Mathematical Modeling of Urban Population Changes
Background of Issue
The growth of population is the issue that caused widespread concern in the world now. As the world’s top 1 populous country, China’s population problem becoming more prominent. Because of the base of large population, although China has implemented the one-child policy to practice family planning, population is still increasing greatly. This huge population pressure has brought a series of problems on China’s social, political, economic, health, employment, etc. therefore, research and solve the population problem is particularity important for China. [3]Usually people will notice that in newspapers about population growth forecast, when it comes to the end of this century or the middle of next century, the whole world or a certain region’s population will reach XX billions. It is important to note that the number of population forecast in the each newspaper will show large difference for the same time, it’s clearly due to result of using different mathematical models in population calculation.

As the human society entered the 20th century, the rapid development in science and technology has made productivity improved strongly, meanwhile, the world’s population is growing in an unprecedented scale. Every unit time for increasing billion in population, has been shorten from one hundred years to two or three decades. The earth we live on, has been carrying its’ 6 billion people entered into the 21 century. For quite a long time, human reproductions has been spontaneously, only because of the rapid expansion of population and dramatically worsen of environment quality, people just suddenly come to realize the truth that it is extremely urgent to research the relationship between human and nature, the variation trend of population, and how to control it.

Mathematical Model in Use
What I choose is the exponential growth model of China’s population, and using this model to make some...

...Mathematics Modeling
Introduction
Mathematics finds its root way back more than 5000 years. Mathematics has helped people solve complex problems, represent different problems and transfer knowledge and skill about the different problems. Mathematical models have often being developed to solve and represent these problems especially in natural sciences and engineering disciplines (Arnold 2000). Mathematical models can be defined as amathematical language that would describe the behavior of a system or rather a problem. Mathematicalmodeling can be done to develop scientific understanding, test a system for change and help in making decision (Anon 2005).
UrbanPopulationchange
The urbanpopulationchange represents one of the most important aspects that define a city. The household composition and their nature differentiate the urbanpopulation from that in the area. Urbanpopulation is growing much faster than the population as a whole. It is prospected that, in the next century, more than half the population will be living in the urban centers. The changes of the population have shaped the cities to function as social, economic and cultural centers. The...

...Mathematicalmodeling is commonly used to predict the
behavior of phenomena in the environment. Basically,
it involves analyzing a set of points from given data
by plotting them, finding a line of "best fit" through
these points, and then using the resulting graph to
evaluate any given point. Models are useful in
hypothesizing the future behavior of populations,
investments, businesses, and many other things that
are characterized by fluctuations. A mathematical
model usually describes a system by a set of variables
and equations which form the basis of the
relationships between the variables.
The variables represent independent and dependent
properties of the system. Models are classified in a
variety of ways. One of these ways is "linear versus
nonlinear." A linear model is any system whose
behavior can be explained or predicted using a linear
equation or an entire set of linear equations. On the
other hand, a nonlinear model uses at least one
nonlinear equation to describe its behavior. Models
may also be classed as either deterministic or
probabilistic. A deterministic model always performs
the same way under a given set of initially occurring
conditions, while a probabilistic model is
characterized by randomness. Another way of evaluating
models is to determine whether it is static or
dynamic. Static models do not account for time, while
dynamic models do take this element into...

...ideal body type through their music. On August 14 of 2012 the rapper, 2 Chainz released the single “Birthday Song”, in which his lyrics were “All I want for my birthday is a big booty hoe” describing his particular taste in women. 2 Chainz isn’t the only African American who prefers the stereotypical enlarged rear, in fact this has been a common trend since 1992 when the release of Sir Mix-a-lot’s song, “Baby Got Back”, commonly known as “I like big butts” as the chorus and repeating line. He also stated in the this song, “36-24-36? Ha ha, only if she's 5'3”. Based on the height and specific measurements we can infer that he favors the physique of urban models. Amber Rose, Rosa Acosta, Kimbella, and Stephanie Santiago are currently the first class urban models in the hip hop industry. Urban models promote themselves in the urban era to the elite of the hip-hop industry. Each of these women are all known for having perfectly sculpted curvaceous bodies otherwise known as the “coke-a-cola” bottle figure, which is full breast, slim waist, and a voluptuous round gluteus maximus. These women are beautiful in the eyes of the black culture standards of beauty opposed to the admired “Barbie” image. This essay is going to depict the standards of beauty that African American males prefer versus the European standards of beauty, males idealize in modern America.
Majority might view this as a trend that people follow...

...help us understand the pattern of populationchange in the UK?
There are many different components that all add together for the reason why population does change in a specific location. This change is considered ‘dynamic’ as it is constantly changing due to many factors that are always effecting the rate of populationchange.
One of the biggest influences of populationchange would be the birth and death rates of an area. Birth/death rate is the total number of births/deaths per 1,000 of a population in a year. The rate of births/deaths in a population is calculated in various ways such as, population counts from a census. The birth rate (along with mortality and migration rate) are used to calculate populationchange.
An ageing population would be the result of when more people are living to an older age. The specific term used to describe this is ‘greying population’. There is currently a greying population occurring in the UK which has resulted in the population increasing as there are more people alive. However, there are factors that stabilise this growth of population. There has been a decrease in the number of children being born because people are choosing to have children later and less of them. This...

...IE 456 MATHEMATICALMODELING AND APPLICATIONS
Homework 1
1. [15 points] Consider the following linear programming problem:
Min z = 3x12x23x3
Subject to
x1+2x2 +x3 14
x1+2x2+4x3 12
x1 x2 +x3 = 2
x3 3
x1; x2 unrestricted
(a) [6 points] Reformulate the problem so it is in standard format.
(b) [6 points] Reformulate the problem so it is in canonical format.
(c) [3 points] Convert the problem into a maximization problem.
2. [20 points] A lathe is used to reduce the diameter of a steel shaft whose length is 36 inches (in.)
from 14 in. to 12 in. The speed x1 (in revolutions per minute), the depth feed x2 (in inches per
minute), and the length feed x3 (in inches per minute) must be determined. The duration of the
cut is given by 36=x2x3. The compression and side stresses exerted on the cutting tool are given by
30x1 + 4000x2 and 40x1 + 6000x2 + 6000x3 pounds per square inch respectively. The temperature
(in degrees Fahrenheit) at the tip of the cutting tool is 200 + 0:5x1 + 150(x2 + x3). The maximum
compression stress, side stress, and temperature allowed are 150,000 psi, 100,000 psi, and 800F. It
is desired to determine the speed (which must be in the range from 600 to 800 rpm), the depth feed,
and the length feed such that the duration of the cut is minimized.
(a) [10 points] In order to use a linear model the following approximation is made: Since 36=x2x3
is minimized if and only if (x2 x3) is maximized, it was decided...

...MATHEMATICAL MODELLING OF MICROWAVE HEATING OF FOOD
By M . SHIVA KUMAR ( 04AG1008 ) Under the guidance of PROF. SURESH PRASAD
ABSTRACT
• The use of microwaves in the food industry is attributed to the lower time needed to increase the temperature of foodstuffs compared to the traditional heating methods.
•However, the heating is not uniform and the products show hot and cold spots.
• In order to analyze the behaviour of foods heated by microwave oven, amathematical method was developed solving the unsteady state heat transfer differential equations.. • It takes into account variable thermal and electromagnetic properties.
•The numerical solution was developed using an implicit finite difference method in one dimensional system (slab).
• It allows predicting temperature profiles. • The model will later be validated with experiments and data on apple fruit.
ADVANTAGES OF MICROWAVE HEATING
• Does not involve a conduction or convection medium • Food material is heated directly due to agitation of the polar molecules contained – namely water • Reduced drying time • Improved final quality of the dried products • Better rehydration
DRAWBACKS OF MICROWAVE HEATING
• Inherent non-uniformity of the electromagnetic field within a Microwave cavity. • Excessive temperatures along the edges and corners of products may lead to overheating and irreversible drying-out resulting in possible scorching and development of off-flavors....

...hapter 8 Homework (EXPLAIN YOUR ANSWERS)
One point questions:
1. a) How can time be incorporated into the theory of consumer behavior (think opportunity costs)?
Time also has a value, so it also should be considered in decision making and utility maximization. The total price of a product should also include the time spent in consuming the product. (how much you make per hour). Usually when people consider their time, their consumer behavior appears to be more rationale.
b) Explain the following comment: “Want to make millions of dollars? Devise a product that saves Americans lots of time.”
Time is money. The point of this expression is for a person who can make so much per hour, every hour spent not working is so much money not made. Americans value productivity and time. So a time-saving device would free the individual up to earn more income.
2. Many apartment-complex owners are installing water meters for each individual apartment and billing the occupants according to the amount of water they use. This is in contrast to the former procedure of having a central meter for the entire complex and dividing up the water expense as part of the rent. Where individual meters have been installed, water usage has declined 10 to 40 percent depending on the number of individual apartments. Assuming a 20 unit apartment building, explain this drop, referring to price and marginal utility.
In the 20 apartment complex, each apartment would be billed for...

...What can be said about populationchange in local government areas in Scotland and the change in age structure for 2000-2010.
In the first part of this assessment I will describe the information provided on the chrorpleth map and a graph by the General Register Office of Scotland to help define the change in population in Scotland also the change in the age structure in Scotland between the years 2000 and 2010. Using figure 1 the chronopleth map I will define some of the main patterns and variations of populationchange which can be seen on the map. Figure 2 will be used to describe the variations in the changing age structure from 2000-2010.
Figure 1 shows a clear distinction in populationchange from 2000-2010. In places like the Highlands, Orkney Islands, Stirling, Fife, and the Scottish boarders the map shows that the populationchange is 4% to less than 8%. Aberdeenshire, Perth & Kinross, Edinburgh city, west & East Lothian have the biggest populationchange at 8% over 10 years. Aberdeen city, Moray, Shetland, Midlothian, Glasgow and the surrounding areas along with Dumfries & Galloway show a change in population at 0% to less than 4%. Leaving the smallest populationchange in Dundee the West Coast and the Western...

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