Multivariable Functions In Real Life Essay

SINDH MADRESSATUL ISLAM

UNIVERSITY

DEPARTMENT OF COMPUTER SCIENCE

FIRST YEAR

2nd SEMESTER

GROUP 2-A

NAME: AHTIQA TABASSUM

ROLL NO.: 15SBSCS05

SUBJECT: MULTIVARIABLE CALCULUS

SUBMITTED TO: SYED AZEEM INAM ASSIGNMENT: 01

Q #1 Find any ten (10) examples of multivariable functions from the real life or computerscience.

Examples of Multivariable Functions from real life and Computer Science:

1. Differential equations and multivariable calculus are both very important in computer science. The reason you won't find then in an undergraduate CS degree is that a BS in CS prepares you for a certain level of programming. That level isn't very high. That is not to say that someone with a BS in CS is not a skilled programmer. There

The set of pairs (x, y) such that f (x, y) = c is called the level curve of f for the value c.

For example, the function f defined by f (x, y) = 1 for all (x, y). (That is, the value of f is 1 for all values of x and y.) The level curve of this function for the value 2 is empty (there are no values of (x, y) such that f (x, y) = 2) and the level curve for the value 1 is the set all points (x, y).

Level surface:

For a function of two variables, above, we saw that a level set was a curve in two dimensions that we called a level curve. For a function of three variables, a level set is a surface in three-dimensional space that we will call a level surface. For a constant value c in the range of f(x,y,z), the level surface of f is the implicit surface given by the graph of c=f(x,y,z).

Example:

Now, we look at the function f(x,y,z)=10e−9x2−4y2−z2. Even though we can't plot the graph of f(x,y,z) (without using four dimensions), we can still visualize the behavior of the function by plotting its level surfaces. We simply plot f(x,y,z)=c for c between 0 and 10. (Note that f(x,y,z) always lies between 0 and 10. The argument of the exponential is always negative or zero, so the value of the exponential is always between zero and

Mathematics helps counting. It helps measuring. It helps comparing things. Addition, subtraction, multiplication and divisions are the basic operations of the mathematics, through which we can define and develop many more operations suiting our practical situation. Some people describe mathematics more of a language in which every symbol and every combination has precise meaning which can be determined by application of logical rules. This language can be used to describe and analyze anything in the universes. This tall claim about mathematics will not appear all that far-fetched when you consider that all the wonderful things that are done by computers today is are done using computer programs that ultimately use just two symbols that are equivalent it the numerals 1 and 0 of mathematics.

Calculus is the branch of mathematics that deals with rates of change and motion. The foundation of Calculus is the limit. From there you learn the derivative and integral. The derivative is used to find an instantaneous rate of change. And the integral is used to find the precise length of a curve and the area under that curve. It's not too hard if you have a strong base in algebra and