## Any good calculus places to start?

Hello, I'm new here! Before I ask, I shall introduce myself. I am Lazernugget! I am probably younger than most people here, yet I am dedicated to sciences and mathematics, so I joined. I am young, as I said, But I am reading a thick trigonometry book, understand very advanced math, (But not all the symbols like: $$\partial$$ or $$\int$$ So) I may not get all the formulas you may show me. I know a BIT of calculus, but that is where my question come in:

Would you mind showing some basic calculus functions, and then explain it for me? I may ask for more advanced ones afterwords. Then I am curious to know what these are for:

$$\int$$ $$\oint$$ $$\sum$$ $$\nabla$$ $$\partial$$ and $$\otimes$$ are? Then use them in a simple mathematical equation.

Thanks! Bye!
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 Quote by Lazernugget Hello, I'm new here! Before I ask, I shall introduce myself. I am Lazernugget! I am probably younger than most people here, yet I am dedicated to sciences and mathematics, so I joined. I am young, as I said, But I am reading a thick trigonometry book, understand very advanced math, (But not all the symbols like: $$\partial$$ or $$\int$$ So) I may not get all the formulas you may show me. I know a BIT of calculus, but that is where my question come in: Would you mind showing some basic calculus functions, and then explain it for me? I may ask for more advanced ones afterwords. Then I am curious to know what these are for: $$\int$$ $$\oint$$ $$\sum$$ $$\nabla$$ $$\partial$$ and $$\otimes$$ are? Then use them in a simple mathematical equation. Thanks! Bye!
Welcome to the PF. This is a reasonable place to start:

http://en.wikipedia.org/wiki/Calculus

And there are links at the end out to other sources of information.

 Ah yes, thanks, I'll try, but Wikipedia can be...long drawn... While I try, could someone explain the symbols I typed above?

## Any good calculus places to start?

It's awesome to see someone so motivated at such a young age. I hope that enthusiasm stays with you. Regarding your question, there are a plethora of resources out there for learning basic calculus. If you prefer learning from a textbook, I like M. Kline's "Calculus." Of course, there's also the gold standard: Stewart's "Calculus." There are also youtube videos and lectures posted on itunes you might want to check out.

Regarding your next question on the specific symbols: the first and the third are something you'll see in your study of basic calculus. The next second, fourth and fifth you'll see in more advanced calculus and the last is the tensor product operator and you probably won't see it for quite a while. Unfortunately, without knowing calculus, it would be impossible to really describe those symbols.
 Recognitions: Science Advisor $$\int$$ Integral. An infinite sum. $$\oint$$ Integration along a closed surface. $$\sum$$ Summation. $$\nabla$$ Del, a derivative operator. $$\partial$$ Partial derivative. Distinguished from a total derivative in that you only differentiate with respect to one out of many variables. $$\otimes$$ Tensor product. If none of that makes sense, then good it shouldn't. Really, you shouldn't focus on the symbols though. What's more important is that you understand what's behind them, so just be patient and you'll get there eventually.
 Sooo...um, Wouldn't an infinite sum just be infinity? (Integral) How do you use those symbols? Thanks...

 Sooo...um, Wouldn't an infinite sum just be infinity? (Integral)
http://www.msstate.edu/dept/abelc/math/integrals.html

 Quote by Lazernugget Sooo...um, Wouldn't an infinite sum just be infinity? (Integral) How do you use those symbols? Thanks...
An integral is just another way of finding area. i.e. the space underneath a curve/line/whatever. it's useful for more advanced calculations like volume of a solid with a weird shape and many, many more applications.

I wouldn't worry too much about these things. Math builds up to that stuff. You'll learn it eventually through practice and application problems.

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 Quote by Lazernugget Sooo...um, Wouldn't an infinite sum just be infinity? (Integral) How do you use those symbols? Thanks...
It's good to know the difference between and integral and an anti-derivative. An anti-derivative is an indefinite integral thus you aren't finding the area, definite integral has a boundary and therefore you are finding the area.
Anti-derivative $$\int f(x)dx$$
Integral: $$\int_a^b \ f(x)dx$$ bounded by $$a,b$$. Finding the area is described by the fundamental theorem of calculus:
$$F(b)-F(a)$$ where $$F(x)$$ is the integral evaluated at the point $$x$$
Del Operator ($$\nabla$$): $$\nabla = \frac{\partial}{\partial x} + \frac{\partial}{\partial y} + \frac{\partial}{\partial z} +...$$
Partial derivative ($$\partial_{x...n}$$): Is an operator in multi-variable calculus in which you differentiate with respect to one variable and treat the others as constants.
Tensor Product ($$\otimes$$): Don't worry about this right now as it shouldn't be learned until you have a grasp of the other branches. A tensor would be identified by $$T_{ij}$$.
Summation : $$\sum$$ is essentially a series, what I mean by that is if you have $$\sum_{n=1}^{3} 2^n = 2^1 + 2^2 + 2^3 = 14$$

I almost forgot! This is a great place to start learning maths: www.khanacademy.org

 Quote by Lazernugget Sooo...um, Wouldn't an infinite sum just be infinity? (Integral)
You have to study the basic stuff before this can make sense. In short, an integral is an infinite sum of infinitely small numbers. Look at the Riemman sum method for approximating the area under a curve. You can think of integration as a Riemman sum with infinitely thin rectangles.
 To understand calculus you need to understand the problem faced without it. Let's say you have a graph of a straight horizontal line between two points on the x-axis. You know how to calculate the area under it because it's just a square. You can do this as well for a slanted line, but you don't know how to do this for curves. It's very difficult to do this geometry without calculus to find the area. So instead you put a bunch of little squares under the curve to try to approximate or roughly guess how much there is under the curve by adding up the area of each square. The squares don't fit perfectly under the curves because they have jagged edges, so you put slimmer squares under it and try to fit it until you do it so much that the slim squares become so thin that it just looks like the squares filled the curve perfectly. These very-very slim squares are infinitesimally thin so you need an infinite summation of all of these squares and this is called the integral. The other fundamental problem is the slope of a curve at a spot at only one point. You know how to calculate the slope between two points on a curve, but when you put these two points closer and closer you can't calculate them because eventually the difference between them is zero and the formula for slope no longer works. So instead you keep calculating what the slope is when it is really really close and you find the a general trend to do this and you call it the derivative. These derivatives can be proven with limits but I don't want to get into that. The signs for these the derivate is the infinitesimal change in x over y (which is the slope of the regular line if it wasnt infinitesimal) known as $$\frac{dy}{dx}$$. The integral is the slim width of the square which is the $$dx$$ times the height of it which is the function evaluated at that point in x and from the start to the end of the sum from a to b (on the x axis) which is $$\int_{a}^{b} f(x) dx$$. Derivatives give the slope of the tangent line and integrals give areas of curves. If you have the infinite sums of the infinitely small what do you get? The integral. It turns out that these two concepts, the derivative and the integral, are related by the fundamental theorems of calculus. Now that you understand the problems I hope you can start reading a calculus book. Wikipedia is not a good place to start. Seem interesting?
 Pauls Online Math Notes has been very helpful in my quest to master calculus. His Calculus I notes are available HERE. I believe somebody else on this thread mentioned khanacadamy.org, but I would like to verify that person's claim that it is a valuable learning tool. I understand where your curiosity comes from with all these new symbols. I was thinking the same way just a few months ago. I wasted probably a month just trying to figure out what all the symbols meant rather than learning what they mean and how to use them one at a time, which is what I have been doing these past few months. Comparing the two study strategies I've used, the latter has been much, MUCH more effective for me; and I assume it would be more effective for most individuals also.
 Recognitions: Homework Help Science Advisor it takes a long time just to understand any one of the symbols you wrote down. You could spend almost a lifetime just on the integral. I am 68 years old and still studying its basic properties, (and it is not my specialty). Just find a book you can understand and start in. Trigonometry is one of the hardest subjects to do well in the beginning since even defining the basic functions cosine and sine requires a function of arc length in terms of x and y coordinates, and then inverting it. This process cannot be done carefully until one has integral calculus in hand, so in a sense trigonometry is more sophisticated than calculus, and comes later. Elementary presentations of trigonometry necessarily do things in an imprecise way. after you have had calculus and learned to make sense of "infinite sums" you can define cos(x) = 1 - x^2/2! + x^4/4! - x^6/6! ±....... which also shows why the function is "even".