## Environmental Science Homework Help

All is connected…. No one thing can change by itself.

-Paul Hawken

The above quote isn’t by any mobile company; it is all about our relationship with Nature. In this high speed technological world we hardly get time to think about environment. So this is just to refresh our connectivity towards our Nature.

A thatched house with a chimney, a big lawn with a tree, birds and cows around. Something like this can be seen only in our dream. But this is what we drew in our childhood. Once Nature was a part of our life, but now it’s part of our children’s studies. We have a separate subject as Environmental Studies to understand our nature.

We all must learn to balance our technological growth with our environment and our technologies must also be invented in such a way that it does not cause any harm to our environment. Today’s educational systems are offering a wide variety of courses to safeguard our nature as well as there are special programs to create awareness among the public. Let’s put little more effort to give a beautiful environment to our future generation.

We have our environmental science homework help specialists for students to regain their interest in the subject.

## APPLICATION OF MATH IN PHYSICS AND ENGINEERING

Mathematics is a branch of science. It can also be considered as a branch of art as such it is an interesting branch of knowledge.

Mathematics was developed by early mathematicians and ancient Greeks Roman’s, have contributed much to mathematics. The number system was developed by Romans. Zero was invented by the Indian mathematician Aryabhatia. The various branch of mathematics are algebra, geometry, trigonometry, differential equations, real analysis, complex analysis etc.

Many of the physical system are converted by either ordinary differential equations or partial differential equations as such a clear knowledge of this is essential concepts to solve physical problems.

For example simple harmonic motion is a physical process which is governed by a second order differential equation. The independent variable is time and the dependent variable is the space variable displacement. From the solution of this we conclude that wave motion is periodic.

Many oscillatory motions are generally best described by simple harmonic motions. The motion of a body in a restricting medium is described by a second order differential equation in which the first order derivative is multiple by a constant called damping co-efficient.

The invention of vector calculus finds interesting application in electromagnetic induction. The vector differential operation gradient, divergence and core are applied in Maxwell’s equations.

Mathematics finds interesting applications in engineering. For example Laplace transform is applicable in electrical engineering. The concept of Laplace transform of a function and its inversion finds interesting application in circuit analysis.

The concept of z-transform finds interesting application in finite element analysis. Difference equation plays a dominant role in describing the state of a physical system. Various techniques were developed in finding the inverse function of a z-transform.

The concept of partial difference equation was much useful in solving so many boundary value problems; the concept of green’s function is useful in expressing the solution as an integral.

## Mechanics

Mechanics is a branch of physics as well as mathematics. It is divided in to two branches dynamics and statics. Dynamics deals with the bodies under motion and statistics deals with the bodies under rest. The basic concepts of dynamics are given below.

**Velocity:**

The rate of change of displacement is called velocity.

**Acceleration:**

The rate of change of velocity is called as acceleration.

Newton’s law of motions:

**Law 1:** Every body continues to be in its state of rest or of uniform motion unless an external force acts to change its state of rest or of uniform motion.

**Law 2**: The rate of change of momentum is directly proportional to the external force acting on it.

**Law 3:** To every action there is an equal and opposite reaction

The equations of motion are given as below.

If ‘u’ is the initial velocity, ‘v’ is the final velocity, ’t’ is the time, ’s’ is the distance travelled in ‘t’ seconds, ‘a’ is the acceleration, then the equations of motion are

** V=u+at
s=ut+1/2 at^2
V^2=u^2+2as**

Thus among the five unknowns, if any four are given the fifth one can be found

**Derivations of the laws:**

**Derivation of the law V=u+at**

Initial velocity =’u’

Final velocity =’v’

Change in velocity =(v-u)/t

But rate of change of velocity is the acceleration ‘a’

Thus (v-u)/t=a

v-u=at

v=u+at

**Derivation of the law s=ut+1/2 at^2**

Distance travelled = Average velocity * time

Initial velocity =’u’

Final velocity =’v’

Average velocity =(u+v)/2

Time =’t’

Thus distance

s=(v+u)/2*t

=((u+at+u)*t)/2

=(2u+at)t/2

=(2ut+at^2)/2

=ut+1/2 at^2

s=ut+1/2 at^2

**Derivation of law V^2=u^2+2as**

We have v=u+at

Square both sides

V^2=(u+at)^2

=u^2+ 2 uat +a^2 t^2

=u^2+2a(ut+1/2 at^2)

=u^2+2as

Thus v^2=u^2+2as

## Introduction to Analytical Geometry with examples

Analytical geometry was invented by the French mathematician Rane De Carte in the early sixteenth century. Its idea is given as below. Analytical geometry is the combination of algebra and geometry.

Consider two perpendicular lines, one horizontal and one vertical line in the plane intersecting at the point ‘o’ called origin. The horizontal line is called x-axis; the vertical line is called y-axis.

Distances measured to the right hand side of the origin are taken as positive and distances measured to the negative side of x-axis are taken as negative. Similarly distances measured above the origin along y-axis are taken as positive and the distances measured below the y-axis are taken as negative. The two axes divide the plane in to four quadrants. These are called first quadrant, second quadrant, third quadrant and fourth quadrant.

Consider a point P in the plane. Drop a perpendicular PM on x-axis. The length of OM is called x-coordinate of the point P and the length PM is called y-coordinate of the point P. Two coordinate x, y are called coordinates of the point P. while measuring the length OM, PM proper sign should be attached to these length. Accordingly, as the perpendicular falls on positive or negative side of the axis. If P is a point having x-coordinate x and y-coordinate y then the point P is denoted by P(x, y).

If P (x_1,y_1) and Q (x_2,y_2) are two points then it can be proved that the distance PQ is ?(?(x_2- x_1) ?^2+?(y_2- y_1)?^2 )

The concept of slope of a line plays a major role in analytical geometry. It is defined as follows. If a line l makes an angle ‘?’ with the positive direction of x-axis then the value ‘tan??’ is called slope of the line L. It is denoted by the symbol ‘m’.

Locus of a curve:

The locus of a plane curve in the (x,y) plane is an algebraic relation between the coordinates of a general point on the curve which is such that every point on the curve satisfies that equation and only points on the curve satisfies that relation. The algebraic relation is called the equation of the curve.

If a straight line has a slope ‘m’ and y-intercept ‘c’ then the equation of the line is y=mx+c

If a straight has a slope ‘m’ and passes through the point (x_1,y_1), then the equation is given by (y-y_1)=m(x-x_1)

If a straight line passes through two points (x_1,y_1)and(x_2,y_2), then its equation is given by (y_2-y_1)=m(x_2-x_1)

If a circle has centre (a, b) and the radius ‘r’, then its equation is

?(x-a)?^2+?(y-b)?^2+r^2

Example:

Find the distance between the points (8,7) and (4,4)

Solution:

Here P = (8, 7) = (x_1,y_1)

Q = (4, 4) = (x_2,y_2)

PQ =?(?(x_2- x_1) ?^2+?(y_2- y_1)?^2 )

= ?(?(8- 4) ?^2+?(7- 4)?^2 )

= ?(16+9)

= ?25

= 5

Find the equation of the line passing through the point (3,-7) and (-8,2)

Here P = (3,-7) and Q = (-8,2)

The equation of the line is

((y-y_1))/((y_2-y_1))=((x-x_1))/((x_2-x_1))

((y+7))/((2+7))=((x-3))/((-8-3))

((y+7))/9=((x-3))/(-11)

-11(y + 7) = 9(x - 3)

-11y - 77 = 9x - 27

9x + 11y + 50=0

## The concept of Hypothesis Testing In Statistics

In mathematical statistics, statistical interface plays a major role. Statistical interface can be categorized into two parts, one is estimation and other one is testing of hypothesis.

To understand the testing of hypothesis we should go through the following paragraph.

In testing of hypothesis the collection of samples and sampling theory is important. There is a parent collection of data called population. A population may be finite or infinite. A small sample collected is taken from the population. Different collection leads to different samples, for example a population of size ‘N’; we can take? N?^C n no. of samples of size ‘m’.

The testing of hypothesis means, from the given sample is done to conclude any evidence about the population parent. The following example illustrates it very clearly.

EXAMPLE:

Null hypothesis H_0: Sample mean is 10

H_1 Alternate hypothesis: H_0 is false.

Test statistics t= ((x ?-?))/(s/?n)

=[8.5-10]/(9.1/?25)

=2.56

Thus the calculated value is 2.56 but the observed value is 2058. Thus H_0 is accepted thus the sample can be assured.

Click here for a detailed statistics assignment help

## ANOVA Homework Help

What exactly is Anova? Is it an important aspect in Statistics? These two always remains as an ambiguous question. The full form of ANOVA is Analysis of variance. It is a form of a statistical test , where we get to know if the means of various groups present in the data are equal.

When there are two or three means in our derived answer , ANOVA acts as a crucial tool in comparing one with the other. Any form of experimental data can be analyzed with the help of ANOVA .

One of the most important topics in statistics is linear regression . ANOVA is always considered as a unique case of linear regression by expert statisticians across the globe. When there are two or more means in a sample data , the best way to statistically compare them will be through ANOVA .

Students who are struggling with ANOVA assignments or homework can seek the help of ANOVA Homework Help services , where expert tutors can guide the students to complete their assignments successfully .

Since ANOVA is an important topic in statistics, students must place due importance to it and understand the importance of it .

Data mining which is gaining a lot of importance and scope in the recent times also uses the concepts of ANOVA in producing perfect results.

ANOVA Homework Help

## About Microbiology

Microbiology is a study about the Microscopic Organisms. Microscopic organisms are defined as any living thing that is either single cell, a cell cluster, or has no cells at all. There are also exceptions such as Viruses and prions . These are considered as living things but still they are studied under microbiology. Microbiology is the mother for virology, mycology, bacteriology and immunology.

The existence of unseen microbiological life was postulated by many yogi’s and visionaries in the history and dates back to 500BC but as there were no enough evidence to prove it , they were not accepted but today’s science is proving their theories. In 1976 Anton van Leeuwenhoek got the name as first man to see bacteria and other micro organisms and he was using a single lens microscope to view them. Anyone in microbiology will have to be familiar with this name.

Scope of microbiology is wide and it has a major role in the field of medicine. Apart from medicine, microbiologists are also needed in other fields like food industry, agriculture, environmental studies, and aero microbiology.

The world has so many mysteries which are unexplored and one of them is micro organisms which are not visible to the human eyes. The existence of this organism was known only by the end of 20th century. So the study of these organisms has just started and there is lot to explore. Scope is more and in developed countries the government itself funds certain amount to the microbiologists for conducting research on new theories.

## Architectural Engineering

Architectural engineering is also known as building engineering. This comes under the various branches of engineering. This study is about designing and constructing buildings. Most of the colleges offer this degree as Bachelor of Engineering in Architecture (B.E. Arch). This is a very interesting field when compared other engineering studies that is related to construction. This branch of engineering is gaining popularity in countries like U.S.A , Canada , and United Kingdom.

Some of the related engineering branches that go with Architectural engineering are Structural engineering, Mechanical engineering and Electrical engineering. These three branches come together in the construction process. Architectural engineer is the one, who builds, Mechanical engineer takes care of the buildings mechanical works, Structural engineer designs the building and the Electrical engineer looks after the electrical works of the building.

All these architectural, structural , mechanical and electrical engineering were grouped as one engineering field, in time and as the importance of these fields has grown now there are different fields separately for architectural, mechanical, electrical and structural. These fields have created a impact in today’s younger generation which has ensured good scope and reliability of job in future.

## What is Metaphysics ?

Metaphysics is a study of fundamental being and nature. It is one of the branches of philosophy. One who studies Metaphysics is called as Metaphysician. Metaphysicians attempt to clarify the fundamental notions like existence, objects, space and time, cause and effect etc.Students who are studying philosophy might need philosophy homework help and you can visit www.questfactory.com

The term as well as the subject of metaphysics, goes back to Aristotelian period. In ancient Greece anyone with a question in Science was sent to metaphysicians, and they answered the questions with their knowledge but during 18th century a question was raised on these metaphysicians “How do you know?”, which led to new branch of philosophy called epistemology. Even Aristotle credited philosophers who were dealing with metaphysics.

Metaphysics was a part of academic inquiry and scholarly education even before the age of Aristotle. According to Aristotle metaphysics was “the Queen of Sciences”. Aristotle’s Metaphysics was divided into three parts they are:

Ontology: Study of being and existence.

Natural Theology: Study of God, nature of religion, existence of divine etc.

Universal science: Study of law of contradiction, species, elements etc.

Some of the topics involved in Metaphysics are, Being, existence and reality, Empirical and conceptual objects, Cosmology and Cosmogony, Determinism and free will, Identity and charge, Mind and matter, Necessity and possibility, Religion and spirituality, Space and time etc.

## Ceramic Engineering

Ceramic Engineering is study if creating objects from inorganic, non-metallic materials. These inorganic and non-metallic objects are done by either action of heat or at low temperature. Ceramic engineering also includes purification of raw materials. This is a study and production of the chemical compounds with their formation and study of their structure, composition and properties. Ceramic materials have a crystalline or partly crystalline structure with long rage order on atomic scale.

The special characters of the ceramic materials give rise to its applications in, material engineering, electrical engineering, chemical engineering and mechanical engineering. As ceramic are heat resistant it is used in a wide range of industries such as mining, aerospace, medicine, food etc.

Ceramic is widely used in the Military sector in instruments like Optical fiber, infrared heat seeking device, IR night vision etc. The products of the ceramic are used in the Space Shuttle Program, ballistic protection, jet engine turbine blades, and missile nose cones. Ceramic plays a major role in wide range of industries, till date it is considered as an important discovery of the mankind. In the future definitely the use of Ceramic will increase and so there is no doubt that the study of ceramic has a wide range of oppurtunity.