It is not so easy to get a good higher education here. To do this, you will need not only to attend lectures, seminars and workshops, but also to complete various independent tasks, such as essays or coursework. In this article I would like to talk about what calculation and graphic work is.

About the concept

First of all, you need to understand the concept itself. Often, when a student hears the abbreviation RGR for the first time, he becomes confused. But there’s nothing to worry about, that’s the abbreviated name for calculation and graphic work. This is a student designed for a more complete assimilation of the material he has covered in a particular subject. It is also worth mentioning that RGR can be part of the course work, that is, its practical component. The essence of this type of work is to provide not only theoretical, but also practical material. Thus, the RGR will necessarily contain certain calculations, possibly graphs, tables, diagrams.

What should it be?

What important elements does the RGR consist of?

1. Justification of the chosen topic. This is a theoretical component where the student must talk about the importance of the work he has done.
2. Characteristic
3. Carrying out basic calculations.
4. Providing the results obtained in a convenient form: tables, graphs, diagrams.
5. Conclusions and possibly recommendations.

Structure

Calculation and graphic work must have its own structure. It is not possible to submit material for consideration in any form. So, the RGR should consist of the following points:

1. Table of contents. Here the student provides information about all sections of his work.
2. Exercise. At this stage, it is necessary to fully “voice” the task given to the student.
3. Initial data. The student provides all existing source data that may be needed to carry out the calculations.
4. This is followed by sections that will contain practical solutions and analysis of the results obtained.
5. Providing calculation results in the most convenient form for understanding.
6. Conclusions.
7. Bibliography.
8. Applications (if any).

Basic moments

There is also a list of special requirements that the student must comply with when preparing calculation and graphic work.

Design of tables and figures

Economics, statistics, theoretical mechanics... Calculation and graphic work can be performed in almost any subject where there are calculations (regardless of the student’s specialty of study). However, it is worth remembering that it is necessary not only to correctly format the text itself, but also to provide all the tables, figures and diagrams.

Computer science

What might computational and graphical work in computer science look like? So, it’s worth saying that there are no specific frameworks here. It all depends on the level of the material taught at the university for a given specialty. So, for humanities students the RGR in computer science will be one, for programmers it will be completely different. This could be simply a demonstration of PC skills (for example, in Word or Excel), or it could be programming, using different number systems to work, performing all kinds of translations between different ones, etc.

BJD

As part of the Life Safety course, some universities also offer students to complete RGR. And again, I would like to say that work in different specialties will differ from each other. After all, each profession has its own precautions and requirements. Calculation and graphic work on heavy-duty railways - what can be studied or researched here? Thus, you can calculate the most comfortable working conditions for a group of workers, you can plan the placement of jobs in a workshop or enterprise, you can analyze, etc. In fact, there are a huge number of topics to consider.

Other items

It is worth saying that calculation and graphic work can be written on almost any subject: economics, electronics, logistics, theoretical mechanics, etc. However, the goal of this work will always remain the same: to teach the student not only to correctly carry out the necessary calculations, but also to be able to correctly present them for consideration.

§1. NUMERICAL SOLUTION OF NONLINEAR EQUATIONS.

1p. General view of the nonlinear equation

Nonlinear equations can be of two types:

1. Algebraic
a n x n + a n-1 x n-1 +… + a 0 = 0

2. Transcendental - these are equations in which x is the argument of a trigonometric, logarithmic or exponential function.

The value x 0 for which the equality f(x 0) = 0 exists is called root equations

In the general case, for an arbitrary F(x) there are no analytical formulas for determining the roots of the equation. Therefore, methods that allow you to determine the value of the root with a given accuracy are of great importance. The process of finding roots is divided into two stages:

1. Separation of roots, i.e. definition of a segment containing one root.

2. Refinement of the root with a given accuracy.

For the first stage there are no formal methods; segments are determined either by tabulation or based on physical meaning or analytical methods.

The second stage, the refinement of the root, is carried out using various iterative methods, the essence of which is that a numerical sequence x i is constructed converging to the root x 0

The output from the iterative process is the following conditions:

1. │f(x n)│≤ε

2. │x n -x n-1 │≤ε

Let's consider the methods most used in practice: dichotomy, iteration and tangents.

2 p. Half division method.

Given a monotonic, continuous function f(x), which contains a root on the segment , where b>a. Determine the root with an accuracy of ε if it is known that f(a)*f(b)<0

The essence of the method

This segment is divided in half, i.e. x 0 =(a+b)/2 is determined, two segments are obtained and , then the sign is checked at the ends of the resulting segments for a segment having the conditions f(a)*f(x 0)≤0 or f(x 0)* f(b)≤0, the x-coordinate is again divided in half, a new segment is again selected, and so the process continues until │x n -x n-1 │≤ε

Let us present the GSA for this method

3p. Iteration method.

Given a continuous function f(x), which contains a single root on the segment , where b>a. Determine the root with accuracy ε.

The essence of the method

Given f(x)=0 (1)

Let us replace equation (1) with the equivalent equation x=φ(x) (2). Let's choose a rough, approximate value x 0 belonging to, substitute it into the right side of equation (2), we get:

Let's do this process n times and get x n =φ(x n-1)

If this sequence is convergent i.e. there is a limit

x * =lim x n, then this algorithm allows you to determine the desired root.

We write expression (5) as x * = φ(x *) (6)
Expression (6) is a solution to expression (2); now it is necessary to consider in what cases the sequence x 1 ... x n is convergent.
The condition for convergence is if the following condition is satisfied in all currents x:

4 p. Tangent method (Newton).

Given a continuous function f(x), which contains a single root on the segment , where b>a are defined as continuous and preserve the sign f`(x) f``(x). Determine the root with accuracy ε.

The essence of the method

1. We choose a rough approximation of the root x 0 (either point a or b)

2. Find the value of the function at the point x 0 and draw a tangent to the intersection with the abscissa axis, we get the value x 1

3.

Let's repeat the process n times If the process is convergent then x n can be taken as the desired value of the root
The convergence conditions are:

│f(x n)│≤ε

│x n -x n-1 │≤ε

Let us present the GSA of the tangent method:

5p. Assignment for RGR

Calculate the root of an equation

On a segment with an accuracy of ε=10 -4 using the methods of halves, iteration, tangents.

6 p. Comparison of methods

The effectiveness of numerical methods is determined by their universality, simplicity of the computational process, and speed of convergence.

The most universal is the method of halves; it guarantees determination of the root with a given accuracy for any function f(x) that changes sign to . The iteration method and Newton's method impose more stringent requirements on the functions, but they have a high convergence rate.

The iteration method has a very simple calculation algorithm; it is applicable for flat functions.
The tangent method is applicable for functions with large slopes, but its disadvantage is the determination of the derivative at each step.

GSA of the main program, methods are formalized by subroutines.

Program on the methods of halves, iteration and Newton's method.

a = 2: b = 3: E = .0001

DEF FNZ (l) = 3 * SIN(SQR(l)) + .35 * l - 3.8

F1 = FNZ(a): F2 = FNZ(b)

IF F1 * F2 > 0 THEN PRINT "REFINE ROOTS": END

IF ABS((-3 * COS(SQR(x))) / (.7 * SQR(x))) > 1 THEN PRINT "DOES NOT CONVERGE"

DEF FNF (K) = -(3 * SIN(SQR(x)) - 3.8) / .35

DEF FND (N) = (3 * COS(SQR(N)) / (2 * SQR(N))) + .35_
IF F * (-4.285 * (-SQR(x0) * SIN(SQR(x)) - COS(SQR(x))) / (2 * x * SQR(x)))< then print “не сходится”:end

"=========Halving method========

1 x = (a + b) / 2: T = T + 1

IF ABS(F3)< E THEN 5

IF F1*F3< 0 THEN b = x ELSE a = x

IF ABS(b - a) > E THEN 1 ‑

5 PRINT "X="; x, "T="; T

"=========Iteration method==========

12 X2 = FNF(x0): S = S + 1

IF ABS(X2 - x0) > E THEN x0 = X2: GOTO 12

PRINT "X="; X2, "S="; S

"========Tangential method=======

23 D = D + 1
F = FNZ(x0): F1 = FND(x0)

X3 = x0 - F / F1

IF ABS(X3 - x0)< E THEN 100

IF ABS(F) > E THEN x0 = X3: GOTO 23

100 PRINT "X="; X3, "D="; D

Answer
x= 2.29834 T=11
x=2.29566 S=2
x=2.29754 D=2
where T,S,D is the iteration number for the method of halves, iteration, tangents, respectively.

« Drawing up a foreign trade contract and settlement

customs payments"

Calculation and graphic work (CGW) is provided for in the curriculum for full-time students.

The RGR provides for the student to work out the terms of a foreign trade contract. Contracts can be for both export and import of goods.

To complete the RGR, the student is given an individual task consisting of the following conditions: name of the product, its price and basic delivery conditions. All these conditions are included in the contract, but in addition to them, a number of contract clauses must be determined.

To write this section of the RGR, the student must familiarize himself with the contents of the foreign trade contract using the lecture materials and these methodological instructions (section 5). When writing a work, the student must provide a justification for each of the 16 listed points based on the characteristics of the product, the term of the contract, the selected counterparty, its geographical location, currency, etc.

For each item, it is required to select any of the options for its wording that is suitable for the type of exported or imported product and does not contradict the basic conditions of delivery, and justify the use of this particular option.

In particular, it is necessary to determine the quantity of the product and the method for determining its quality. Set the delivery date or period, the method of fixing the price, the possibility of applying and conditions for providing discounts on the price of the goods.

The basic delivery conditions are provided for in the assignment issued, but when performing the work, the student is required to formulate, according to INCOTERMS 2000, the responsibilities of the party for whom he is drawing up the contract, i.e. if the contract is for export, then the obligations of the seller should be described, and if it is an import contract, the obligations of the buyer should be described.

Then the payment procedure is determined, according to which you should select the payment currency, its term, method, form of payment and justify your choice.

The exporter (or importer) company and its counterparty should be invented independently.

Based on the developed conditions, the student draws up a foreign trade contract and calculates customs payments: customs clearance fees, customs duties, excise taxes, value added taxes. The methodology for calculating the listed payments is given in sections 6.1 – 6.4. methodological instructions.

In the final part of the RGR, the student must determine how much customs payments are in total and per unit of goods, how much the cost of the goods will be after making all customs payments, and by what percentage or how many times the cost of the goods increases after these payments.

Composition and volume of the explanatory note of the calculation and graphic work:

1. Task for performing RGR.

2. Elaboration of the terms of the foreign trade contract.

3. Drawed up foreign trade contract.

4. Calculation of customs duties.

5. Determination of the cost of a unit of goods, taking into account customs duties paid and calculation of the increase in the cost of goods after their payment.

The total volume of the PP is 8 - 10 pages. The design must comply with the rules.

The test is provided for in the curriculum for part-time and part-time students.

In addition, according to the conditions of the control work, an installment plan was provided for the payment of customs duties on the security of the goods, which at this time are registered in a temporary storage warehouse (TSW). The student must calculate the interest on the installment plan (see section 6.5) and determine the amounts to be paid to repay the installment plan, including interest.

The result of the control work is the calculation of the amount of all payments and the cost of a unit of goods, taking into account customs duties and interest on installments.

To complete the test, the student is given an individual assignment, consisting of the following conditions: name of the product, its price, basic delivery conditions, payments for which installments are provided, installment period, payment terms.

The test work includes:

1. Assignment to complete the test.

Oh, that’s not what the student was thinking about when he was choosing a university. Who wanted for themselves such a share as writing RGR? In the meantime, the work will still have to be done, and according to all the rules. Don’t panic, dear friends, may we be with you! We read and absorb.

So, here are the basic rules for preparing calculation and graphic work according to GOST:

1. The RGR must be completed and passed in stages.
2. The RGR is completed and submitted on white A4 sheets. In some cases, it is possible to use checkered sheets.
3. Each sheet should have clearly defined margins 2-3 cm wide.
4. All calculations, text and graphics must be done manually. Any information is provided only on one side of the sheet.
5. Each new RGR must be performed on a new sheet on top of each sheet there must be a “header”. Each worksheet should have its own task attached to it.
6. The numbering of the RGR must correspond to the model that can be taken from the department in the methodological literature or according to GOST.
7. Any graphics, any drawings are made only on graph paper. If you do not have small graph paper (smaller than A4), it should be pasted onto standard white A4 paper. In the coordinate axis area, you need to indicate arrows, names of functions and variables, and scale units.

By the way! For our readers there is now a 10% discount on

Useful little things: additions to the rules for registering RGR

Each section must be numbered. Numbering must be in Arabic numerals.

Formulas and equations should only be used on separate lines. A blank line should be used at the top or bottom of each formula used to visually highlight the information.

All new symbols and numerical coefficients should be entered on a new line in the order in which they appear in the formula. In this case, the first line of explanations should begin with the words: “Where” without a colon after the word.

Numbering and tables

It should be remembered that all formulas must also be numbered. Numbering occurs in Arabic numerals and within each specific section.

When using tables in the RGR, you must briefly indicate the name of each table. The table name is written at the top.

Now you know how to prepare calculation and graphic work (CGW) with examples. In general, performing computational and graphic work is too difficult for most students. Not only is there often not enough time for this, but knowledge often fails.

So, if you want to save time, just ask for help in writing the RGR from specialists who will do everything quickly and efficiently.

Sakun M.A SA-22

Department of Information Technologies

Calculation and graphic work

in the discipline "Informatics"

“Using MathCAD and MS Excel packages to perform calculations”

Gomel, 2013

Assignment for calculation and graphic work

MINISTRY OF EDUCATION OF THE REPUBLIC OF BELARUS

Educational institution "Belarusian State University of Transport"

Department of Information Technologies

Assignment for calculation and graphic work

Student Sakun Mikhail Aleksandrovich _Group__SA – 22 Option 15

Calculation and graphic work in the discipline “Informatics” for second-year students of the Faculty of Civil Engineering consists of four main sections:

Section 1

Task №1 Process tabular data in the Microsoft Excel environment, using the built-in functions and graphical capabilities of this spreadsheet processor. (Make calculations and present the results in formula display mode

Solve problem No. 2 using the Search for a solution method. Use only car types

and gondola cars provided according to the option

Task No. 2

Form a train with a length of 250±5 m with the greatest total carrying capacity.

Section 2

Task No. 1 Process tabular data (see above) in a mathematical calculation package Mathcad,

using math toolbar operators and built-in functions Mathcad.

Solve problem No. 2 in the package of mathematical calculations Mathcad using physical formulas,

corresponding to the task, symbolic processor capabilities and dimensions (units of measurement).

Task No. 2 A train of maximum permissible gross mass starts moving from the station. On a section of track 1 km long, it develops a constant traction force F = 4∙105 N, and its speed increases from 10 to 20 km/h. Determine the coefficient of friction.

Section 3

Solve a problem using a programming language Pascal

Task Minimum internal length

Section 4 Creating a presentation by RGR using MSPowerPoint.

Calculation and graphic work assignment 1

Introduction 4

Setting goals 6

1 Section 1 8

1.1 Condition of task No. 1 8

1.2 Solving problem No. 1 in the Microsoft Excel 9 spreadsheet environment

1.3 Condition of task No. 2 10

1.4 Solution to problem No. 2 11

2 Section 2 13

2.1 Condition of task No. 1 13

2.2 Solution of problem No. 1 in the MathCAD 13 package

2.3 Solution of problem No. 2 in the MathCAD 15 package

3 Section 3 17

3.1 Executing a task in Pascal 17

3.2 Problem condition: 17

3.3 Solving the problem in Pascal 17

3.4 Results of task 17

4 Section 4 18

1.1Description of presentation 18

Conclusion 19

References 20

Introduction

In calculation and graphic work we will calculate characteristics, operational indicators, traffic indicators of freight railway transport and solve other problems in a spreadsheet processor MSExcel, package Mathcad and on the tongue Pascal. As initial data for calculations, we will use the characteristics of the rolling stock units presented in Appendix B. According to our option, we select the diesel locomotive model, types of covered cars and gondola cars, and initial characteristics.

Option 15 record book number 12040024 Date of Birth April 1, 1995

Setting goals

	Diesel locomotive model	Types of covered wagons			Types of gondola cars		Characteristics
							Car tare weight	Height (internal)	Loading hatch length	Length (inner)	Overall width

Estimated indicators of level I						Estimated indicators of level II
Number of rolling stock units	Max. tare weight of a wagon in a moving wagon	Maximum internal height of rolling stock units	Wed. arithm. loading hatch length value	Wed. arithm. length value of rolling stock units	Overall width of the train	Maximum area of ​​the loading hatch in the composition	Maximum possible volume of placed cargo

1 Section 1

		Characteristics of rolling stock units
Diesel locomotive model and types of cars	Number of rolling stock units	Car tare weight, t	Height (internal), m	Loading hatch length, m	Length (internal), m	Overall width, m	Load capacity

According to individual instructions, we will composetable of rolling stock characteristics andwe will formalize it inMS Word ;

Running a job in a spreadsheet environmentMicrosoftExcel

1.1 Condition of task No. 1

6. Overall width of the train

1.2 Solving problem No. 1 in a table processor environment Microsoft Excel

Let's imagine the calculations in the formula display mode: We use standard calculation formulas as well as skills in working with MSExcel

1.3 Condition of task No. 2

Form a train with a length of 250±5 m with the greatest total carrying capacity

Solution of problem No. 2 in the Microsoft Excel spreadsheet environment

We copy the data from the table of characteristics of railway transport units into MS Excel.

We get the table:

Let's imagine the calculations in formula display mode:

1.4 Solution to problem No. 2

We solve the problem using the solution search method.

Call the “search for solution” command. In the window that appears, configure the parameters:

We optimize the objective function.

Select minimum search

We set restrictions: the length of the cars must be positive, an integer, and the total length must be less than or equal to 250m.

Changing the column with the length of cars

In formula display mode:

Results report:

2 Section 2

2.1 Condition of task No. 1

1. Number of rolling stock units

2. Max. tare weight of a wagon in a moving wagon

3. Maximum internal height of rolling stock units

4. Wed. arithm. loading hatch length value

5. Wed. arithm. length value of rolling stock units

6. Overall width of the train

7. Maximum area of ​​the loading hatch in the composition

8. Maximum possible volume of placed cargo

2.2 Solution to problem No. 1 in the package MathCAD

IN MS Word in the table created according to the task, select the numeric values ​​and convert the table into text

\

2.3 Solution to problem No. 2 in the package MathCAD

A train of maximum permissible gross mass starts moving from the station. On a section of track 1 km long, it develops a constant traction force F = 4∙10 5 N, and its speed increases from 10 to 20 km/h. Determine the coefficient of friction.

3 Section 3

3.1 Running a task in the environmentPascal

3.2 Condition of the problem :

Find the minimum inner length

3.3 Solving a problem in language Pascal

3.4 Results of the task

4 Section 4

1. Description of the presentation

This presentation will present the progress of the work, as well as its content.

« Document MS Power Point »

Conclusion

During the execution of the RGR, the characteristics of the rolling stock were calculated. Thanks to this work, we generalized our knowledge and skills in working with MathCad, MSExcel, MSWord packages, and also learned how to systematize and present the obtained data in the form of a presentation.

Bibliography

N.I. Gurin. Working in a Windows environment with Excel and Word programs//Tutorial-Mn. : BSTU, 1997.

A.P. Lashchenko, T.P. Brusentsova, L.S. Moroz, I.G. Sukhorukova. Informatics and computer graphics. - Mn.: BSTU, 2004.

3. N.N. Pustovalova, I.G. Sukhorukova, D.V. Zanko. Computer graphics.