Calculus

[IYAAYAS]

This is my first vanity post, I wasn't going to post this until I realized there is a "vanity" option under topics. Anyone care to help out a freeper?

I'm about to begin the three part calculus sequence followed by differential equqations and I'm starting to get nervous. I would like advice from those who are there or have been there.

I am an adult student who has decided to return to school, I have re-taken trig and precalculus (both A's)as a refresher.

I'm looking for any kind of advice, general or specific. What things are inportant for the study of caculus? Should I start to memorize certain formulas now? If so, what? Is threre a certain method you used to visualize concepts? anything really...

[Paul L. Hepperla]

I remember it well. Calc I was pretty easy and set up a baseline. Then, people generally fell into two categories. Those that do well in Calc II will do well in Diffie-Q's. Those who do well in Calc III will do well in Advanced Math (class after Diff-Eq's).

My only advice...do the homework problems assigned every night religiously! If these classes, if you don't do the homework, you'll suffer miserably. It's a mathematical process that rules in these classes and homework helps you nail down the process.

There are no easy answers in these classes no matter how many times you write down, if x=0 then the equation fits.

[Ipinawetsuit]

No big deal.

No need to memorize anything yet, if ever. I never liked math too much until calculus. Yes, it can be hard, but once you realize that it is more art than science, it gets really interesting.

Most of the formulas you may have to memorize are probably shown on the inside covers of your books, which begs the question - "why memorize them?"

The first thing you are going to do is take any old quadratic equation (f(x)= Ax^2 + Bx + C) and learn to take the derivative the hard way... It sucks and takes way too long. Then you learn the easy way (see the art part?). Then you realize that the quadratic shows "position" as a function of time (keep in mind that f(x)=y in algebraic terms, so the equations are easily graphable and a graphic calculator is VERY helpful), the first derivative shows velocity (remember y=mx+b from algebra?), second derivative is accelleration ("m" AKA the slope of the first derivative), third is impetus (that jolt you feel when the rollercoaster just gets started...).

Then you start to to integrate... Even more fun

Just keep in mind that calculus is nothing more than a mathematical model of things that change over time... it is not the truth, just a model or tool to explain... Keep applying it to real world examples and it can be fun...

Best of luck.

[jimt]

Calculus and differential equations are extremely useful in understanding how things work in physics and engineering.

My advice - find a good prof with a good book. My buddy had a Chinese grad student who was unintelligible and wrote with both hands simultaneously (no joke). I had a guy who made multi-colored diagrams on the board, spoke logically and intelligently, and illustrated the uses of calculus clearly.

Of course, when I had diff eq, I had three losers in a row. I gutted out the last one, learning virtually nothing, but getting a passing grade. Two years later, in the first week of a course in automatic control systems, I learned ten times what was taught in the stupid diff eq course, and it's stuck. When you get to diff eq, check out Laplace Transforms. The light will come on, especially when you find out the math department's vaunted "classical solutions" are virtually worthless.

[RightWhale]

English speaking profs

Important in the first few weeks. Otherwise it will be middle of the semester before you understand the prof, and that is fatal in a math class.

[Treebeard]

One more like that and you're going to end up in L'Hopital...

[Indy Pendance]

Exactly, sometimes the group can figure out a more difficult concept. Calc was a blast once you understood integrals and differentials. My first year prof was a theorist, (and blew many theories on the blackboard, which of course we copied digilently, only to find out a mistake was made 3 blackboard previous) and if we would have learned those two concepts first (actual problem solving) instead of the theory, the theory would have been much better understood later in the semester. Once I got to the actual problems, all the bells and whistles went off, it all clicked.

[DannyTN]

From my experience...

If you advance to "Differential Equations with the imaginary number 'i'"

Date the really cute girl who wants to study with you. Do not act surprised if she doesn't know what a multiple is, because she is going to blow you away when she starts using set theory to solve some of this stuff.

But you have at least three college calculus courses before you get to that.

[RonHolzwarth]

There is a small car, going up and down the hills on the mountains, and you are viewing it FROM THE SIDE!!!

the road represents the graph of the equation, so

WHEN are the headlights EXACTLY HORIZONTAL???

at the tops and at the bottoms! (when slope is = ZERO!)

what is the angle of the headlights, as the wheelbase of the car is approaching zero? that is the SLOPE at that point!

[headsonpikes]

Then you start to integrate...even more fun.

And you thought I made a bad math joke!

;^)

[RightWhale]

the math department's vaunted "classical solutions" are virtually worthless

That's a fact. Acquire a variety of calculus texts from used book sales. Even something simple as the Fundamental Theorem of Integral Calculus will have a different expression in each text. Some are practical, some aren't.

[FourPeas]

I agree with a lot of the above: relax, study, good prof, practice, study group AND how incrdibly sensible and useful Calc is. I found I did a lot of graphing, so if you're at all rusty in sketching geometric figures/conic sections, bone up on that. Also, if you're like me and prefer to graph on graph paper you might look for some good sales. If you've not used engineering paper (sometimes called engineer's pads) before take a look. For my money it's the most useful graph paper.

[PoorMuttly]

Muttly want Calculus !

Muttly now have nice terrarium (aquarium ?) for new Calculus to run around in, and maybe rear its young.

What things are important for the study of caculus?

Can Muttly get a breeding pair ?

[FourPeas]

*groan*

[HOYA97]

Selecting the correct teacher is important.

This is absolutely the most important thing to learning Calculus. This is especially important as you learn second and third year calulus. Some of these professors are true genius's but they have issues with getting the information from their brain to their mouths. Trust me on this one!

[martin gibson]

Calculus, differential equations and trigonometry are just linear manifestations of the patriarchy!!!

What's really important is how you feel about the process...

[Pest]

As an engineer, I took all the calculus classes. Two things:

1) Do as many problems as possible.

2) Pick up an HP48GX calculator. It may not be allowed during exams, but it's a great way to check yourself.

[Fudd]

I'll just echo what most of the other posters said.

Do the homework.

Do the practice problems (I had a prof who copied the test problems verbatim from the text, made test-taking easier).

Do the homework.

Put it in terms of real-world things (that's how I figured it out). If I know my car's velocity over time, I can differentiate to find its acceleration, or integrate to find its position.

Do the homework.

Have fun!

[Mudboy Slim]

"To: IYAAYAS
11 posted on 11/03/2003 2:55 PM EST by IYAS9YAS"

Y'all related?!

MUD

[EERinOK]

I am about one year out of the Calc 1,2,3 + Diff. Eq. series, and also an adult (38 yrs ole) going back to college after a long acedemic layoff.

I did not take pre calc trig and algebra over again and made all A's in the calc and a B in the Diff eq.

my keys were

1)go to class.
2) listen and learn, do not take much notes in class unless its a particular example you are stuck on. it's in the book. just jot down basics, and topical things. there was an inverse correlation to my volume of notes taken and comprehension. just know what material you are responsible for.
3) for about every hour in class, study by just working problems for a good 2 hrs. double that in test weeks.
4) take advantage of help where/when available. i found that I could waste alot of time (hours) on one problem if i let myself. move on, and get help occasionally. thee seem to be more of those resources available tody than 20 years ago too.

that's how i got thru them.

not to get you overconfident or anything but i found college level math and science much easier second time around. much i can attibute to maturity and focus, but i also sense that today's professors are less apt or pressured to make things difficult than they were 20 years ago. in fact, this time around, i see them going out of their way to be lenient to a level I often think is a bit ridiculous.

[BMiles2112]

This is pretty much how I learned it. My Calc class bored me right from the start with theories of reducing "delta X" to 0 and things like that. I took a Calc based Physics at the same time, and the prof opened with showing the integral as the area under the curve, the derivative as the slope of the line, etc., and it made perfect sense. He used the simple y= ax^2 + bx + c and showed the r-ship between displacement, velocity, acceleration, and a thing called "jerk". Calc isn't only used to model change over time, but it's the easiest way to make sense of it.