1545 Words7 Pages

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*…show more content…*

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*…show more content…*

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

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

Related

## The Role Of Numeracy In Literature

989 Words | 4 PagesMany core elements of numeracy associate with others across the literature. They include using mathematical knowledge including concepts, skills and problem-solving strategies (Gieger, goos & dole). The role of numeracy technician foregrounding mathematical knowledge and understandings (Forrest). The dispositions of confidence, flexibility, adaptability, attitudes, self-perception and willingness to use these skills to engage with life related tasks, firstly as a prerequisite for all learning. (Gieger, goos & dole) (Scott)(Frankenstein).

## Thermodynamics: Concept Of Variational Calculus

852 Words | 4 PagesVariational Calculus is the branch of mathematics concerned with the problem of finding a function for which the value of a certain integral is either the largest or the smallest possible. That integral is technically known as a functional. Many problems of this kind are easy to state, but their solutions often entail difficult procedures of differential calculus. In turn these typically involve ordinary differential equations (ODE) as well as partial differential equations (PDE). The isoperimetric problem —that of finding, among all plane figures of a given perimeter, the one enclosing the greatest area —was known to Greek mathematicians of the 2nd century BC.

## Mathematical Proof Research Paper

1309 Words | 6 PagesI chose this topic because it helps answer several concerns that arise at attempts to teach and to learn about proofs. Through a diagram that made the statement obvious, the result may be sensed or discovered intuitively. Hence it helps the viewer internalize the idea by gaining an insight into why the idea was correct, and it makes more discernable relationships between parts or parameters of a mathematical statement. Proof without words can be one step proof, or even a proof that does not start with fundamental axioms. It is very effective not only for learning mathematical statements, but also for developing a feeling for mathematics as a discipline.

## Rigid Constraints: Goal Programming Models

930 Words | 4 PagesGoal Programming Models SML304 Nikhil Sahu 2011CS10237 Goal Programming is a optimization methodology where there are multiple, probably conflicting goals that need to be achieved simultaneously. Rigid Constraints Goals Goal programming formulations do not contains inequalities. Every constraint is written as an equation. We introduce a extra non-negative variable to convert a inequality into a equality and that is called a slack or surplus variable. Thus any linear programming problem can be converted into a standard form: Max c1x1 + c2x2 + ........ + cnxn subject to a11x1 + a12x2 + ........ + a1nxn = b1 .... .... .... am1x1 + am2 x2 + ........ +

## Correlation Analysis: Nt1310 Unit 6 Assignment 1

908 Words | 4 PagesError of Kurtosis .468 .468 The table shows that the in the data set, the GPA variable is a left skewed distribution of -.053 and a left kurtosis of -.811. The final variable indicates that the left skewed distribution stands at -.334 and a left kurtosis of -.334. Section 3: Research Question, Hypotheses, and Alpha level Research Question: Is there a relationship between the performance at the GPA and the final? Null Hypothesis: There is no difference between the GPA performance and the final. On the Asymptomatic significance test, the significance level is 0.05.

## Case Study: The Leggett-Garg Inequalities

1480 Words | 6 PagesThis observation leads to the clumsiness loophole (see section 2.2). \subsection{Correlation Functions} These assumptions lead to some properties of correlation functions $C_{ij}$, essential for the proof of (\ref{LGI}). Consider firstly their definition: Where $Q_{i}$ is the value of a dichotomous observable measured at time $t_{i}$, and the joint probabilities are obtained repeating the experiment. Postulate 1 provides that Q(t) is a well defined quantity for every time t, even for times different from $t_{i}$ and $t_{j}$. Thus it is possible to define a three-time probability and to obtain $P_{ij}(Q_{i},Q_{j})$ as its marginal, for notation simplicity set $i=1$ and $j=2$.

## Essay On Significant Figures

712 Words | 3 PagesHowever, there are three classes of zeros: leading zeros, captive zeros, and trailing zeros. Leading zeros, which precede all nonzero integers, such as in the number 0.0071, are not significant. Captive zeros, which are zeros found between nonzero integers, such as in the number 2001, are always significant. Trailing zeros, which are found at the right end of a number, such as in the number 7.0, are only significant if there is a decimal point. The rules of significant figures, along with measurements and calculations, are absolutely necessary for

## The Accidental Universe: The World You Thought You Knew '

461 Words | 2 PagesThe book is related to science because it discusses a lot of physics, science, math, and some psychology. The psychology part is mostly related to the physics and science components, because Lightman discusses what drives us to find the answers to questions about the universe and the world. Most of my favorite parts of the book are the sections where he discusses math and symmetry, and how math can be applied to practically anything in this universe, and beyond this

## George Bole's Theory

700 Words | 3 PagesOperation can be a conjunction or a disjunction; and not only propositions, but also the result of combinations, are true or false. This means they can be expressed by a binary system: true or false; Yes or no. The binary mathematical system is a numerical system mostly used in computers. Computerized systems consist of magnetic cores that can be started or stopped; the numbers 0 and 1 are used to represent the two possible states of a magnetic core. The methods of logical calculation of Boolean algebra have come to constitute the "intelligence" of many everyday objects such as engineers design circuits for personal computers, calculators, CD players, phones and a lot of other types of electronic products, but do not enable them

## The Riemann Sphere

1045 Words | 5 PagesThis equation gives us the point P(A) on sphere S corresponding to point A on the complex plane Z. The general equation for finding point (a,b,c) on S corresponding to point (x,y) on Z which is given being (Proof 2) Another way of looking at line L would be by connecting point ∞ to point P(A) in figure 3. Line L can be defined as: (University of Oxford, 2012) This is the same line L as in the first proof but in a different perspective that will help in explaining the next proof. The vector v, (a¦█(b@c-1)) is the vector used to move from point ∞ to point P(A). This can be found by subtracting the coordinates of point P(A) by the coordinates of point ∞.

### The Role Of Numeracy In Literature

989 Words | 4 Pages### Thermodynamics: Concept Of Variational Calculus

852 Words | 4 Pages### Mathematical Proof Research Paper

1309 Words | 6 Pages### Rigid Constraints: Goal Programming Models

930 Words | 4 Pages### Correlation Analysis: Nt1310 Unit 6 Assignment 1

908 Words | 4 Pages### Case Study: The Leggett-Garg Inequalities

1480 Words | 6 Pages### Essay On Significant Figures

712 Words | 3 Pages### The Accidental Universe: The World You Thought You Knew '

461 Words | 2 Pages### George Bole's Theory

700 Words | 3 Pages### The Riemann Sphere

1045 Words | 5 Pages