Is anyone good at math?

[Oxylepy]

So I finished going through Calc 2 for Dummies in preparation for my next semester and started working on reading my Physics for Sci/Eng book, then got extremely bored (because I'm taking 1 which assumes I havent been through Calc 1 yet, so a lot of it was algebra with really basic calculus) and scounged around to find my Differential Equations for Dummies book. Anyway, I just got a major shock when going through it: I have no idea how to work with Logarithms...

Anyway I'm gunna spend some of tomorrow figuring them out since it seems all I knew was that e and ln were opposites ~_~

But if I run into more issues I was wondering if anyone around here knew advanced calculus concepts and could help me out (you know when I go on to second order diff eqs and end up with my brain running out my ears).

[claytonfaulkner]

Just calm down, no need to worry now. Learn it as it comes..

How basic are you talking about? Like ln(e^(x))=x?

I used purple math a lot for algebra, it helped more than anything else.



Then again when I learned factoring in 9th grade I assumed I would never use it again and didn't really learn it.... I'm taking cal 2 now, we still use it... and I'm still no good.

[Oxylepy]

How is Calc 2? I have like a month and a half til the fall semester and when I start taking it. While working through the Differential equations it all seemed easy then the guy ended up doing some substitution and various things I know from working with exponents is how it's done but I never remember to do it that way with logarithms.

He went from 1/x dx = (v^3)/(v^4 + 1) dv, integrated both, ln x = ln(v^4+1)/4 +c.

That was easy, but then he chose -ln k = c switched the sides the c was on, got ln kx (I would have NEVER thought of that) and multiplied each side by 4 and got v^4 + 1 = (kx)^4 then he substitutes back in for v and solves for y

I didnt even know that a ln x = ln x^a or that ln x + ln k = ln k

So that just took me by surprise and took forever to figure out all he did. I picked up on some rules, but... Jees, I knew I was bad with logarithms, but had no idea I had almost no understanding of how they work.

[claytonfaulkner]

Remember the class will vary from state to state, school to school. So far its been nothing but integrals. Integration by parts, trig integrals, improper integrals, area between curves, volumes of revolution,and the last lecture was series, sequences, and the like.

There's been quite a few limit problems which I hate.

And do be honest, I've maybe done 5 diffrentials in my life, I think I had 2 questions on my. Cal 1 final involving diffs

[Oxylepy]

Yeah that seems to be what my class will be going over (went though the book itself before Calc 2 for Dummies) and by far the hardest thing I had to get my mind around was the concept of volumes (from integrals). I was stumped for about a month (from when I went though the chapter to about a week after I got Calc 2 For Dummies) and the functions they chose always seemed random, sometimes it would be one function inside another, other times it would be multiplied... it drove me insane, I couldnt see the logic and neither Calc 2 for Dummies nor my textbook really got through to me. Ultimately I sat there with all the functions in front of me (defined as some function of x as opposed to what they actually wrote down) and it ultimately dawned on me. It was all areas. If using an area function the change would be inside, if using a perimeter function the change was multiplied.

Anyway, it all ended up seeming easier than I was lead to believe it would be, it's kind of lucky that in highschool they made us do a project that involved something from calculus to explain to the class (this was in pre-calc) and while everyone else chose things I still havent seen (Fractals etc) I chose infinity, which ultimately included limits to as well as series/sequences/sets.

[kellysballs]

Well now I know who to ask when I am floundering in Calc 1 in the spring. The only thing I was good at in precalc was matrix's and factoring.

[rabernet]

Welp....count me out - you guys completely lost me at hello! It's been over 20 years since I cracked a calc book.

[Oxylepy]

You're perfectly set up for higher order Differential Equations then. Matrix operations are the only thing I dread, and go figure they rear their ugly heads again in Diff Eqs.

Personally I suggest grabbing the "For Dummies" series BEFORE you take the class. That way you have some idea of what you are going to deal with.

Calc 1 circles around: Graphs, Continuity, Limits, Derivatives, and introduces Integrals (both as anti-derivatives and the actual function)

Graphs/Continuity should be easy, just memorize the basic graphs and if you can factor (and remember when things arent continuous) you're fine with Continuity.

Limits are a fairly basic concept: As a variable reaches a number, what value will you get from either side of that number, but not at that number. Its like saying "okay what would y= when x=3 with the function (x^2-9)/(x-3)" since you can factor the x-3 out and get simply x+3 the answer would be 6. However limits dont need to factor it, pretty much you end up taking the values close to 3 (2.9 2.99 2.999 3.001 3.01 3.1) and figure out what you approach.

Derivatives just builds off limits and the slope function (change in y/change in x). You remember that, right? But what you're looking for is the slope at a point, instead of the slop over 2 points). Well instead of calling it y we call it f(x) and the change we want will be 0 (thus narrowing it down to a point), but since it's a limit we name the change as h. Thus we look at it this way:

Change in f(x)
-------------
Change in x

f(x2)-f(x1)
----------
x2-x1

the difference between x2 and x1 is h so x2-x1=h and x2 = x1+h

f(x+h)-f(x)
----------
h

Now we want this at 0 so we add the limit which would be "lim h->0" and that just goes before the function. Thus giving you the slope at some point (x,f(x)).

You'll do a few of these from the limit (which pretty much involve finding ways to cancel out the h), then you'll prove the various rules, then you'll just get handed the rules and your teacher will be like "haha, all you had to do was this all along "

Alright, so you work with harder and harder derivatives until you think your eyes are going to pop out from your brain swelling. Then you will get the concept down and be able to figure a derivative in your sleep.

Then you work with reverse derivatives which are called antiderivatives. Pretty much use the rules from before but just reverse directions (simple rules, it wont be that hard).

Then you will work with Summation Notation, which you probably already have some idea about. When you're done there your teacher will say "time to find the area under functions" and you'll get a bunch of stupid ways to do them involving limits at infinity and the sum of an infinitely thin rectangle with width (change in x) and height f(x). You'll be so good at drawing sigmas that you'll be doing them in your sleep. Ultimately you find out that these are called "Integrals" and you will find out that they are antiderivatives (usually).

That's the end, hope to do well on the final.

Then enters Calc 2, which was described before but is simply "Hey, we're going to work with integrals until you can do them on your toes, oh and we will throw in series and sets right at the end of the semester while you are panicking about your finals coming up.

But when you get done you cant just give up. You have now just spent an entire year of your life learning how to work with 2 dimensional stuff you never will, are you seriously going to waste a year of your life when 1 semester more will make it all worth it? Of course not. Now you work with multivariable calculus and if your school will let you/you want to go into science take differential equations at the same time.

Multivariable Calculus is simply 3 dimensional calculus and the concepts of working in 3 dimensions. And differential equations are simply a function, it's derivatives, some function involving them, leading to some answer. Your goal is to then figure out what the original function was that all those derivatives are derived from. Very useful if you are working in any science, or if you want to map human behavior/snake behavior/anything's behavior.

[WesleyTF]

Math is my jam.

I had fun in calc 1/2 and multi-v and diff eq are fun for applications to physics, but the apex (for me anyway) is linear algebra.

One thing I'd suggest is to get into working with a computer algebra system early and really know it well. All the higher maths you'll be taking will use it. I LOVE mathematica but most people find Maple much easier to start with and plenty of schools use matlab. Find out what the school you're going to be going to uses and work with that.

[mainbutter]

I'm not very fresh but I've done enough that I might be able to help you out with specific questions. Just post em and I'll see what I can do.