Introduction to Mathematical Modelling and Mechanics

О.В. Степанова

English

For students of Mechanics

And Mathematical Modelling

 

Ижевск 2014

УДК 802 - 07 (07)

ББК 81.4 Англ я 81

С 79

Рецензенты: Н.А. Атнабаева, канд. филол. наук, доцент кафедры «Иностранные языки» Ижевской государственной сельскохозяйственной академии; Л.Н. Пирожкова, доцент кафедры «Английский язык» Ижевского государственного технического университета имени М.Т. Калашникова

 

Составитель: О.В. Степанова, старший преподаватель кафедры «Английский язык» Ижевского государственного технического университета имени М.Т. Калашникова

 

Рекомендовано к изданию на заседании кафедры «Английский язык» ИжГТУ имени М.Т. Калашникова (Протокол № ____ от « » мая 2014 г.).

 

 

Рекомендовано учебно-методическим советом ФГБОУ ВПО «ИжГТУ имени М.Т. Калашникова» для использования в учебном процессе в качестве учебно-методического пособия для студентов профиля 010800 «Механика и Математическое моделирование» факультета «Математика и Естественные Науки» при изучении дисциплины «Иностранный язык (английский)»

 

 

English for students of Mechanics and Mathematical Modelling («Английский язык для студентов Механики и Математического моделирования»). Учебно-методическое пособие для студентов профиля 010800 «Механика и математическое моделирование» факультета «Математика и Естественные Науки»/ О.В. Степанова. – Ижевск: Изд-во ИжГТУ, 2014. – 46 с.

 

 

Учебно-методическое пособие подготовлено на кафедре «Английский язык» факультета ЭПиГН ИжГТУ им. М.Т. Калашникова.

 

CONTENTS

Part I

Введение ………………………………………………………………………….p. 5

 

Lesson 1. Introduction to Mathematical Modelling and Mechanics ………..….… p. 6

 

Lesson 2. Force Around Us ……………………………………………..……..... p. 10

 

Lesson 3. Newton’s Law of Gravitation …………………………….…….…..... p. 13

 

Lesson 4. Using Math in Mechanics ……………………………………............. p. 16

 

Lesson 5. The Math Requirements for Diesel Mechanics ……………………… p. 20

 

Lesson 6. How Do Mechanics Use Math in Their Job? …………….………..… p. 24

 

Part II

 

Cliché s and Connecting Words for Writing Pré cis and Annotations …..……. p. 28

Additional Readings ………………………….…………………………...….…. p. 31

 

Part III

Mathematical Modelling in Practice ……………………..…………..…….….... p. 37

Appendix ……………………………… ………………….…….………….……. p. 43

Заключение ……………….…………………………………………….…………p. 45 Библиография ………………………………………….………….…………..… p. 46

Введение

 

Предлагаемое учебно-методическое пособие по английскому языку предназначается для студентов первого года обучения факультета «Математика и Естественные Науки», обучающихся по профилю 010800 «Механика и Математическое моделирование».

Пособие ставит своей задачей подготовить студентов к коммуникации в условиях иноязычного общения в рамках тем общематематического профиля.

Пособие состоит из трех разделов.

Первый раздел включает шесть уроков, содержащих тексты профессионально-ориентированной тематики, упражнения на закрепление новой лексики, совершенствование навыков чтения, перевода, аудирования, видеопросмотра и говорения.

Во втором разделе представлены тексты для общего ознакомления и последующего написания реферата и аннотации к текстам, в помощь данному виду работы приведены вводные выражения и клише.

Третий раздел представляет собой пример практического применения знаний из области математического моделирования.

 

Part I

Lesson 1

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Introduction to Mathematical Modelling and Mechanics

This chapter is about the use of mathematics in solving realistic problems. Traditionally the discipline in which the use of mathematics is studied has been called Applied Mathematics, and this term has often been associated with the application of mathematics to science and engineering. But mathematics occurs in many other subjects, for example in economics, biology, linguistics, transport as well as in industry, commerce and government.

Applying mathematics to such a wide range of subjects requires not only good mathematical problem solving skills but also the ability of the mathematician to start with a problem in non-mathematical form and to give the results of any mathematical analysis in non-mathematical form. In between these start and end points, the mathematician must formulate the problem into a form that allows the use of some mathematical analysis, solve any mathematical problems that have been set up and then interpret the solution in the context of the original setting. This process is called mathematical modelling and can be illustrated by the diagram opposite.

Central to mathematical modelling is the representation of the real world problem by a mathematical structure such as a graph, an equation or an inequality. Such a representation is what is meant by a mathematical model.

Formulation

Real World Mathematical

World

Interpretation

For example, the equation s 15t describes the distance travelled, s, in time t, when travelling at a speed of 15 ms. The equation s 15t is a simple example of a mathematical model.

The first step in trying to devise a mathematical model for a given situation is to identify the quantities which can be measured and whose values will describe the real situation. In mechanics these quantities might be position, velocity, mass etc. In economics you might be interested in sums of money, inflation, depreciation, interest rates etc. Such quantities are called variables.

Broadly speaking, a mathematical model is a relation between two or more variables. The challenge to the applied mathematician is formulating a model which accurately describes or represents a given situation. To become skillful at mathematical modelling requires much hard work through experience gained at problem solving. This course on mechanics will provide the framework for you to learn about good models and to develop good problem solving skills.

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. The discipline in which the use of mathematics is studied has been called ___________________, and this term has often been associated with _____________ of mathematics to science and engineering.

2. Applying mathematics to a wide range of subjects requires ___________________ problem solving skills and the ability to start with a problem in non-mathematical form and __________________ ___________.

3. Central to mathematical modelling is the representation of the real world problem by a mathematical structure such as __________, ___________ or _______________.

4. The first step in trying to devise a mathematical model for a given situation is to ____________________ which can be measured and whose values will _______________________.

5. In economics you might be interested in sums of money, inflation, depreciation, interest rates etc. Such quantities are called _____________.

6. Broadly speaking, a mathematical model is a _________________.

7. To become skillful at mathematical modelling requires much __________ through experience gained at _______________.

 

2. Work in pairs to find out:

1. What has the term Applied Mathematics often been associated with?

2. What must the mathematician do in mathematical modelling?

3. Is the representation of the real world problem by a mathematical structure such as a graph, an equation or an inequality central to mathematical modelling?

4. The first step in trying to devise a mathematical model for a given situation is to identify the qualities which can be measured and whose values will describe the imagined situation, isn’t it?

5. What framework will the course on mechanics provide to learn about and to develop?

 

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Basics of Mathematical Modelling and Mechanics. Present this information to the group.

Lesson 2

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Force Around Us

If an object which is initially at rest suddenly starts to move, then something must have caused the motion to start. For the object to start moving it must be acted upon by a net force. For example, a yacht moored in a harbour may begin to move when the sail is hoisted; the cause of the movement is the wind in the sail.

Suppose that you are towing a car up a 1 - in - 5 hill; it is important to know that the tow rope is strong enough not to break! What forces are acting in such a situation? You may have some idea already: there is the tension in the rope, the weight of the car, the reaction between the car and the road (hopefully the brakes are off! ).

Examples of force are all around us. You probably have an intuitive idea of force from your own experience of pushing and pulling things. But what is a force? It is difficult to define a force precisely but what you can do is to describe the effect of a force. It has already been said that a force can start motion. A force is required to stop motion: for example, the American space shuttle returning from orbit glides towards the airforce base in California without any power. To stop the shuttle on landing, a force is produced by a parachute.

A force is required to make an object move faster or slower. For example an ice puck in ice hockey can glide across the ice in a straight line with constant speed; to make it go faster a player hits the puck. If the puck is hit in its direction of motion then it will continue in that direction. However, if hit across its path, the puck will change its direction.

So, in summary, a force can: start motion (1); make an object move faster or slower (2); stop motion (3); change the direction of motion (4).

In other words a force causes a change in motion. As you will see, a force is not required to maintain motion. An object can move with constant speed with no force acting on it. For example a spacecraft in deep space, far from the influence of all planets, can maintain a constant speed without using its engines; only if it needs to change its motion does it need to uses its engines.

 

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. For the object to start moving it must be acted upon by ___________.

2. It’s difficult to define a force ________ but what you can do is to _______.

3. A force is required to make an object move __________ or ___________.

4. If hit across its path, the puck will change its ______________.

5. A force causes a change in __________________.

6. An object can move with ___________ speed with no force acting on it.

 

2. In each of the ten situations give a brief description of the motion:

(a) a table tennis ball hit without spin;

(b) a table tennis ball hit with spin;

(c) a train on its journey from Plymouth to London;

(d) a ball thrown horizontally from a tower;

(e) an aircraft coming in to land at Heathrow;

(f) a ball rolling down a hill;

(g) a snooker ball sliding over the table (a 'stun shot');

(h) a swimmer diving from a springboard;

(i) cyclists going round a corner;

(j) a person in the chairoplane ride at Alton Towers.

3. Find in the text ing-forms, and say if they are Gerunds, Participles or forms of Progressive Tenses. Define the function in the sentence, give translations.

4. Consider the following situations and discuss whether there is a change in motion:

· An apple falling off a tree.

· A parachutist falling at a constant rate.

· A bouncing ball while it is in contact with the ground.

· A person in a car going round a roundabout.

· An astronaut floating freely close to an orbiting satellite.

 

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Force in Our Life. Present this information to the group.

Lesson 3

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Newton’s Law of Gravitation

Earlier in this section the force of gravity on an object of mass m near the earth’s surface was introduced as a force of magnitude 9.8m kg in the vertically downwards direction. Galileo, after dropping many objects from the leaning tower of Pisa, deduced that an object fell to the earth with an acceleration of 9.8 ms². So Newton with his second law was able to deduce the force on the object as 9.8 m.

However, one of Newton’s great achievements was to generalize gravity in his law of gravitation. Newton postulated that the force of gravity on an object near the earth depended on the mass of the object, the mass of the earth and inversely on the square of the distance between the earth’s centre and the object.

To validate his law of gravitation, Newton clearly could not carry out experiments since he could not measure the mass of the earth and could not move objects very far from the earth’s surface. Indeed, Newton studied the work of Kepler and realised that if he could ‘prove’ Kepler's laws using the law of gravitation and his law of motion, F = ma, then he was on to a winner! History tells us that Newton got it right and in the process developed Calculus.

Sir Isaac Newton (1642 – 1726) was, in fact, a prolific scientist and mathematician and turned his hand to a variety of problems including alchemy, optics and planetary motion. He was elected in 1689 as M.P. for Cambridge, and in 1699 accepted the post of Master of the Mint. Although he wrote that " if I have seen further than Descartes, it is because I have stood on the shoulders of giants", he undoubtedly must be regarded as one of the most influential mathematicians and scientists of all time. With the success of the law of gravitation applied to the planetary system, Newton postulated the Universal Law of Gravitation.

 

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. Galileo, after dropping many objects from the leaning tower of Pisa, deduced that an object fell to the earth with ____________________ of 9.8 ms².

2. One of Newton’s great achievements was to _____________ in his law of gravitation.

3. To validate his law of gravitation, Newton clearly could not carry out experiments since he could not ___________________ and could not move objects very far from the _______________________.

4. Sir Isaac Newton was a prolific scientist and mathematician and turned his hand to a variety of problems including ___________, ___________ and ___________.

5. With the success of the law of gravitation applied to _______________, Newton postulated the Universal Law of Gravitation.

2. Work in pairs to find out:

1. How did Galileo deduce that an object fell to the earth with an acceleration of 9.8 ms²?

2. What did Newton postulate about the force of gravity?

3. Why couldn’t Newton carry out experiments?

4. Whose work did Newton study and what did he realise?

5. What happened to Newton in 1689 and in 1699?

6. Must he be regarded as one of the most influential mathematicians and scientists of all time?

7. With the success of the law of gravitation applied to the planetary system, Newton postulated the Universal Law of Gravitation, didn’t he?

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning The Law of Gravitation. Present this information to the group.

Lesson 4

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Technical Manuals

According to the University of Missouri, diesel mechanics need basic mathematics to read and understand technical manuals. Basic math involves addition, subtraction, multiplication and division.

Conversions

Diesel mechanics work with liquid engine components, so they need to be able to perform basic unit conversions like metric to imperial. For example, if a mechanic has a 12 liter tank, but the liquids come in gallons, he needs to be able to convert between gallons and liters.

Technical Skills

More and more diesel vehicles are being built with computers. Computers make a mechanic's job easier in some ways (for example, they can pinpoint a problem area), but in other ways, they make the job more technically and mathematically challenging. For example, if the manufacturer does not list resistance or other component value, the mechanic will have to make that calculation using an equation like R=V/P, where R=total resistance, V=total voltage and P=total power.

Instrument Use

A diesel mechanic uses a variety of tools that need mathematics. For example, engine bolts need to be tightened in a certain order and at a certain angle. Diesel mechanics must also be able to use instruments like a micrometer, which is used to measure the outside diameter of a sphere or cylinder. Other equipment used that involves math includes a gas analyzer, which measures gasses found in exhaust, requiring knowledge of percentages and ranges. For example, the range of carbon monoxide reported by a gas analyzer might be 0 to 4000 parts per million with a 2 percent accuracy. It is vital for a mechanic to know what this means in terms of vehicle analysis.

Stephanie Ellen

http: //www.ehow.com/list_6370184_math-requirements-diesel-mechanics.html

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. Diesel mechanics maintain and repair diesel engines on a variety of machinery, including ______________, ______________ and ____________.

2. Diesel mechanics work with ________ engine components, so they need to be able to perform basic unit conversions like metric to ___________.

3. Computers make a mechanic's job easier in some ways, but in other ways, they make the job more _________ and ___________ challenging.

4. If the manufacturer does not __________ or other component value, the mechanic will have to make that calculation using an ____________.

5. Diesel mechanics must also be able to use instruments like a _____________, which is used to measure the outside diameter of a __________ or _______________.

6. Equipment that involves math includes a ______________, which measures gasses found in exhaust, requiring knowledge of _______________ and __________________.

 

Work in pairs to find out:

1. What kinds of machinery do diesel mechanics maintain and repair?

2. For what purposes does a diesel mechanic need basic mathematics?

3. Diesel mechanics work with liquid engine components, don’t they?

4. In what ways do computers make a mechanic's job easier?

5. What kinds of tools that need mathematics are used by a diesel mechanic? Give an example.

6. How does a gas analyzer work?

7. Can you explain the equation R=V/P. Where is it applied?

 

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Using Math in Mechanics. Present this information to the group.

Lesson 5

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

 

Two Different Systems

Mechanics use mathematics all the time in their daily routine of repairing and modifying internal-combustion automobiles. Their use of numbers takes on many forms; from determining the size of the wrench they need to loosen a bolt to calculating torque, today's mechanics need to have a good head for numbers. They also have to deal with two different numeric systems: metric and American (sometimes called British). The metric system is based on a 10-digit numerical system, but the British system, which we also use here in the United States, is based on the English foot (which comes in units of 12, yet still uses the same 10-digit number system). As a result, most modern mechanics are constantly switching from one system to another – an activity that is not as difficult as it sounds.

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Application of Mathematical Modelling in Different Spheres of Life. Present this information to the group.

 

 

Lesson 6

 

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

 

The Mechanic's World

A mechanic is, by definition, any person who works with machinery. Since machinery requires building, and building requires putting parts together, machinery is thus comprised of parts that must be designed and arranged in an organized way. The mechanic is the person who can see how these parts fit together and how they work within a machine. Just like the number " 9" can be seen as a single number, it can also be seen as many numbers such as " 3+3+3" or " 1+1+1+1+1+1+1+1+1." These are the ways that " 9" can be built, just like a car can be built with engines and wheels and gears and wires and seats and lights and....... you get the idea. Even the " +" symbol can be seen as a part in the " machine of 9, " like a hinge for the other numbers to attach to. A mechanic will use these parts not with numbers, but with machines, and decide if the parts are working correctly. If they are not, he will fix the parts or replace them. As you can see, doing math is very similar to building machines.

The Mechanic's Tools

Given that math is simply a way to look at the world, a mechanic will see his world in metal, screws, gears, heat or lubricant. A mechanic will use tools like wrenches and hammers instead of pencil and paper. These tools are designed to perform the jobs a mechanic requires. Wrenches can come in different sizes, like 1/2 inch or 5/16 inch, and their uses depend on the job. The mechanic needs to be able to figure out these numbers correctly by measuring the parts of his machine.

Math and the World

Whether a mechanic knows it or not, he's always using the mathematical part of his brain to calculate various things. For example: How much force to put into pushing a wrench and in what direction; or knowing the strength of materials and whether they can withstand the forces they'll be put through. Mechanics typically have less addition and subtraction to deal with, and more physics, which is math of the moving world. Since mechanics are most often dealing with moving parts, they must apply these mathematical principles to their work.

Jin Sunszine

http: //www.ehow.com/how-does_5008919_mechanics-use-math-their-job.html

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. A mechanic is, by definition, any person who ________________.

2. Since machinery requires building, and building requires putting parts together, machinery is thus comprised of parts that must be _________ and __________ in an organized way.

3. A mechanic will use tools like ___________ and __________ instead of pencil and paper.

4. Wrenches can come in different sizes, like _______ inch or _______ inch, and their uses depend on the job.

5. A mechanic is always using the mathematical part of his brain to ____________________________.

6. Mechanics typically have less ________ and __________ to deal with, and more _________, which is math of the moving world.

2. Work in pairs to find out:

1. What parts is machinery comprised of?

2. How will a mechanic use the parts?

3. In what way will a mechanic use tools?

4. What is the mechanic able to do?

5. A mechanic is always using the mathematical part of his brain to calculate various things, isn’t he?

6. What is typically the part of mechanics’ addition and subtraction to deal with? What about physics?

7. Since mechanics are most often dealing with moving parts, what principles must they apply to their work?

 

3. Find in the text ing-forms, define whether they are Participle I, Gerund or ing-Nouns. What is their function in the sentence? What is the role of Participle II: find them in the sentences and give their translations.

 

4. Define the following word combinations. Use them in the sentences or situations of your own:

· by definition

· be comprised of

· must be designed

· in an organized way

· fit together

· be very similar

· given that

· be designed to

· needs to be able to

· by measuring

· must apply

Project work

Consult Internet, Encyclopedia or other sources of information to find some interesting and important facts concerning Application of Mechanics in Different Times. Present this information to the group.

 

Part II

Additional Readings

Skim the articles to find the main idea. Write the annotation and the pré cis:

Part III

 

Fractions

A fraction is a part of a whole. If we divide a cake into five equal-sized pieces, we are dividing it into fifths. One piece of our cake is a fifth of the whole. This is a fraction, and mathematicians would write this fraction as 1/5. This way of writing down fractions tells us two important things. The number at the bottom of the fraction tells us into how many parts the cake (the whole) has been divided. In this case, the cake has been divided into fifths. The number at the top of the fraction tells us how many of the slices of the whole we have.

 

Curves

Much of our knowledge of geometric curves comes from the work of the Greek mathematician Hypatia (AD 370-415).She developed the studies of the Greek mathematician Apollonius (262 BC-190 BC). Hypatia formed common curves, such as the circle, the ellipse, the parabola, and the hyperbola, by slicing a cone at different angles. This method of creating curves is known as conic sectioning. Another way of creating a geometric curve is to trace the path of a point as it moves according to certain conditions. For example, by tracing the path of a moving point that is always the same distance from another fixed point, we can form a circle.

 

заключение

 

Учебно-методическое пособие по английскому языку, ориентированное на студентов первого года обучения факультета «Математика и Естественные Науки» профиля 010800 «Механика и Математическое моделирование», способствует формированию различных навыков.

Упражнения на развитие языковых и речевых навыков в пособии нацелены на формирование профессионально-ориентированного вокабуляра и основ коммуникативной компетентности.

Пособие предназначено не только для становления и совершенствования специальных лингвистических и коммуникативных компетентностей, но и формирования и развития учебно-познавательных компетентностей, предполагающих самостоятельную творческую и поисковую работу студентов. С этой целью в пособие включены упражнения под рубрикой «Проектная работа» (Project Work), требующая поисковых и презентативных навыков обучаемых.

Библиография:

1. Ellen, S. http: //www.ehow.com/list_6370184_math-requirements-diesel-mechanics.html (accessed March 15, 2014)

2. Hewitt, D. Proceedings of the British Society for Research into Learning Mathematics 26 (2) June 2006. – P. 92 – 93. (http: //www.bsrlm.org.uk/IPs/ip26-2/BSRLM-IP-26-2-16.pdf.(accessed April 6, 2014))

3. Степанова, О.В. Topics. Dialogues. Discussions. – Ижевск: Изд-во ИжГТУ, 2010. – 128 с.

4. http: //www.ehow.com/how-does_5008919_mechanics-use-math-their-job.html (accessed March 10, 2014)

5. http: //www.ehow.com/list_6370184_math-requirements-diesel-mechanics.html (accessed April 28, 2014)

6. http: //www.mathsisfun.com/algebra/mathematical-models.html (accessed March 16, 2014)

7. Modelling and Mechanics // ULR: http: //www.cimt.plymouth.ac.uk/projects/mepres/alevel/mechanics_ch1.pdf (accessed March 11, 2014)

8. http: //www.youtube.com/watch? v=c2bO20DFcpA (accessed April 5, 2014)

9. http: //www.youtube.com/watch? v=GnlgGmLNn5o (accessed May 5, 2014)

10. http: //www.youtube.com/watch? v=i4fhMtDhAFQ (accessed April 9, 2014)

11. http: //www.youtube.com/watch? v=i6VBPiA-eBk (accessed April 18, 2014)

12. http: //www.youtube.com/watch? v=QG6zpNL-vek (accessed May 2, 2014)

13. http: //www.youtube.com/watch? v=Rkzxr1ojA4I (accessed May 3, 2014)

 

 

О.В. Степанова

English

For students of Mechanics

And Mathematical Modelling

 

Ижевск 2014

УДК 802 - 07 (07)

ББК 81.4 Англ я 81

С 79

Рецензенты: Н.А. Атнабаева, канд. филол. наук, доцент кафедры «Иностранные языки» Ижевской государственной сельскохозяйственной академии; Л.Н. Пирожкова, доцент кафедры «Английский язык» Ижевского государственного технического университета имени М.Т. Калашникова

 

Составитель: О.В. Степанова, старший преподаватель кафедры «Английский язык» Ижевского государственного технического университета имени М.Т. Калашникова

 

Рекомендовано к изданию на заседании кафедры «Английский язык» ИжГТУ имени М.Т. Калашникова (Протокол № ____ от « » мая 2014 г.).

 

 

Рекомендовано учебно-методическим советом ФГБОУ ВПО «ИжГТУ имени М.Т. Калашникова» для использования в учебном процессе в качестве учебно-методического пособия для студентов профиля 010800 «Механика и Математическое моделирование» факультета «Математика и Естественные Науки» при изучении дисциплины «Иностранный язык (английский)»

 

 

English for students of Mechanics and Mathematical Modelling («Английский язык для студентов Механики и Математического моделирования»). Учебно-методическое пособие для студентов профиля 010800 «Механика и математическое моделирование» факультета «Математика и Естественные Науки»/ О.В. Степанова. – Ижевск: Изд-во ИжГТУ, 2014. – 46 с.

 

 

Учебно-методическое пособие подготовлено на кафедре «Английский язык» факультета ЭПиГН ИжГТУ им. М.Т. Калашникова.

 

CONTENTS

Part I

Введение ………………………………………………………………………….p. 5

 

Lesson 1. Introduction to Mathematical Modelling and Mechanics ………..….… p. 6

 

Lesson 2. Force Around Us ……………………………………………..……..... p. 10

 

Lesson 3. Newton’s Law of Gravitation …………………………….…….…..... p. 13

 

Lesson 4. Using Math in Mechanics ……………………………………............. p. 16

 

Lesson 5. The Math Requirements for Diesel Mechanics ……………………… p. 20

 

Lesson 6. How Do Mechanics Use Math in Their Job? …………….………..… p. 24

 

Part II

 

Cliché s and Connecting Words for Writing Pré cis and Annotations …..……. p. 28

Additional Readings ………………………….…………………………...….…. p. 31

 

Part III

Mathematical Modelling in Practice ……………………..…………..…….….... p. 37

Appendix ……………………………… ………………….…….………….……. p. 43

Заключение ……………….…………………………………………….…………p. 45 Библиография ………………………………………….………….…………..… p. 46

Введение

 

Предлагаемое учебно-методическое пособие по английскому языку предназначается для студентов первого года обучения факультета «Математика и Естественные Науки», обучающихся по профилю 010800 «Механика и Математическое моделирование».

Пособие ставит своей задачей подготовить студентов к коммуникации в условиях иноязычного общения в рамках тем общематематического профиля.

Пособие состоит из трех разделов.

Первый раздел включает шесть уроков, содержащих тексты профессионально-ориентированной тематики, упражнения на закрепление новой лексики, совершенствование навыков чтения, перевода, аудирования, видеопросмотра и говорения.

Во втором разделе представлены тексты для общего ознакомления и последующего написания реферата и аннотации к текстам, в помощь данному виду работы приведены вводные выражения и клише.

Третий раздел представляет собой пример практического применения знаний из области математического моделирования.

 

Part I

Lesson 1

Read the text. Find out the items revealing different aspects of the theme given. Define the key facts of the text:

Introduction to Mathematical Modelling and Mechanics

This chapter is about the use of mathematics in solving realistic problems. Traditionally the discipline in which the use of mathematics is studied has been called Applied Mathematics, and this term has often been associated with the application of mathematics to science and engineering. But mathematics occurs in many other subjects, for example in economics, biology, linguistics, transport as well as in industry, commerce and government.

Applying mathematics to such a wide range of subjects requires not only good mathematical problem solving skills but also the ability of the mathematician to start with a problem in non-mathematical form and to give the results of any mathematical analysis in non-mathematical form. In between these start and end points, the mathematician must formulate the problem into a form that allows the use of some mathematical analysis, solve any mathematical problems that have been set up and then interpret the solution in the context of the original setting. This process is called mathematical modelling and can be illustrated by the diagram opposite.

Central to mathematical modelling is the representation of the real world problem by a mathematical structure such as a graph, an equation or an inequality. Such a representation is what is meant by a mathematical model.

Formulation

Real World Mathematical

World

Interpretation

For example, the equation s 15t describes the distance travelled, s, in time t, when travelling at a speed of 15 ms. The equation s 15t is a simple example of a mathematical model.

The first step in trying to devise a mathematical model for a given situation is to identify the quantities which can be measured and whose values will describe the real situation. In mechanics these quantities might be position, velocity, mass etc. In economics you might be interested in sums of money, inflation, depreciation, interest rates etc. Such quantities are called variables.

Broadly speaking, a mathematical model is a relation between two or more variables. The challenge to the applied mathematician is formulating a model which accurately describes or represents a given situation. To become skillful at mathematical modelling requires much hard work through experience gained at problem solving. This course on mechanics will provide the framework for you to learn about good models and to develop good problem solving skills.

Comprehension work:

1. Insert necessary words and word combinations according to the text:

1. The discipline in which the use of mathematics is studied has been called ___________________, and this term has often been associated with _____________ of mathematics to science and engineering.

2. Applying mathematics to a wide range of subjects requires ___________________ problem solving skills and the ability to start with a problem in non-mathematical form and __________________ ___________.

3. Central to mathematical modelling is the representation of the real world problem by a mathematical structure such as __________, ___________ or _______________.

4. The first step in trying to devise a mathematical model for a given situation is to ____________________ which can be measured and whose values will _______________________.

5. In economics you might be interested in sums of money, inflation, depreciation, interest rates etc. Such quantities are called _____________.

6. Broadly speaking, a mathematical model is a _________________.

7. To become skillful at mathematical modelling requires much __________ through experience gained at _______________.

 

2. Work in pairs to find out:

1. What has the term Applied Mathematics often been associated with?

2. What must the mathematician do in mathematical modelling?

3. Is the representation of the real world problem by a mathematical structure such as a graph, an equation or an inequality central to mathematical modelling?

4. The first step in trying to devise a mathematical model for a given situation is to identify the qualities which can be measured and whose values will describe the imagined situation, isn’t it?

5. What framework will the course on mechanics provide to learn about and to develop?

 

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