Mathematical modeling in ecology. Start in science

Khamzin Idel Fanisovich

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Municipal educational institution
“Staroromashkinsky secondary school”
Chistopol municipal district of the Republic of Tatarstan

Subject:

"Ecology and Mathematics"

Section: “Ecology”

Completed : Khamzin Idel Fanisovich,

4th grade student

MBOU "Staroromashkinskaya Secondary School"

Chistopol district of the Republic of Tatarstan

Supervisor : Khamzina Gulnaz Rinatovna, primary school teacher,

Second qualifying

Kinskaya Secondary School" Chistopolsky

District RT

Chistopol, 2015

INTRODUCTION………………………………………………………………..…3

Main part

I. “Numbers” in the surrounding air……………………………..…..…5

II. Trees are a priceless part environment ….……………7

III. Mathematicians warn: “Don’t pour water in vain”…………9

IV. Damage to soil from bags……………………………………......11

V. Mathematics bees………………………………………….……12

VI. Learning to save for the benefit of the environment…………………..…….14

CONCLUSION…………………………………………………….…..….…15

REFERENCES…………..………...……………………………......16

APPLICATION…………………………………………………………

Introduction

Environmental pollution has a history almost as long as the history of humanity itself. For a long time primitive man was not much different from other species of animals and, in an ecological sense, was in balance with the environment. Moreover, the human population was small.

Over time, as a result of the development of the biological organization of people, their mental abilities, the human race stood out among other species: the first species of living beings arose, the impact of which on all living things was a potential threat in nature.

At all stages of his development, man was closely connected with the world around him. But since the emergence of a highly industrialized society, dangerous human intervention in nature has sharply intensified, the scope of this intervention has expanded, it began to express various manifestations and now threatens to become a global danger to humanity. Man has to increasingly intervene in the economy of the biosphere - that part of our planet in which life exists. The Earth's biosphere is currently subject to increasing anthropogenic impact.

For life a person needs fresh air, high-quality water, uncontaminated soil, plants, energetic resources and others, but with the development of civilization harmful effects people into nature becomes a threat to it. Can mathematics help the environment? Let's look at an example.

Our school is located in a beautiful place, in the center of the village. Not far from the village there is a small forest. We really want the forest to be clean, well-groomed, so that birds can always be heard in it, and squirrels and bunnies please the eye. Therefore, we, school students, are concerned about environmental issues. In mathematics lessons, we decided to find out how knowledge in mathematics can help in solving environmental issues.

I started my research with the air, because it is our habitat, without which our life is impossible. The quality of life greatly depends on the quality of air, and it is worth getting to know the air in more detail. Air is a mixture of gases that make up the Earth’s atmosphere: nitrogen (78.09% by volume), oxygen (20.95%), noble gases (0.94%), carbon dioxide(0.03%) and many (about two thousand) microimpurities. The average density of air under normal conditions is 1.29 grams per liter, solubility in water is 29.2 cubic centimeters per liter. But this is clean air. The actual air we breathe can be very different from these parameters.

Unfortunately, the air we breathe in cities and indoor spaces is a terrible cocktail of... industrial emissions, automobile exhaust gases, odors from landfills, dust, tobacco smoke and other toxic substances, as well as bacteria and viruses.

The purpose of my work is to prove the role of mathematics in ecology.

Tasks:
- getting to know the environmental problems of our village and finding solutions to these problems;

Application of knowledge in solving environmental problems.

1. "Numbers" in the surrounding air

Clean air is the key to health, not only on the street, but also indoors, for example, in the classroom. In the room, the amount of oxygen decreases and carbon dioxide increases. According to experts, as a result of human activity, 25.5 billion tons of carbon oxides, 190 million tons of sulfur oxides, 65 million tons of nitrogen oxides, and 1.4 million tons of chlorofluorocarbons enter the Earth’s atmosphere annually. IN last years greatest number harmful substances emitted into the atmosphere with vehicle exhaust gases, and their share is constantly increasing. For example, in Moscow, emissions of harmful substances from vehicles exceed 800 thousand tons per year, which is 70% of the total amount of pollutants entering the city’s atmosphere per year.

There are 90 cars and 6 trucks in our village. Road transport is one of the main environmental pollutants. For research, we chose Central Street in our village. The length of the section is 2000 meters.

First, the number of vehicles of 2 types (passenger cars, trucks) passing along the street at different times was counted, and then all the necessary calculations were made.

The length of Central Street is 2000 meters = 2 km

Cars passing

Passenger cars –20

Freight – 10

Average number of cars passing along Tsentralnaya Street per day

20 passenger cars

10 trucks

Carbon monoxide emissions are:

For a passenger car – 2 g/km

For truck– 10 g/km

How much carbon monoxide does one car emit when driving along Central Street?

A car:

2 g/km * 2 km = 4 g/km

Freight car:

10 g/km * 2 km =20 g/km

How much CO is emitted by all cars driving along the street? Central.

4 * 20 = 40g of CO emitted by passenger cars;

20 * 10 = 200 g of CO emitted by trucks;

40 + 200= 24 0g of carbon monoxide emitted by all cars in one day.

Carbon monoxide release

For a week: 240*7 =1680g =1.68 kg.

For a month: 240 * 30 = 7200 g = 7.2 kg.

For the year: 7.2*12 =86.4 kg.

Maximum permissible concentration of CO in the air: 0.02 mg/l

Conclusions:

1. Carbon monoxide negatively affects human health. The basis of exhaust gases that are harmful to human health and the environment are: carbon monoxide, nitrogen (IV) oxides, hydrocarbons, lead.

2. To reduce the harmfulness of fuel, it is necessary to use hydrogen engines. Their exhaust gases are water vapor and are completely environmentally friendly. But these engines, unfortunately, have not yet found widespread use.

1. Trees are an invaluable part of the environment

They purify polluted air, produce oxygen, and purify the air of pathogenic microbes. Many species of plants, animals and microorganisms find a table and a home in the forests.

The lifespan of different tree species is not the same. Aspen lives relatively short - less than 100 years. The age of spruce can reach 600 years. For pine trees native to the White Mountains of eastern California, 500 or even 1,000 years is not old. Like all living things, trees die from age and disease.

And in recent years, the area of ​​cut down and burned forests is 7 times greater than the area of ​​​​the territories where new trees were planted. It turns out that deciduous forests are 2 times better at cleaning the air from dust than coniferous ones. Imagine, if every resident of our country grows at least one tree in their lifetime, then their number will increase by 141.93 million trees. Our school site is very large. There are 50 birches and 10 large pine trees growing on the site. In 2011, schoolchildren and teachers planted 30 oak seedlings and 35 pine seedlings.

Data:

In one sunny day, 1 hectare of forest absorbs 120-280 kg of carbon dioxide from the air and releases 180-200 kg of oxygen;

One tree average size produces enough oxygen to breathe for 3 people (2.5 kg per day). The average person needs 0.83 kg of oxygen per day;

One hectare coniferous trees retains 40 tons of dust per year, and deciduous - 100 tons. Interested to know how much oxygen the trees in our school site produce?

10 pine trees + 50 birches = 60 trees

60 woodX2.5kg oxygen=150kg oxygen

150 kg of oxygen: 0.83 kg = 180 people. Our school has 59 students, 16 teachers, 4 technical staff - a total of 79 people. Consequently, the oxygen released by trees is sufficient for us, so it is useful for us to ventilate the classroom more often.

Conclusion: The forest is a unique ecological system. It’s not for nothing that forests are called the lungs of the planet. An obvious fact: without forests on the planet, even today’s 6 billion population of the Earth will not be able to survive, but what will happen tomorrow, when the population once again doubles, and the forests become half as numerous? A hundred years ago, forests covered three-quarters of the land. By now there is a quarter left. Great damage to forests is caused by fires, which have become more frequent in Lately: Every year in many countries of the world millions of square kilometers of forests burn out. Therefore, we must protect our forests and plant trees.

1. Mathematicians warn: “Don’t waste water”

Everyone understands how great the role of water is in the life of our planet and especially in the existence of the biosphere.

The biological need of humans and animals for water per year is 10 times greater than their own weight. Even more impressive are the domestic, industrial and agricultural needs of humans. Thus, “to produce a ton of soap requires 2 tons of water, sugar - 9, cotton products - 200, steel 250, nitrogen fertilizers or synthetic fiber- 600, grain - about 1000, paper - 1000, synthetic rubber - 2500 tons of water.”

Water used by humans ultimately returns to the natural environment. But, apart from the evaporated water, this is no longer pure water, but domestic, industrial and agricultural wastewater, usually not treated or not treated sufficiently. Thus, freshwater bodies of water - rivers, lakes, land and coastal areas of the seas - are polluted.

We all use water, so we also have a responsibility to protect it from pollution and save it. About 70% of the earth's surface is covered by seas and oceans, and fresh water accounts for only 2% of the planet’s total water reserves.

Quality standards drinking water contained in a special document - State standard"Drinking water". This quality standard sets the maximum permissible levels of chemical substances, found in natural waters or added to water during its treatment. Thus, the aluminum content should not exceed 0.5 mg per 1 liter of water, beryllium - 0.0002 mg per 1 liter, molybdenum - 0.25 mg per 1 liter, arsenic - 0.05 mg per 1 liter, lead - 0. 03 mg per 1 l, fluorine – 0.07 mg per 1 l, polyacrylamide – 2 mg per 1 l. Also included in the group of drinking water quality indicators are iron (no more than 0.3 mg/l), manganese (no more than 0.1 mg/l), copper (no more than 0.1 mg/l), polyphosphates (no more than 3, 5 mg/l), zinc (no more than 5 mg/l). The dry residue formed after evaporation of water should not exceed 1000 mg/l.

How much water does a person need every day? For domestic purposes, water is used for drinking, cooking, washing, washing, flushing sewage into the sewer and watering the garden. It turned out that our family of 4 uses more than 322 liters of water per day. The consumption rate per person per month is 2.5 m3. 2.5m3X4=10m3.=10000dm3=10000l. 1000l:31day =322l. This is a large volume. Qualitatively clean water there is not enough on Earth. Imagine if each person saves at least 1 liter of water per day, and there are about 6.8 billion people in the world, that means saving 6800000000 liters of water per day around the world.

642 people live in our village. Suppose that most of them keep the tap open all the time when brushing their teeth, while the rest open it only while they are brushing and rinsing their mouths. On average, this procedure takes about 3 minutes, and during this time water flows from the tap at a speed of 2 l/min. If all residents brush their teeth with the tap constantly open, twice a day in the morning and in the evening, then they will use 2 liters X 3 minutes = 6 liters, 6 liters x 2 times = 12 liters, 12 liters x 642 resident = 7704 liters of water in one day. But when saving water they can save 1L X 1min=1 L, 1L X 2 times=2 L, 2L X642 resident=1284 L,

7704 l -1284=6420 l of water.

Conclusion:

Scientists say that when used modern technologies household water consumption can be reduced by ⅓, in agriculture- twice, and in industry - almost 10 times.

SAVE WATER!

1. Damage to soil from bags

The soil is fertile - it is the most favorable environment habitat for the vast majority of living things. It is also significant that in terms of their biomass, the soil (land of the Earth) is almost 700 times greater than the ocean, although land accounts for less than 1/3 of the earth's surface. Soil is often called the main wealth of any state in the world, since about 90% of humanity's food is produced on it and in it. Soil degradation is accompanied by crop failures and famine, leading to poverty in states, and soil loss can cause the death of all humanity. Under normal natural conditions, all processes occurring in the soil are in balance. But often people are to blame for disturbing the equilibrium state of the soil. As a result of development economic activity human contamination occurs, changes in the composition of the soil and even its destruction. In a week our family alone uses more than 10 plastic bags. There are 200 families living in our village, if each family uses more than 10 plastic bags, then 200X10 bag = 2000 bag. It takes 200 years for such bags to decompose. If we recklessly throw away bags now, then for decades the soil will contain harmful substances.

Conclusion:

Soil is the most important natural resource, which does not decrease with prolonged use, but is preserved and even improved.

The soil must be protected from destruction and protected from pollution. You should always pick up trash after yourself and put it in specially designated places. Most What we throw away (plastic, metal, glass, paper) can be reused.

1. Mathematics bees

In the school area of ​​our school, flowers attract bees with their aroma all summer. These insects are “good” at mathematics. In cross section, the honeycomb cells have a hexagonal shape, which allows you to get maximum space for storing honey with minimum cost wax.

Mathematicians were looking for an answer to this question and after lengthy calculations came to an interesting conclusion: the most The best way to build a warehouse with maximum capacity, but with minimal material consumption, is to make the walls hexagonal. If the same space is built up, the hexagons will require less material than squares or triangles. Another amazing quality of bees is their cooperation among themselves in the construction of honeycombs. Seeing the fully built honeycombs, you might think that they were created as a single block. In fact, the construction of honeycombs begins from completely different points simultaneously. Hundreds of bees begin building honeycombs in three or four different locations. They continue building until they meet in the middle. There is not the slightest error or mistake at the junction. Bees also calculate the angle of individual cells relative to each other when building a honeycomb. Cells touching sides are always at an angle of 13 degrees to the ground. Thus, both walls of the honeycomb are directed upward at an angle. This angle prevents honey from leaking out.

Bees are "mathematicians", the honeycombs they build have the most robust construction, the dimensions are observed with unprecedented precision: the cell angle is always 109*28" degrees. To prepare 100 grams of honey, a bee sometimes flies 46 thousand kilometers, this is the same as flying around the entire globe along the equator. For 1 dm² of honeycomb on both sides there are 800 cells.

In our village, 5 families keep 12 hives. For good sunny summer 1 family of bees collects approximately 60 kg of honey. 12 family X 60kg=720kg honey.

Honey is a favorite delicacy since childhood and at the same time a storehouse of vitamins and beneficial microelements. The uses of honey are extremely multifaceted, as are the properties of honey, from cooking to medicine and even the judicial system.

Honey contains many substances necessary for the body and has an extremely positive effect on the body’s immunity and the functioning of various organs. Honey has excellent antibacterial properties.

Flower honey is formed when bees process honeydew and honeydew, which they collect from the stems and leaves of plants. Common in nature:

• linden honey - fragrant, pleasant aroma, light amber color;
• buckwheat - pleasant specific taste and aroma, in liquid form it is dark yellow, golden or brown, contains iron in its mineral substances;
• mixed - prefabricated, flower honey bees collect from various plants.

Bees bring benefits to people not only in the form of honey. No less important for humans is their ability to pollinate plants; bees as pollinators are extremely important in agriculture.

Royal jelly. The bees use it to feed the larvae and the queen. Royal jelly solutions kill 19 types of bacteria and protozoa, as well as viruses.

Value: high antimicrobial effect. Used to treat skin and tuberculosis diseases.

Conclusion:

And in truth bees are mathematics. After all, they fly 46 thousand kilometers without a map or compass and find their home.

1. Learning to save for the benefit of the environment

Electromagnetic fields are manifestations of energy invisible to the eye. Electromagnetic pollution of the environment is especially dangerous for children. How to make it safe to use a computer? Using mathematical calculations, scientists found that electrical household appliances (TV, computer) should be installed at a distance of at least 1 meter from oneself, and watch TV from a distance of at least 2 meters. The computer monitor should be at a distance of at least 50-60 cm. You cannot work on the computer for more than 4 hours a day, and do it for 10 minutes. rest breaks every 30 minutes.

We must conserve the planet's energy resources. Energy saving light bulbs are the most economical and ecological way lighting. When a conventional incandescent lamp operates, more than 95% of electrical energy is spent on heat generation and only 5% on light. An energy-saving lamp consumes 5 times less energy than an incandescent lamp and lasts 8 times longer.

In my classroom there are 18 energy-saving lamps, if instead there was an incandescent lamp, how much damage would there be to the school.

18 energy saving lamps X 0.04kw=0.72kw

0.72 kW X 2.02 rubles = 1.45 rubles

18 incandescent lamp X 0.1 kW = 1.8 kW

1.8 kW X 2.02 rubles = 3.64 rubles

If they burn for 3 hours a day. 1.45 rubles X 3 hours = 4.35 rubles

3.64 rubles X 3 hours = 10.92 rubles

Per month: 4.35 rubles X 26 day = 113.1 rubles

10.92 rubles X 26day=283.92 rubles

Savings for the school per month 283.92 rubles - 113.1 rubles = 170.82 rubles

I solved this problem and realized how beneficial it is to use an energy-saving lamp at school and at home.

Conclusion

So, based on my observations, I can conclude: ecology is a science that is closely related to other sciences, in particular mathematics. When studying ecology, many questions arise, the answers to which can be obtained using mathematics. Mathematics allows you to carry out precise measurements, make calculations and confirm observations. I want to say that you don’t have to be a great mathematician to protect nature and cleanse our green planet of pollution.

Every year, every day, every hour, animals and plants disappear on Earth. 25 thousand plant species are in danger. Water bodies are polluted, forests are cut down, soils are destroyed. We must help nature. After all, nature is our common home.

Tree, grass, flower and bird

They don't always know how to defend themselves.

If they are destroyed,

We will be alone on the planet.

Literature

1. “I'm exploring the world. Ecology". A.E. Chizhevsky - Astrel - 2003
2. "Ecology of Russia". B.M. Mirkin-M: JSC MDS, Unisam, 1995, -232 p.
3. "Protection of Nature". A.V. Mikheev-Enlightenment, 2000. 144 p.
4. Encyclopedia for children. "Mathematics". – M.: Avanta +, 2003. – 688s.
5. Internet

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Introduction.

Goal of the work:

Find out what contribution mathematics makes to ecology.

Show practical use mathematics in environmental ecology.

Job objectives:

Explore environmental issues

Quantify the condition natural objects and phenomena, positive and negative consequences of human activity.

Explore questions about what is happening to the environment on our planet.

Perform hands-on research calculations

Offered to the reader's attention research is devoted to the connection between mathematics and ecology.

Relevance and practical significance of the ongoing The research is that environmental problems have become of paramount importance in the world, and there is a need to involve us, the younger generation, in solving them.

Vladimir Putin signed a Decree on holding in 2017 Russian Federation Year of Ecology. In order to attract public attention to issues environmental development Russian Federation, conservation of biological diversity and ensuring environmental safety. Mathematics and ecology are closely related. It’s not for nothing that mathematics is called the queen of sciences, because it is used in many disciplines, even where it seemed difficult to imagine its application. Every person who loves his work does not require additional incentives to admire the originality of the solution and its grace. The statements of some guys, philologists, artists, ecologists, who say: “We don’t need mathematics,” are jarring. Once I get a grade on my certificate, I’ll forget math.” Not so. I immediately want to convince such people, to “turn” them towards mathematics. After all, it is not the subject itself that is interesting, but the exploration of the surrounding world through this subject. This is the study of the relationships between living organisms and their environment that the science of ecology deals with. Mathematics in ecology studies models of environmental objects and processes. Ecological processes are modeled by mathematical ecology. That is, with the help of mathematics it is possible to predict what changes will occur in nature after a change in the ecological situation.

Chapter 1. Environmental problems of our time.

1. What is happening to the forests on our planet?

It's interesting that the present time total area forests on the planet are 42 million square meters, of which 45% are Russian forests.

About 10 thousand years ago globe The dense forests rustled. Their area was more than 60 million square meters.

In recent years, the area of ​​cut down and burned forests is 7 times greater than the area of ​​the territories where new trees were planted.

Every year approximately 400 thousand sq.m. are cut down. forests. 125 million trees are cut down just for paper production.

1.2. What happens to fauna and flora?

Every year there are fewer and fewer wild animals on our planet. Since the beginning of the 20th century, scientists have discovered about 50 species of previously unknown animals and birds. But during the same time, at least 100 other species completely disappeared from the face of the Earth. In addition, 25 species of mammals have disappeared.

People, without thinking about tomorrow, about their future, the future of fauna and all living nature, predatorily destroyed animals.

The Carolingian parrot, great auk, prairie chicken, dodo, great auk are bird species exterminated by humans. Tur, tarpan, zebra quagga, Steller's cow - animals that we will not see again.

Many other species of animals and plants are on the verge of extinction, since human activity greatly changes their habitat and deprives them of food sources.

In one sunny day, 1 hectare of forest absorbs 120-280 kg of carbon dioxide from the air and releases 180-200 kg of oxygen;

One average-sized tree produces enough oxygen to breathe for 3 people (2.5 kg per day). The average person needs 0.83 kg of oxygen per day;

One hectare of coniferous trees retains 40 tons of dust per year, and deciduous trees - 100 tons.

All of the above allows us to draw the following conclusions: The forest is a unique ecological system. It’s not for nothing that forests are called the lungs of the planet. An obvious fact: without forests on the planet, even today’s 7 billion population of the Earth will not be able to survive, but what will happen tomorrow, when the population once again doubles, and the forests become half as numerous? A hundred years ago, forests covered three-quarters of the land. By now there is a quarter left. Fires, which have become more frequent recently, cause great damage to forests: every year in many countries of the world millions of square kilometers of forests burn out. Therefore, we must protect our forests and plant trees.

1.3 Clean air.

Clean air is the key to health, not only on the street, but also indoors, for example, in the classroom. In the room, the amount of oxygen decreases and carbon dioxide increases. According to experts, as a result of human activity, 25.5 billion tons of carbon oxides, 190 million tons of sulfur oxides, 65 million tons of nitrogen oxides, and 1.4 million tons of chlorofluorocarbons enter the Earth’s atmosphere annually. In recent years, the largest amount of harmful substances has been emitted into the atmosphere through vehicle exhaust gases, and their share is constantly increasing.

The car is the main source environmental problems.

A passenger car requires 2.5 kg of oxygen to burn 1 kg of gasoline. On average, a motorist travels 10 thousand km per year. And it burns 10 tons of gasoline, consuming 35 tons of oxygen and emitting 160 tons of exhaust gases into the atmosphere.

Each car, by washing its tires, annually releases 5-8 kg of rubber dust into the atmosphere.

1 hectare of forest absorbs at least 5 tons of carbon dioxide per year and releases 10 tons of oxygen. In 1 hour, this section of the forest absorbs all the carbon dioxide that is released by the breathing of 200 people.

Motor transport is one of the main environmental pollutants. I made calculations about how much carbon monoxide the cars on my street emit and whether it exceeds the norm. For research, I chose Kolomenskaya Street in our city. The length of the street is 820 meters.

First, the number of vehicles of 2 types (passenger cars, trucks) passing along the street at different times was counted, and then all the necessary calculations were made.

The length of Kolomenskaya street is 820 meters

Cars passing

Passenger cars -120

Freight - 10

Average number of cars passing along Kolomenskaya street per day

120 passenger cars

10 trucks

Carbon monoxide emissions are:

For a passenger car - 2 g/km

For a truck - 10 g/km

How much carbon monoxide does one car emit when driving along Kolomenskaya Street?

A car:

2 g/km * 0.82 km = 1.64 g/km

Freight car:

10 g/km * 0.82 km =8.2 g/km

How much CO is emitted by all cars driving along Kolomenskaya Street.

1.64 * 120 = 196.8 g of CO emitted by passenger cars;

8.2 * 10 = 82 g of CO emitted by trucks;

196.8 + 82 = 278.8 g of carbon monoxide emitted by all cars in one day.

Carbon monoxide release

For a week: 278.8 * 7 = 1951.6 g = 1.95 kg.

For a month: 278.8 * 30 = 8364 g = 8.4 kg.

For the year: 8.4 * 12 = 100.8 kg.

Maximum permissible concentration of CO in the air: 0.02 mg/l

As a result of my research, I found out that

1. Carbon monoxide negatively affects human health. The basis of exhaust gases that are harmful to human health and the environment are carbon monoxide, nitrogen oxides (IV), hydrocarbons, and lead.

2. To reduce the harmfulness of fuel, it is necessary to use hydrogen engines. Their exhaust gases are water vapor and are completely environmentally friendly. But these engines, unfortunately, have not yet found widespread use.

1.4 Water.

Everyone understands how great the role of water is in the life of our planet and especially in the existence of the biosphere.

Seas and oceans cover about 70% of the earth's surface, and fresh water accounts for only 2% of the planet's total water reserves.

On average, every city dweller in the world uses 100 liters of water daily.

Imagine if every person saved at least 1 liter per day. Water, and there are approximately 7.3 billion people in the world, which means savings per day will amount to 7,300,000,000 liters of water.

The biological need of humans and animals for water per year is 10 times greater than their own weight. Even more impressive are the domestic, industrial and agricultural needs of humans. Thus, “to produce a ton of soap requires 2 tons of water, sugar - 9, cotton products - 200, steel 250, nitrogen fertilizers or synthetic fiber - 600, grain - about 1000, paper - 1000, synthetic rubber - 2500 tons of water.”

Water used by humans ultimately returns to the natural environment. But, apart from the evaporated water, this is no longer pure water, but domestic, industrial and agricultural wastewater, usually not treated or not treated sufficiently. Thus, freshwater bodies of water - rivers, lakes, land and coastal areas of the seas - are polluted.

We all use water, so we also have a responsibility to protect it from pollution and save it. Seas and oceans cover about 70% of the earth's surface, and fresh water accounts for only 2% of the planet's total water reserves.

Drinking water quality standards are contained in a special document - the State Standard “Drinking Water”. This quality standard sets maximum acceptable levels for chemicals found in natural waters or added to water during water treatment. Thus, the aluminum content should not exceed 0.5 mg per 1 liter of water, beryllium - 0.0002 mg per 1 liter, molybdenum - 0.25 mg per 1 liter, arsenic - 0.05 mg per 1 liter, lead - 0. 03 mg per 1 l, fluorine - 0.07 mg per 1 l, polyacrylamide - 2 mg per 1 l. Also included in the group of drinking water quality indicators are iron (no more than 0.3 mg/l), manganese (no more than 0.1 mg/l), copper (no more than 0.1 mg/l), polyphosphates (no more than 3, 5 mg/l), zinc (no more than 5 mg/l). The dry residue formed after evaporation of water should not exceed 1000 mg/l.

How much water does a person need every day? For domestic purposes, water is used for drinking, cooking, washing, washing, flushing sewage into the sewer and watering the garden. It turned out that our family of 4 uses more than 322 liters of water per day. The consumption rate per person per month is 2.5 m3. 2.5m3X4=10m3.=10000dm3=10000l. 1000l:31day =322l. This is a large volume. There is not enough high-quality clean water on Earth.

Scientists claim that using modern technologies, water consumption in everyday life can be reduced by ⅓, in agriculture - by half, and in industry - by almost 10 times.

I compared two families. One of which saves water, the other does not. All calculations are shown in the table.

The research allowed me to draw the following conclusion:

If a family that does not save water saves at least 20% of tap water from the amount it usually uses, then in a year this amount of water can form a lake with a diameter of 200 m and a depth of 2 meters.

1.5 Soil.

The soil is fertile and is the most favorable habitat for the vast majority of living beings. It is also significant that in terms of their biomass, the soil (land of the Earth) is almost 700 times greater than the ocean, although land accounts for less than 1/3 of the earth's surface. Soil is often called the main wealth of any state in the world, since about 90% of humanity's food is produced on it and in it. Soil degradation is accompanied by crop failures and famine, leading to poverty in states, and soil loss can cause the death of all humanity. Under normal natural conditions, all processes occurring in the soil are in balance. But often people are to blame for disturbing the equilibrium state of the soil. As a result of the development of human economic activity, pollution occurs, changes in the composition of the soil and even its destruction. Our family alone uses more than 10 plastic bags in a week. There are 200 families living in our village, if each family uses more than 10 plastic bags, then 200X10 bag = 2000 bag. It takes 200 years for such bags to decompose. If we recklessly throw away bags now, then for decades the soil will contain harmful substances.

Garbage accumulation and soil poisoning are an environmental problem. On average, a person throws out 10 kg of garbage every year.

About 3.5 billion tons of waste are generated annually in Russia. Experts have calculated that if the garbage is not destroyed, then in 10-15 years it will cover our Planet with a layer 5 meters thick.

The majority of waste consists of plastic items (70%), followed by glass and tin items (25%), and wood and paper waste (5%) in third place.

I did the calculations and found out that my family throws away 540 bottles a year (milk, drinks, vegetable oil etc.)

In St. Petersburg, according to 2017 data, there are 5,200,000 people. On average there are 4 people in a family, then: 5,200,000:4= 1,300,000 families.

What area would 78,000,000 bottles occupy if they were laid out in a row?

The diameter of one plastic bottle is 9 cm, the length of the bottle is 32 cm, the area occupied by one bottle is 9*32=288 sq. cm.

Area occupied 78,000,000 plastic bottles: 288*702000000 =202176000000 sq. cm=20217600 sq. m

To summarize the above, it is necessary to note the following:

Soil is the most important natural resource, which with long-term use does not decrease, but is preserved and even improved.

The soil must be protected from destruction and protected from pollution. You should always pick up trash after yourself and put it in specially designated places. Most of what we throw away (plastic, metal, glass, paper) can be reused.

Chapter II Solutions.

1. Let's start with ourselves - we will throw garbage only into garbage cans and trash cans - “It’s clean not where they clean, but where they don’t litter!”

2. We will hold community clean-up days more often.

3.Hang up posters with an environmental theme in the forest, in places where landfills may appear.

4. Elimination of waste in unauthorized landfills within the city.

5. Treat textbooks with care.

6. Collect waste paper.

7. Return to nature the forest that was cut down to make our textbooks and notebooks (plant more trees, colors)

8. Save water

Conclusion

All of the above allows us to draw the following conclusions:

My assumption that mathematics is directly related to ecology was confirmed.

When studying ecology, many questions arise, the answers to which can be obtained using mathematics.

Mathematics allows us to make precise measurements, make calculations, and confirm observations.

Mathematics creates the conditions for the ability to give a quantitative assessment of the state of natural objects and phenomena, the positive and negative consequences of human activity in nature and the social environment. Text tasks have the opportunity to reveal questions about the environment, caring for it, rational use of natural resources, restoration and enhancement of its natural

Bibliography:

“I'm exploring the world. Ecology". A.E. Chizhevsky -Astrel - 2003

"Ecology of Russia". B.M. Mirkin-M: JSC MDS, Unisam, 1995, -232 p.

"Protection of Nature". A.V. Mikheev-Enlightenment, 2000. 144 p.

Encyclopedia for children. "Mathematics". - M.: Avanta +, 2003. - 688s.

Internet resources

The supraorganismal systems that ecology studies - populations, biocenoses, ecosystems - are extremely complex. There are many interconnections in them, the strength and constancy of which are constantly changing. The same external influences can lead to different, sometimes directly opposite, results, depending on the state of the system at the time of the influence.

It is possible to predict the response of a system to the action of specific factors only through a complex analysis of the quantitative relationships and patterns existing in it. Therefore, the method of mathematical modeling has become widespread in ecology as a means of studying and predicting natural processes.

The essence of the method is that with the help of mathematical symbols an abstract, simplified similarity of the system being studied is constructed. Then, by changing the value of individual parameters, they study how this artificial system will behave, i.e., how the final result will change.

Models are built on the basis of information accumulated in field observations and experiments. To build a mathematical model that would be adequate, that is, correctly reflect real processes, significant empirical knowledge is required. It is unrealistic to reflect all the infinite number of connections of a population or biocenosis in a single mathematical scheme. However, guided by the understanding that supraorganismal systems have an internal structure and, therefore, the principle “not all connections are essential” applies, it is possible to identify the main connections and obtain a more or less correct approximation to reality.

In formation mathematical models complex processes, the following stages are distinguished.

1. First of all, those real phenomena that one wants to model must be carefully studied: the main components are identified and the laws that determine the nature of the interaction between them are established. If it is unclear how real objects are interconnected, building an adequate model is impossible. At this stage, the questions that the model should answer should be formulated. Before building a mathematical model natural phenomenon, you need to have a hypothesis about its flow.

2. A mathematical theory is developed that describes the processes being studied with the necessary detail. On its basis, a model is built in the form of a system of abstract interactions. Established laws must be expressed in precise mathematical form. Specific models can be presented in analytical form (by a system of analytical equations) or in the form logic circuit machine program. Model of natural

phenomena are a strict mathematical expression of a formulated hypothesis.

3. Model verification - calculation based on the model and comparison of the results with reality. In this case, the correctness of the formulated hypothesis is checked. If there is a significant discrepancy in information, the model is rejected or improved. If the results are consistent, the models are used for forecasting by introducing various initial parameters into them.

It should be noted, however, that the mathematical model itself cannot serve as an absolute proof of the correctness of a particular hypothesis, since it may turn out that different hypotheses lead to similar results, but it serves. one of the ways to analyze reality.

Calculation methods, in the case of a correctly constructed model, help to see what is difficult or impossible to verify in experiment, and allow one to reproduce processes that would require a lot of effort and long periods of time to observe in nature. In mathematical models you can “lose” different variants- identify different connections, combine individual factors, simplify or complicate the structure of systems, change the sequence and strength of influences - all this makes it possible to better understand the mechanisms operating in natural conditions.

At the same time, mathematician V. Volterra identified similar patterns for the predator-prey system by processing statistical data from fisheries. One of the laws he derived - the “law of the periodic cycle” - states that the process of destruction of one species by another can lead to periodic fluctuations in the population size of both species, depending only on the growth rates of the predator and prey populations and on the initial relative abundance.

The equations of A. Lotka and V. Volterra were extremely simplified, since they were based on a number of unrealistic assumptions: that a change in the population size of one species immediately causes a response from the population of another species, that the “appetites” of a predator are unlimited, the search for prey is random, that the fertility of predators is proportional the size of the entire victim population.

As G.F. Gause (1934, 1935) showed, even under the conditions of a simplified experiment with protozoa, it is difficult to achieve compliance with these assumptions. In his experiments with ciliates, he managed to obtain only two predator-prey cycles, after which the system came to destruction. In nature, population fluctuations are more complex. In interactions between predator and prey, the “lag” effect is widespread due to differences in reproduction rates; indicators such as the degree of saturation (“functional response”) of predators, the time spent by them searching for and catching prey, and the ability to switch to other food play a role. , protective adaptations of victims, their placement in space and territorial behavior, age and sex structure of populations and much more. In addition, population growth may be restrained by other reasons, including intraspecific relationships.

Predator-prey models play a big role in planning fishing, whaling, and hunting, since the removal by humans of part of a population of wild animals from an ecological point of view is an analogue of natural predation. The maximum degree of exploitation that a population can withstand varies among different types. It is important to notice in time the symptoms indicating that removal from the population is approaching the maximum permissible level, after which its reproductive capacity may be impaired.

For example, based on the results of machine experiments with whaling statistics in the 60s, indicators of acceptable scales of production and symptoms of disastrous exploitation of the blue whale population were identified. If a population is exploited intensively, but not excessively, then the models show a decrease in the size and average age of individuals, and survival curves change, but not so much that the fertility of the herd as a whole is affected. In reality, the symptoms of disastrous exploitation of the whale herd predicted by the models were discovered - a reduction in the proportion of pregnant females, strong changes survival curves, decreasing catch sizes per unit of fishing effort, and the inability of the population to quickly recover after the cessation of fishing. There are so few blue whales left that, despite an international ban on their hunting, adopted in 1967, the population remains low and the animals are listed in the Red Book.

Modeling of trophic relationships is of great importance for solving problems of pest control, regulation of population numbers, and stabilization of communities.

Mathematical modeling is widely used in solving environmental problems associated with anthropogenic impacts on the natural environment. In modern mathematical models, tactical and strategic models are distinguished. Tactical models of ecosystems and populations serve for ecological forecasting of their state, including under various kinds of exogenous influences. Strategic models are built mainly for research purposes, to reveal general laws functioning of biological systems, such as stability, diversity, resistance to influences, and the ability to return to their original state. To tasks strategic models includes using a computer to study the consequences of different ecosystem management strategies in order to be able to choose the optimal one.

Models that describe the interaction between society and nature and that take into account not only environmental, but also economic, demographic and social indicators are called ecological-economic models. Such models are developed for long-term forecasting of economic growth and overall assessment of the impact of human activity on the natural environment.

Ecology is a developing interdisciplinary field of knowledge, including ideas from almost all sciences about the interactions of living organisms, including humans, with the environment. Until the mid-20th century, ecology was one of the biological disciplines, namely, the science of the interaction of organisms with the environment. Modern ecology, along with this, includes science and practical methods control over the state of the environment - monitoring, environmental protection, the doctrine of biogeocenoses and anthropological impacts on natural ecosystems, environmental-economic and environmental-social aspects. All this determines the subject mathematical ecology, combining mathematical models and methods used in solving environmental problems.

The foundation of mathematical ecology is the mathematical theory of population dynamics (see. Population dynamics), in which fundamental biological ideas about the population dynamics of animal species, plants, microorganisms and their interactions are formalized in the form of mathematical structures, primarily systems of differential, integro-differential and difference equations.

Any ecosystem consists of nonlinearly interacting subsystems that can be ordered into some hierarchical structure. As components, or subsets, are combined into larger functional units, these new units develop properties that are not present in its constituent components. Such qualitatively new “emergent” properties of an ecological level or ecological unit are not a simple sum of the properties of the components. The consequence is the impossibility of studying the dynamics of complex ecosystems by dividing them hierarchically into subsystems and subsequent isolated study of these subsystems, since in this case the properties determined by the integrity of the system under study are inevitably lost.

Impact external factors on the ecological system also cannot be considered independently of each other, since the combined effect cannot be reduced to a sum operating factors. Especially challenging task is a quantitative description of the response of a complex system to the complex influence of various factors.

All these circumstances lead to the impossibility of describing complex ecosystems using simple reduced “mechanical” models. What is needed is either complex simulation models that combine into one complex system at the model level knowledge about the elements of the system and the types of their interactions, or simplified integrated impact-response models that integrate data from a large number of observations of the ecosystem.

Simulation computer models include ideas about the components of systems and their relationships both in the form of actual mathematical objects: formulas, equations, matrices, logical procedures, and in the form of graphs, tables, databases, operational information environmental monitoring. Such multidimensional models make it possible to combine heterogeneous information about an ecological or ecological-economic system, “play out” various development scenarios and develop optimal management strategies on the model, which is impossible to do on a real system due to its uniqueness and limited time.

The simulation approach, as well as modeling ecosystems using response functions, requires highly developed computer technology, therefore mathematical ecology, as a developed and practically used science, became widespread only in the last decades of the 20th century. The widespread use of mathematical tools stimulated the development

theoretical ecology. The construction of mathematical models requires ordering and classification of available information about ecosystems, leads to the need to plan a data collection system and makes it possible to combine at a meaningful level a set of physical, chemical and biological information and ideas about individual processes occurring in ecosystems.

Modern mathematical ecology is an interdisciplinary field that includes all kinds of methods of mathematical and computer description ecological systems. The theoretical basis for describing interactions between species in ecosystems is population dynamics, which describes basic interactions and provides a qualitative picture of possible patterns of behavior of variables in the system. To analyze real ecosystems, system analysis is used, and the degree of integration of the model depends on both the object and the goals of the modeling. Modeling of many aquatic ecosystems, forest cenoses, and agroecosystems is effective means development of a method for optimal control of these systems. The construction of global models makes it possible to assess global and local changes in climate, temperature, and type of vegetation cover under different scenarios of human development.

Assessment of air and land surface pollution.

Important practical. The task of mathematical ecology is to calculate the spread of pollution from existing enterprises and plan the possible location of industrial enterprises in compliance with sanitary standards.

The process of distribution of industrial emissions occurs due to their transfer by air masses and diffusion caused by turbulent air pulsations. If you observe a smoke plume from a factory chimney, you will notice that this plume is entrained by the air flow and gradually swells as it moves away from the source due to small-scale turbulence. The torch has the shape of a cone, elongated in the direction of the movement of air masses. Then the torch breaks up into isolated vortex formations, carried away by long distances from the source.

Almost all impurities eventually settle on the Earth's surface sooner or later, heavy ones under the influence of the gravitational field, light ones as a result of the diffusion process. Impurities consisting of large particles soon begin to sink under the influence of gravity in accordance with Stokes' law. Gaseous impurities such as oxides represent the light fraction and are especially dangerous for the environment.

Great importance In the propagation theory, pollution fluctuates in the direction of the wind over a long period of time - about a year. During such a period, air masses that carry impurities away from the source repeatedly change direction and speed. Statistically, such long-term changes are described by a special diagram called a wind rose, in which the magnitude of the vector is proportional to the number of repeating events associated with the movements of air masses in a given direction. The maximums of the wind rose diagram correspond to the prevailing winds in a given area. This information is the starting point for planning new industrial facilities. When assessing acceptable pollution of enterprises located among a large number of environmentally significant zones ( settlements, recreation areas, agricultural, forest lands, etc.) pollution from existing enterprises in the region should also be taken into account.

The assessment of pollution of the atmosphere and underlying surface by passive and active impurities is carried out using mathematical models built on the basis of partial differential aerodynamic equations, as well as their finite-difference approximations.

In Russia, a great contribution to this direction was made by the work of the school of academician G.I. Marchuk. Models of this type are widely used in Europe and the USA when resolving lawsuits brought by the public or local authorities industrial enterprises in connection with the infliction of certain damage. To assess the damage caused using mathematical modeling, an examination is carried out, as a result of which the amount of the fine that the polluting enterprise is obliged to pay to state or local authorities is quantified. Such measures turned out to be very effective and led to developed countries to almost universal introduction of cleaning technologies

Models of the transfer of pollutants in this type of model are associated with a procedure for calculating the main functional of the problem, which can represent the total number of deposited impurities, the sanitary hazard of impurities, include damage to public health, agricultural land, forest areas, soil, costs of environmental restoration and other indicators. In simplified versions, the response function method is widely used (see above).