Tag Archives: Calculus

Numerical Integration Please!

If you read my introduction, you probably already knew which lab I would pick. This lab is talking about Integration. It explains different way we can integrate, such as: Riemann Sum (Rectangle), Trapezoid Sum (Trapezoid, and Simpson’s Rule (parabola (dotted)). Integrations help us to calculate the approximate area underneath a given curve.
A question that will come up while working on this lab may be about comparing the few integration techniques listed previously. We will also be working with the difference of left hand, right hand and midpoint integration.
The reason I would like to work on this lab is because I have taken two and half calculus classes working with integrals and I would like to see if this opens my mind more to what exactly we are doing when we integrate.

Samantha Intro For Funsies

I am Samantha (obviously). I am only three and a half semesters away from graduating with my Math Ed degree. Many of my current classes are not “new” to me. We are working on more of the teaching aspect. However, I am in Calc 3, that stuff is new. I love Calculus. I would rather not teach it, but I love working out the problems. Currently we are working with Integrals again. Integrals would be in my list of “Favorite Math Topics”. If you would like to know all about integrals, Wikipedia knows it!….: http://en.wikipedia.org/wiki/Integral
This is what they look like:
$\int_a^bf(x)dx$
In Calc three we are working with multi-variables, so they look like this:
$\int_a^b\int_c^dF(x)dxdy$

Fun, right?!

Marc on why Calculus is the Bomb

My name is Marc and I am a math student at Boise State University in Boise, Idaho which is best known for its potatoes as well as recreational opportunities. One area of mathematics that I enjoy learning and studying about is calculus. Calculus is the study of limits, derivatives, and integrals which are useful in studying continuous functions. Limits play a massive role in a variety of fields ranging from economics to engineering, and limits help to define derivatives. Derivatives are functions that describe the slope of a continuous function. The opposite of a derivative, an integral, can be used to find areas under curves in two dimensions as well as volumes in three dimensions. All of these tools can be used for optimization purposes which are significant in practically any field.

For more information about calculus, you can visit the Wikipedia page here.

Because the derivative represents the slope of a function,  the derivative of a function is thus calculated with this idea of change in distance in mind. The equation associated with the derivative is:

$m=\lim_{h\to 0 }\frac{f(a+h)-f(a)}{h}$

Notice that this equation represents a change in distance on a graph. Slopes are meant to represent changes of functions and functions represent a variety of trends! For example, the derivative of a position function in physics would produce a velocity graph which represents speed, or how the distance is changing over time. The derivative of a velocity function would give an acceleration function which reveals how the speed is changing over time. Pretty cool, isn’t it!?