2006-03-26T01:24:00.000-08:00

I cannot possibly do this by myself. That is why I provide this ePortfolio with links that can help me explaining these incredible subjects.
Starting from Finite Mathematics and Calculus, I got this website called, "Finite Mathematics & Applied Calculus Resource Page" by Stefan Waner and Steven R. Costenoble has the best and most complete information about Finite Mathematics and Calculus. For Differential Equations, "Introduction to Differential Equations" by Jim Tomberg and Lang Moore describes it very well and thorough. At last, for Linear Algebra, I include PDF-file-lecture-notes by Keith Matthews, "Elementary Linear Algebra."

Finite Mathematics

Finite Mathematics is the basic of all the mathematical functions and equations ever exist. Here is where we first learn about "functions" and we give it a name: F(x) or F(t). Those names differ the variables we are using (between x or t). However, since in Finite Mathematics we use xy-axis, then our "equation" usually is:
y = F(x)
as we set y as a function of x. As we get more advance in this course, we can not only find y having x given, but we can also find x, given y.

Calculus (Single Variable)

I can never forget what my former instructor, John Sawka, told me that "straight lines are simpler than curvy lines." This is, basically, the main idea of Calculus. In Finite Mathematics, we learn about functions. In calculus, we learn about the rate of change (or derivative) of a function. To do this, we approach it by looking at a curve and say that the curve is made of a lot of straight lines changing its slope every time. As I have said in the introduction of this ePortfolio, we cannot get an actual value of velocity at every moment because then, the time will be zero and the velocity will also be zero as we approach the actual number. Instead, we use estimation. In this course, we are introduced to a "limit function"; a function that estimates the value of the rate of change of a function extremely closes to the real value. This is where derivatives and integral originated from.
In real life, we can see this clearly applied on Physics. We know that a moving car has a position (x) which changes every time. The rate of change in position is called the velocity (v). If the velocity is changing over time, the rate of change is called acceleration (a).
As we move along with the course, we see that we can also get the anti-derivative (or integral). Using integral, we can find the velocity of a car, knowing its acceleration; we can find the position of the car, knowing its velocity.

Calculus (Multivariable)

As we get more advanced in this course, we are not only looking at a function with one variable. x is not only the variable for y. Instead, we are looking at x and y as a function of z, for instance. However, just as the course title suggests, the variable can be more than two. The variable can be infinitely many, and the functions become imaginary (since we cannot picture it anymore in three dimensional worlds).
Still, in this course, we are using derivatives and integrals. However, since there are more than one variable, than one derivative or one integrals will not be enough. Hence, we get the terms "partial derivatives", and "double/triple integral".
This is a very interesting field of study, because we have to work with vectors (a quantity specified by a magnitude and a direction). This course is very crucial for people with science majors, such as Physics, Chemistry, and Biology.

Differential Equations

This subject is very similar to Calculus, except for the fact that here, we are learning about deeper differential equations. Its applications are, basically, similar to the applications of Single and Multivariable Calculus. However, here, we also learn how to build "models".
Some differential Equations, which were not solvable, using Calculus, are now solvable. Just like before, first we try to find something from one thing that we know as variable, and then we try to find the variable form the result. In Differential Equations, we are not trying to find derivative nor integral anymore. Instead, we try to get y from its own derivatives (y', y'', y''', and so on).

Linear Algebra

Linear Algebra is the most fascinating mathematics class I have ever taken. If you are still in algebra class, you will not have imagined that we can solve a great number of equations with a great number of variables using a single matrix. And if we can use a calculator, we can solve those equations in a matter of seconds.
This is really fascinating, moreover, in the field of Economics and Accounting. Linear Algebra solves the thousands of numbers in the economics and solve the inter-relation between them all. It is proven that even a social science subject such as Economics, itself, actually has interdependent between its variables (price, human behavior, money cycle, etc.). Linear Algebra also can be applied in computer system and programming. Linear Algebra discusses how to make this letter come out on the screen, how to make it italicized, how to make it bolded, etc. Using matrix transformation, it is not hard to do.

Mathematics makes life a lot easier. In science field, or in social field, everybody has to know something about mathematics. In arts, I believe, music is one of the arts that highly related to mathematics.

-Loire-