, quadratics, and it wouldn't hurt to have memorized formulas for difference of perfect squares, binomial factors, etc. Other topics might include exponents and their laws, logarithmic functions, basic geometrical area formulas, and shapes such as circles, ellipsis, parabolas, hyperbolas, etc. I would check out what your college pre-calc class covers and pick the topics you're less familiar with. Anything with matrices you can forget until Linear Algebra.
 
+1 on everything above, plus a few things.

Factoring! Factoring! Factoring! Did I mention that it's important to know how to factor accurately?

Know how to work with quadratics, and practice completing the square too--it's useful. Don't forget your point-slope and slope-intercept forms and how to interconvert between them. You'll need to know how to calculate the formula of a line when you know just the slope and a point.

Also, you'll need to be solid with logarithms and exponents--take the time to review the properties of logs and exps now. Know how to work with logs of bases other than e (although e is the most used) and how to interconvert them (change of base formula.)

If you struggle with absolute values and inequalities, you'll struggle when you need to study the epsilon-delta proofs.

+1 on knowing your trigonometry. But I found that if you're even half-competent in trig, it's the algebra that kills. My college algebra professor told her class that "to really learn to DO algebra, study calculus." Words of truth. Algebra+trig is the language of calculus.

Study the inverses of the trig functions: arcsin, arccos, arctan, etc. Know what they look like on a graph, how they relate to their parent functions, and know their domains.

If you plan on going further in Calculus, then you'll need to remember trig identities also, so start re-memorizing them now (especially the pythagorean, double-angle, and power-reduction.)

It's definitely helpful to remember some formulas from geometry: circumference/perimeter of a circle/square; area of a rectangle/triangle/circle; volume of a cube/cone/sphere; etc.

The first chapter of most calculus books is an succinct review of relevant topics in algebra and trigonometry. Use it as a pre-calc. study guide or as needed for review; either way it's a valuable resource.

Good luck! I thought that learning to take functions apart (taking the derivative) was fun; and now I'm finding that putting them back together (integrating) is even more fun! :)
 
calc 1 is a joke. don't worry about anything until calc 3
 
joking, well...half joking. but seriously my advice is general advice for learning and not just calculus. Don't learn how to use formulas. learn the concept behind them and use that concept to use the formula properly. Equations are only a weapon. The weapon is only as good as the person using it.

Memorization is over rated also. If your calc teacher makes you memorize those arctan integrals and stuff, don't memorize them and do worse on the tests in a childish attempt to get back at the prof vicariously through your mark.
 
+1 on what dacruick said about memorization. I don't retract what I said about memorizing the identities (or any formulas) though. You HAVE to understand how they work--why they are what they are, not just how to use them. You'll save yourself a lot of time if you don't have to rederive them every time you need to use them though. OTOH, memorization is temporary, understanding is permanent, so if you do understand them, you can rederive them later as needed IF you do happen to forget.

Cheers.
 
dacruick said:
Memorization is over rated also. If your calc teacher makes you memorize those arctan integrals and stuff, don't memorize them and do worse on the tests in a childish attempt to get back at the prof vicariously through your mark.
2h2o said:
+1 on what dacruick said about memorization. I don't retract what I said about memorizing the identities (or any formulas) though. You HAVE to understand how they work--why they are what they are, not just how to use them.

This advice is very true. It's better to understand the formulas and where they came from. I had classmate's trying to memorize double trig. identities, but never try to derive these identities or understand them. I forgot to understand or derive them, thus; I will review a lot in trig. this weekend.
 
Knowing algebra very well and trig. fairly well will get you good marks... but only if you commit to learning the principles of calculus. If your goal is to gain a true understanding of calculus, then don't stress so much about your algebra and trig.

However, if your tests are timed, and you are assigned large amounts of graded homework; then you'd better spend your free time reviewing all that stuff you thought you learned back in high school.

Also, on long and tedious homework assignments that you already have a firm grasp on, a ti-89 will save your life. The 89 and calculators like it aren't generally allowed in class or on tests, for good reason, so if you do get one make sure you don't become dependent on it.
 
robertm said:
a ti-89 will save your life. The 89 and calculators like it aren't generally allowed in class or on tests, for good reason, so if you do get one make sure you don't become dependent on it.

I just bought the Ti-89 and I like the features in this gizmo, but I agree on "don't become dependent on it" because a calculator can hinder your math skills.
 
Yeah, the TI-89 is pretty awesome, but it can easily become a crutch. Same with Wolfram|Alpha. I only use them to check my answers, or if I'm completely stumped, to give me an idea of either what to do next or what I should be aiming for (and then work a similar problem without!)

If you don't already know about it, there's an AWESOME graphing program at www.geogebra.org. It's free (open source, actually), runs on anything that has Java installed, and very useful as a visual aid.
 
Make sure to learn the concepts. If you know the concepts you can derive what you need at a later time. Understand the basics - what areas under a curve represent, what an integral is physically doing in terms of summation.

In my experience becoming intimate with why your are doing something will wet your appetite for understanding how to do something, which will, in turn, increase your overall comprehension and memorization anyway - otherwise bring a pillow.
 
Well, the first thing I'll say is don't be too reliant on a calculator. I wasn't permitted to use a calculator in any of my calculus classes, only for homework. This was kind of a rude awakening for me, so I try and warn every first year calc student that asks me about the course. Also, brush up on algebra mostly, the trig stuff will be heavier in calc II (most likely!) and calc I will deal in limits and derivatives mostly. This means getting good with your algebra. You probably won't see an integral until the last unit or so and than it will continue on into calc II from there, so don't worry so much about that now. Another thing that helped me a little bit was a computer program called Maple, my teacher actually recommended it to us, and provided us with a link so I don't know if it costs anything for individuals, but it was great for checking my mathematics and graphing functions and such. Read the book and most importantly practice problems daily. I was hesitant about calculus when I started too, but I absolutely loved it once the course got underway, so you may be surprised. Good luck.
 
As far as a ti-89 I don't understand what good that does you in calculus. A calculator can do the easy parts, if you understand the problem well enough to put it into a ti-89 you are fine. Just take calculus as seriously as you can, its the last course you will take that will get you an easy A.
 
I feel horrible today. I flunked the first calc. exam! It will be dropped, but I'm see a path of hardships. I did feel that i needed more practice, but on the calc. questions.
I hate math questions! They are bunch of wordiness crap that I can never understand. I wish they were more specific on what they want me to find. I rather deal with numbers, graphs, and formulas.
 
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kaos86 said:
... I hate math questions! They are bunch of wordiness crap that I can never understand. I wish they were more specific on what they want me to find. I rather deal with numbers, graphs, and formulas.

Newton invented the calculus to help explain the concept of "speed" and "acceleration" at any given moment in time; therefore, one is going to have to become comfortable with word problems in calculus because they are inextricably attached at the hip. :biggrin:
 
kaos86 said:
I feel horrible today. I flunked the first calc. exam! It will be dropped, but I'm see a path of hardships. I did feel that i needed more practice, but on the calc. questions.
I hate math questions! They are bunch of wordiness crap that I can never understand. I wish they were more specific on what they want me to find. I rather deal with numbers, graphs, and formulas.

Sorry to hear about your angst. I'll offer up some advice though: First, don't worry so much about the wordiness of the problems. Looks for key words and terms that you know. A good trick I like to use when a wordy problem (in any subject) presents itself is to read the problem once, than a second time but cutting out the details. That way I'm left with only the actual question at hand. Second, when I took calculus I had to know the formulas very well. Now, I've heard of some Professors letting students have a "cheat sheet" with formuli on it but mine certainly didn't. So if you have to know the formulas the best advice I can give you is to write out the formula and the proof a few times, and memorize them like anything else. The formulas are the single most important part of calculus, if you don't know them you will most definitely fail. And third, ask your teacher for the correct answers to the exam and try and do the questions until you get them right. Extra help/tutoring may not be a bad idea also. Good luck and practice.
 
kaos86 said:
IThey are bunch of wordiness crap that I can never understand.
As you do more math, you will discover that much of it is translating from English into mathematical objects. If you can't handle the translation, life will be hard. This is particularly true for applied math like Calc I, II and III.

Practice practice practice. Just reading the textbook is never enough.

Also:
https://www.amazon.com/dp/069111966X/?tag=pfamazon01-20
 
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Dembadon said:
Newton invented the calculus to help explain the concept of "speed" and "acceleration" at any given moment in time; therefore, one is going to have to become comfortable with word problems in calculus. :biggrin:

You are correct. I'm just in a panic mode right now because this will determine my goals as a theoretical physicist.
 
Sankaku said:
As you do more math, you will discover that much of it is translating from English into mathematical objects. If you can't handle the translation, life will be hard. This is particularly true for applied math like Calc I, II and III.

Practice practice practice. Just reading the textbook is never enough.

I will take your advice at heart. I will practice all through the days of my life. I might have to become an insomniac to reach my goals.
 
sEsposito said:
Looks for key words and terms that you know. A good trick I like to use when a wordy problem (in any subject) presents itself is to read the problem once, than a second time but cutting out the details. That way I'm left with only the actual question at hand.

Very good advice, I was doing bad because maybe i had that "panic" when i was taking the test and I felt i needed more practice. I need to manage my time with other classes i have.
 
kaos86 said:
Very good advice, I was doing bad because maybe i had that "panic" when i was taking the test and I felt i needed more practice. I need to manage my time with other classes i have.

That's one of the most difficult things about college -- for everyone, so don't worry. You'll figure out a method that works for you.
 
Some advice I offered in another thread:

Read the problem, as sEsposito suggests, then write down everything you know (known values/variables, relevant equations, unit conversions, etc.). You don't have to think about solving the actual problem yet, just write what you know. After you've done this, what is not known about the problem will seem much less intimidating and a great deal more manageable. :smile:

Do lots of practice problems as well, even if they are not a part of your homework and you'll be well on your way to becoming a professional problem solver.
 
kaos86 said:
Very good advice, I was doing bad because maybe i had that "panic" when i was taking the test and I felt i needed more practice. I need to manage my time with other classes i have.

Some of the best advice I was ever given regarding this issue is to start assignments the day they are assigned. You don't have to finish them, just start them. You'll find that they are easier to continue once they've been started, and you'll have a better idea on how much time you'll need to invest in said assignment which will allow you to use your time more efficiently.
 
Sorry about your troubles kaos86, it is unfortunate. Don't worry to much though, if you really are committed to being a life long scholar of physics a slight postponement in passing a Calc I class will not matter much.

If you are sure that you are dropping the class I would definitely suggest that, in your studies, you act as if you are still in the class. Keep practising and working on the fundamentals, so that next semester (or whenever you retake it) you will have a leg up and the confidence to do well.

Sometimes when I am working on a topic new to me in mathematics, I will spend upwards of 3 or 4 hours banging away at a single exercise until I learn how to arrive at a solution; and it is one of my most favourite things to do. You have to really want to know this stuff; I think success will be much more likely if you learn to love the subject and get some satisfaction in working out long complicated word problems. Good luck to you!
 
My grades waver from extremely mediocre to high in most math classes but the one way I stay consistently above failing any tests is that I always write out EVERYTHING I can think of that could earn me a mark... I barely passed one of my calc tests (I am in calc 2 right now) but I passed because I wrote out formulas and in one case I couldn't figure the answer out so I just derived it 3 times for the hell of it and got part marks.
 

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