Matcad trial version. Mathcad Express is a free mathematical editor that few people know about

In this section you will find free examples problem solving and laboratory work, made using the Mathcad package. Use these examples or order your work to professionals.

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Solved tasks in Matkad online

Task 1. Calculation and design work is devoted to solving typical problems of analysis, synthesis and optimization of the parameters of a control and measuring device (ID). Structural scheme(g) selected in accordance with individual option tasks (Fig. 1.1, see file).
1.1. Determine (two different ways) sensitivity coefficient of the control unit, if the sensitivity coefficients of its links are known.
Note: the answer must be obtained in the form of the formula $K=K(k_1, k_2, k_3)$, connecting the value of the overall sensitivity coefficient of the DUT with the sensitivity coefficients of its links. The obtained result is used in subsequent calculations.

Task 2. Calculate using Simpson's formula definite integral from the function: $f(x)=\sqrt((1+x)(x^2-1))$, $a=2$, $b=32$ with step $h_1=(b-a)/10$ and with step $h_2=(b-a)/20$. Estimate the absolute error using Runge's rule. Give your answer taking into account the Runge amendment.
Using the Mathcad system, determine the number of steps required to achieve a calculation accuracy of $10^(-5)$.

Task 3. A harvest from a vineyard of a certain area annually allows one to obtain $A=75$ deciliters of young wine, 70% of which is sold immediately at a price of $P_1=9$ francs per liter. The remaining part goes on sale a year later at a price of $P_2=28$ francs per liter. 80% of annual revenue is invested in production, which makes it possible to annually increase the area under vineyards and expand production. At the same time, for each franc invested, an additional $B=0.2$ liter of wine is obtained. Find the amount of revenue for each of the 5 years. Solve the problem analytically and using the Mathcad system.

Task 4. Find the root isolation segment graphically and calculate the value of the root with an accuracy of 0.001 using the iteration method. Perform all calculations to four decimal places. $$e^(0.5x)+2x-6=0$$

Task 5. Make a table of values ​​of the function $y=f(x)$ on the segment $$ with step $h$. In function values, keep three decimal places. Carry out calculations with three decimal places. Using quadratic interpolation from the resulting table, calculate the value of the function at the point $x=x^*$. Perform calculations in two ways:
1) according to the Lagrange formula;
2) according to Newton's formula.
Make a drawing showing the points of the table. Directly calculate the value of the function $y=f(x)$ at the specified point $x^*$ and compare with the values ​​obtained as a result of interpolation.

Task 6. 1. Determine which approximation is more accurate by comparing relative errors.
2. Find the maximum absolute and relative errors if they have only correct numbers
a) in a narrow sense
b) c in a broad sense
3. Calculate and find the maximum absolute and relative errors of the result

Task 7. Find in MatKad a numerical solution to a linear boundary value problem for a second-order differential equation using the finite-difference method, using the approximation of the second-order derivative and step $h = 0.1$.

Task 8. Laboratory work
1. Launch the Mathcad program
2. Create matrices
3. Perform actions with matrices
4. Find the rank of matrix A
5. In symbolic form, transpose matrix B and invert matrix A
6. FIND inverse matrix K. Find the determinant of matrix A

From the very beginning, the computer was conceived and created as perfect assistant, capable of performing complex calculation procedures. As the technical base improves and software component, the computing unit began to make it possible to perform increasingly voluminous and complex calculations, in which both mathematical specialists and professionals in various technical specialties were interested.

The most famous and almost universally used automatic design system is the program MathCAD.

notice, that free download Matkad in Russian You can follow the link at the bottom of the article (official website).

The Russian version of Matkad is no different from the English one, the program is an extremely convenient and very advanced tool mathematical modeling for any user who needs to perform almost any mathematical / engineering calculations.

At the same time, the functionality allows you to successfully work not just on single tasks, but also to work on very large complex tasks. And even such a high efficiency of the program is not the limit of its capabilities: the application’s arsenal has extensive capabilities for integration with a number of related software products, which allows you to increase its effectiveness by at least another order of magnitude. And given the fact that Matkad is perfectly compatible with the office software package, you can carry out efficient exchange data and successfully resolve any issues in the field of certification, verification and development with capabilities further publication results.

Note that in addition to the desktop version, there is also the so-called Mathcad online - this is PTC Mathcad Gateway, which is a web-based application for performing engineering calculations of any level of complexity. Allows you to solve various examples in mathematics (may be of interest to students and schoolchildren).

Some main features of Matkad software:

• the ability to solve systems of equations and carry out various calculations in symbolic form and their further simplification;
• finding solutions for differential equations using a variety of numerical methods;
• the ability to build not only two-dimensional, but also 3D graphics for any functions;
• performance various operations not only with numerical values, but also with vectors or matrices;
• the ability to use Greek letters not only in the equations themselves, but also in the text part (the so-called “mathematics in text”);
• allows you to create your own algorithms based on your own programming language;
• template support;
• interaction office packages from Microsoft;
• can do calculations various tasks theory of probability and mathematics. statistics;
• works with subroutines and executes them based on instructions from high-level algorithms;
• functional module for documenting all performed engineering calculations.

As incomprehensible as mathematical science seems to many people, just as confusing and unusual appears at first glance to the user. software interface MatKada.

However, this impression disappears in just a couple of hours of work, because it becomes clear: all the available tools are created and arranged in such a way that it allows you to interact with the system on an almost intuitive level.

The key features of the interface are several toolbars that allow you to work with tabular forms and formulas. The richness of the algebraic base of calculations is also taken into account: the program supports all significant logical functions and operators, the number of which in the latest versions reaches several hundred. This allows the user to successfully find solutions to problems not only in numerical form, but also in symbolic form.

But if the problems that the user solves have some special mathematical specificity, considerable capabilities of the application can be further expanded to suit specific task: on the official website of the developers you can download a whole list for free additional modules, which will most likely allow you to solve the problem with the least amount of time. Let us remind you that Matkad itself can be downloaded for free (Russian version) for Windows computer under 32 or 64 bit. There are both paid and free versions of Mathcad.

However, both in the world of science and in the sphere of production, it is not enough to simply carry out calculations - you need to correctly formatted and in a form convenient for a person to display on paper (print). Just for these purposes, MatKad provides a wide range of tools for step-by-step documentation of all calculations performed, and has the necessary functionality for displaying and printing the results obtained.

Thanks to these operating mechanisms, the user has virtually no opportunity to random error, and all obtained data can be reliably stored in the form that is most appropriate for their further use.

Natural area of ​​use matkad programs becomes the sphere of development of a wide variety of projects - the system already at the first stages allows you to speed up development several times, and the quality of the calculations performed turns out to be significantly higher (compared to similar systems or in the case of manual calculations).

It should be remembered that Matkad, of course, is aimed at the widest possible audience of users and programming skills are not required to work with the application. However, this system mathematical modeling is used to its fullest in projects bordering on complex calculations, which means that from time to time the application of domain knowledge may be required traditional languages programming.

Mathcad - software tool, an environment for performing a variety of mathematical and technical calculations on a computer, equipped with an easy-to-learn and easy-to-use environment graphical interface, which provides the user with tools for working with formulas, numbers, graphs and texts. More than a hundred operators and logical functions designed for numerical and symbolic solutions are available in the Mathcad environment mathematical problems of varying complexity.

To automate mathematical, engineering and scientific calculations, a variety of computing tools are used - from programmable microcalculators to ultra-powerful supercomputers. And yet, such calculations remain difficult for many. Moreover, the use of computers for calculations has introduced new difficulties: before starting calculations, the user must master the basics of algorithmization, learn one or more programming languages, as well as numerical calculation methods. The situation changed significantly after the release of specialized software systems for automation of mathematical and engineering calculations.

Such complexes include software packages Mathcad, MatLab, Mathematica, Maple, MuPAD, Derive, etc. Mathcad occupies a special position in this series.

Mathcad is an integrated system for solving mathematical, engineering and scientific problems. It contains a text and formula editor, a calculator, scientific and business graphics tools, as well as huge database reference information, both mathematical and engineering, designed in the form of a reference book built into Mathcad, a set e-books and ordinary “paper” books, including those in Russian

A text editor is used for entering and editing texts. The texts are comments, and the mathematical expressions included in them are not executed. The text may consist of words, mathematical symbols, expressions and formulas.

The formula processor provides a natural “multi-story” set of formulas in familiar mathematical notation (division, multiplication, Square root, integral, sum, etc.). The latest version of Mathcad fully supports Cyrillic letters in comments, formulas and graphs.

The computer provides calculations using complex mathematical formulas, has big set built-in mathematical functions, allows you to calculate series, sums, products, integrals, derivatives, work with complex numbers, solve linear and nonlinear equations, as well as differential equations and systems, minimize and maximize functions, perform vector and matrix operations, statistical analysis etc. You can easily change the bit depth and base of numbers (binary, octal, decimal and hexadecimal), as well as the error of iterative methods. Dimensions are automatically controlled and converted into different systems measurements (SI, GHS, Anglo-American, and custom).

Mathcad has built-in tools symbolic mathematics, allowing you to solve problems through computer analytical transformations.

The GPU is used to create graphs and charts. It combines ease of communication with the user with great capabilities of business and scientific graphics. The graphics are focused on solving typical mathematical problems. Maybe rapid change type and size of graphs, overlay on them text labels and moving them anywhere in the document.

Mathcad is universal system, i.e. can be used in any field of science and technology - wherever mathematical methods are used. Writing commands in the Mathcad system in a language very close to the standard language of mathematical calculations simplifies the formulation and solution of problems.

Mathcad is integrated with all others computer systems accounts.

Mathcad makes it easy to solve problems such as:

· entering various mathematical expressions on the computer (for further calculations or creating documents, presentations, Web pages or electronic and regular “paper” books);

· carrying out mathematical calculations (both analytical and using numerical methods);

· preparation of graphs (both two-dimensional and three-dimensional) with calculation results;

· input of initial data and output of results into text files or files with databases in other formats;

· preparation of work reports in the form printed documents;

· preparation of Web pages and publication of results on the Internet;

· obtaining various reference information

and many other tasks.

Starting from version 14, Mathcad is integrated with Pro/ENGINEER (as well as SolidWorks). The basis of the Mathcad and Pro/ENGINEER integration is the two-way communication between these applications. Their users can easily link any Mathcad file to a Pro/ENGINEER part and assembly using the Pro/ENGINEER analysis feature.

Mathcad creates a convenient computing environment for a wide variety of mathematical calculations and documentation of work results within the framework of approved standards. Mathcad allows you to create corporate and industry certified calculation tools in various fields of science and technology, providing a uniform methodology for all organizations included in the corporation or industry

Mathcad 14

The latest version of Mathcad supports 9 languages, allowing for more powerful and clear calculations.

NEEDHAM (Massachusetts). On February 12, 2007, PTC (Nasdaq: PMTC), a CAD/CAM/CAE/PLM systems development company, announced the release of Mathcad 14.0, the most latest version popular system automation of engineering and technical calculations. Since acquiring Mathsoft in April 2006, PTC has focused its efforts on further expanding the geographic reach of Mathcad technology and significantly increasing its user base. Mathcad 14.0 significantly expands the capabilities of users in solving the ever-growing computing tasks, improves the connectivity of settlement documents throughout the entire product development process.

In modern conditions of global division of the product development process, scientific and technical calculations are becoming extremely important. With the release of Mathcad 14.0, PTC provides full support Unicode encodings and will offer in the near future this product in nine languages. New among them will be languages ​​such as Italian, Spanish, Korean and both Chinese - traditional and simplified. Expanded language support in Mathcad 14.0 will allow geographically dispersed teams to perform and document calculations in their local language and, as a result, increase productivity by increasing speed and accuracy, as well as reducing errors that occur when translating from one language to another.

Mathcad 14.0 also allows you to perform more complex calculations while keeping them clear with new workbench features. WorkSheet(a document opened in the Mathcad environment), additional tools for online numerical estimation and an extended set of symbols. This will help users in deriving formulas, displaying the computational process and documenting the calculations. Ultimately, special additional features will allow users to work with a wider range of engineering tasks.

The basis of the Mathcad and Pro/ENGINEER integration is the two-way communication between these applications. Their users can easily link any Mathcad file to a Pro/ENGINEER part and assembly using the Pro/ENGINEER analysis feature. Basic quantities calculated in the Mathcad system can be converted into parameters and dimensions of a CAD model for controlling a geometric object. Parameters from the Pro/ENGINEER model can also be entered into Mathcad for subsequent engineering calculations. When parameters change, the mutual integration of the two systems allows you to dynamically update the calculations and drawing of the object. Moreover, the correctness of Mathcad-controlled Pro/ENGINEER models can now be validated using Pro/ENGINEER calculation modules such as Pro/ENGINEER Mechanica®, Structural And Thermal Simulation, Fatique Advisor Option and Mechanism Dynamics Option.

What's new in Mathcad 14.0?

· New tandem of interface operators (“Two in one”)

· Format of numbers on graphs

· Changes to Find/Replace commands

Compare Team

· New in solving ODE

· New means of symbolic mathematics

· Unicode code table support

User Interface

The user interface refers to a set of tools graphical shell Math CAD, providing easy control of the system, both from the keypad and using the mouse. Management means simply a set of necessary symbols, formulas, text comments, etc., and the ability to fully prepare documents (Work Sheets) and e-books in the MathCAD environment with their subsequent launch in real time. User interface The system is designed so that a user who has basic skills in working with Windows applications can immediately start working with MathCAD.

Edit window.

Main menu of the system.

The second line of the system window is the main menu. The purpose of its commands is given below:

File – work with files, the Internet and email;

The drop-down menu contains commands that are standard for Windows applications.

Edit – editing documents;

The drop-down menu also contains commands that are standard for Windows applications. Most of them are only available if one or more areas are selected in the document (text, formula, graph, etc.)

View – change the viewing tools;

Toolbars - allows you to show or hide the Standard, Formatting, Math toolbars.

Almost any engineering or physical problem involves a large number of mathematical calculations. For a long time it was a routine and took great amount time, or to be more precise, approximately 80%. With the invention of the computer, and later of special tasks, such calculations became much easier. Today, MathCad is considered one of the most popular and easiest to use.

History of creation

The first version was released in 1986 and at that time was an indispensable assistant engineers. Even then, in addition to simple and complex algebraic calculations, it was possible to create 2D graphics. A little later, the program was taught to build 3D graphics. However, development was greatly hampered by the weak computing capabilities of computers.

Alen Razdov, the man who invented and wrote the first version of the program, understood perfectly well what most users needed and by the 5th version he implemented what in the future became one of the main advantages of MathCad. This was the opportunity to connect your own functions to the program.

The required function could be written in C, compiled and attached to the program via a DLL mechanism. To make it clearer what’s so cool about this, we can give an example.

Every day at work an engineer faces big amount miscalculations. Surely certain pieces of calculations are repeated from time to time. Yes, MathCad has already made it possible to even copy already written formulas and simply change the input values, but at the same time the calculations still remained visually large. The program made it possible to hide this entire algebraic part by creating a function. In the future, all this will be replaced with just one line. Convenience and comfort.

Speaking of convenience, one cannot fail to mention the wonderful, friendly interface. The functions that are most often used are displayed on a separate panel, which, by the way, can be changed to suit you. The second point is to use the principle “what you see is what you get.” That is, when working in the program, you visually observe everything in the same way as if you wrote everything on paper. This is also an advantage when you need to print a document. In fact, you can downloadMathCad and after just 30 minutes of studying, start working fully in it. In worldwide network, you can also download mathcad torrent at high speed.

There is no particular point in examining the early versions of the program in detail, and therefore we will immediately move on to 2006, when the Mathsoft company, created by Alan Razdov, was bought by PTC Corporation. Together they began to develop MathCad 14.

Features of MathCad 14

The main thing to note is the change in the core of the program. The previously used Maple subsets were replaced with the algebraic kernel MuPad. This increased the accuracy and quality of calculations, which is undoubtedly a plus, but added problems for users. The fact is that some files created in earlier versions now they could simply not open on the 14th. And if they did open, there was no confidence that everything was working correctly. Therefore people who for a long time We had already worked with MathCad and were very reluctant to switch to the new version.

There were many changes in the program, for example, the introduction of full support for all Unicode fonts or spell check in 15 languages ​​of the world, but all these are trifles. What is really important for the user is the introduction of the tandem operators “… := … = …”. Now it was possible to assign variable expression and get a solution immediately. It would seem that this is not significant at all, but this is another step towards the standard and usual recording of calculations and a move away from program and machine recording.

Three new solution algorithms have also been added differential equations and several new features in the character processor.

It can't be said that MathCad14 download Many people wanted it, but the decisive factor for some was integration with the Pro/ENGINEER package. This provided enormous opportunities in the complex of engineering and design work. Now it has become much simpler and easier to build a model using calculations or carry out calculations taking into account the geometry of the model. Even those who did not particularly like one or the other program switched to this combination, simply because of the time savings.

MathCad 15

MathCad 15 could be downloaded already in 2010. A number of functions were improved and integration with various databases data such as KnovelMath and Truenumbers. That is, PTC continued to make the program as convenient as possible and expand its capabilities.

The most important thing that can be noted in the difference between MathCad 15 and previous version is an extension of the calculation functionality for planning experiments. And of course, we added support for the then new Windows 7 and Excel 2007.

MathCad Prime

The next significant stage in the development of the program after the purchase of MathSoft by PTC Corporation and the replacement of the algebraic core was the release of MathCad Prime. You could say it's perfect new program, simply written taking into account previous experience gained from creating “digital versions”. MathCad Prime was indeed written completely from scratch and has an updated package of functions, including for planning experiments. Works without problems on Windows 7 and supports MS Excel.

MathCad has also become more “alive”. Simple new interface and text notes for calculations very quickly made it a favorite program of higher education educational institutions and small companies. It is difficult to find a modern engineering student who neglects this program. It allows you to easily and quickly make both strength calculations and solve problems based on discrete mathematics. At the same time, if errors occur, and they do occur, then it is enough to correct several variables and not have to recalculate everything again. The program changes everything for you. This approach also greatly facilitates the solution of design problems in which there are several rounds of iteration.

MathCad Prime 3.0

Today, the latest version is MathCad Prime 3.0, which was released to the public on October 16, 2013. The developers themselves highlight following features and features:

• Global definition of variables. This means that you can set the value of a variable anywhere in the worksheet without worrying about the sequence of calculations. If the calculation scheme is not standard and the program does not define it, then you can use software functions"if" and "then".
• Mathematics and text are one. After all the calculations have been carried out, you will not need to formalize them and bring them to a presentable form in some other program. MathCad has a good built-in text editor, which allows you to add various notes, explanations and entries. At the end, you will receive a document that you are not ashamed to print out and take to the teacher for checking.
• Creating templates. When you often use the program and are engaged in one area, it will be quite convenient to create templates that already include specific set formulas, text, etc. This frees you from having to do the same work every time, moving on to another task.
• Formatting. As mentioned above, MathCad has a built-in text editor with a sufficient range of capabilities. But you can use it to edit and format formulas.
• Function integration. Despite the fact that more than 3 thousand functions are built into MathCad, it is impossible to cover absolutely all disciplines. Therefore, it is possible to program and add your own functions for further convenient use.
• Integration with Excel. Most often, a large amount of data after various measurements or the like is stored in Excel tables. But many are not satisfied with the charting functionality that this software provides. MathCad easily recognizes such tables and makes it possible to both export and import them.
• Symbolic calculations and formulas. It is not always possible, and sometimes even the desire, to carry out all the calculations numerically. MathCad makes it possible to calculate everything character by character, enter the initial data and only at the end get the force value.
• Graphical tools. Need to build a complex spatial graph? You just need to download Matcad and do it easily and quickly with it.

Can complex engineering calculations be trusted? spreadsheets? Never. That's why engineers choose PTC Mathcad as their calculation tool. In the spring of 2017, PTC released the most anticipated version by users software Mathcad Prime 4.0, which makes it easier to manage and protect your calculations so you can share them securely with others. The main innovations in the program concerned primarily security, performance and ease of use. A new version lets you organize and interact with large, complex documents, offers security and region locking so you can control access levels, and you can now embed content created in other applications into PTC Mathcad documents. If you want to try it, click download MathCad Prime 4 freely. So why should you choose the new Matcad Prime:

• Secure transfer of design intent and design knowledge.
• Clear calculations using standard mathematical representation.
• Create professional-quality documents using active mathematical formulas, graphs, text and images.
• Adaptation of standard calculations.
• Increases productivity by fully supporting calculation units throughout the calculation.
• Accelerate learning and adoption with instant access to eLearning content.

With the purchase of Mathsoft by PTC, marketing also changed. Not everyone needs it full version programs. Therefore, it was decided to split MathCad into different packages. It is possible to download the most lightweight and stripped-down version of Matkad for free. Next comes the division into an individual version, a multi-user version and a special educational version, which comes at a very reduced price and does not require certain confirmations and requests from educational institutions.

A special web interface has also been developed for which you do not need to purchase or install the program itself. However, this will not be superfluous, since with a purchased license the web interface gives more high level access.

If you want to download Matkad Russian version, which we also have, you can do it here.

Do you need a smaller version that can be run from any media?

The portable version of MathCad does not require installation, you can use it on any device, run the project immediately from a flash drive or other storage media. Russian-language interface allow you to quickly master the program.

MATHCAD
Mathematical
plastic bag
MathCad
Associate Professor, Department IPS
Pogrebnoy A.V.

MathCad
The MathCAD system is a package designed for
carrying out mathematical calculations, which
contains a text editor, calculator,
GPU
MathSoft Inc. (USA) released the first version
systems in 1986. Main distinctive
The peculiarity of the MathCAD system is its
input language, which is as close as possible to
natural mathematical language,
used both in treatises on mathematics and
generally in scientific literature. Used
WYSIWYG principle What You See Is What You Get

MathCAD subsystems

MathCad
MathCAD subsystems
A text editor is used to enter and
text editing. The text may
consist of words, mat. expressions and formulas.
MathCAD uses the generally accepted math.
Symbolism.
The computer provides calculations based on
mat. Formulas and has a large set of mats.
Functions
The GPU is used for
construction of graphs and surfaces.

Problems to be solved

MathCad
Problems to be solved
preparation of scientific and technical documentation containing
text and formulas in a form familiar to a specialist;
calculating the results of mathematical operations with
constants, variables and dimensional physical
quantities;
vector and matrix operations;
solving equations and systems of equations;
statistical calculations and data analysis;
plotting;
analytical transformations and analytical solution
equations and systems;
analytical and numerical differentiation and
integration;
solving differential equations.

MathCad main window

MathCad
MathCAD document structure
MathCAD document presents
is a set of areas for
placement of mathematical
expressions, graphs, text. Each
the area is shaped like a rectangle
and can be placed anywhere
document. Visible part of the document
limited by screen size.
MathCAD sets direction
performing calculations and constructing
document graphs “right-down”.

MathCAD document structure

MathCad
Variables
A variable is a memory cell that can be
different values ​​can be recorded. Names
variables are usually made up of
the following characters: letters, numbers,
underscore (_), Greek letters.
Mathcad distinguishes between uppercase characters in names
and lower case.
Use following methods for recruitment
Greek letters:
1. Print the Roman equivalent. Then press
G.
2. Click on the corresponding symbol on
palette of Greek symbols. To open this
palette, click on the button marked αβ on
button strip under the menu or use
command View > Toolbars > Greek

Variables

MathCad
Predefined Variables
Mathcad contains eight variables whose values
determined immediately after starting the program. These variables
called predefined or built-in
variables. Predefined variables or have
common meaning, like p and e, or used as
internal variables that control the operation of Mathcad,
similar to ORIGIN and TOL.
Although these variables already have values ​​when you start Mathcad,
they can be overridden. For example, if you need to use
a variable called e with a value other than
used by Mathcad, enter a new definition, for example
e:=2 . The variable e will accept the new in the working document
the meaning is everywhere below this definition.

Predefined Variables

MathCad
Numbers
In Mathcad to separate the fractional part decimal used
period (.) and comma (,) are used to separate numbers from each other.
Types of numbers:
Imaginary numbers. To enter an imaginary number, follow it
module, enter the imaginary unit symbol i or j, for example, 1i or 2.5j.
Dimensional values ​​are numbers associated with one of the dimensions:
mass, length, time, charge and temperature. Mathcad
uses them to monitor compliance with dimensions and
unit conversions. To enter a dimension value,
type the number followed by lowercase or uppercase
in Latin letters: M for mass, L for length, T for time,
Q is for charge, K is for temperature. For example, 4.5m represents 4.5
units of mass.
Octal integers (accompanied by lowercase Latin
letter O)
Hexadecimal integers (followed by lowercase
Latin letter h). To indicate digit values ​​greater than 9,
Use uppercase or lowercase Latin letters from A to F.
Scientific representation of numbers. To enter numbers into
scientific notation, simply multiply the mantissa by
power of ten. For example, to write, type 3*10^8.

Predefined Variables

MathCad
Assignment and result operator
The assignment operator in MathCAD looks like this:
name:= expression
Here the name could be:
variable name (simple and indexed),
function name,
array name,
an array whose elements are
simple variables.
Entering the assignment character ":=" is equivalent to
pressing the ":" (colon) key. For example,
enter y:m*x+b to see y:=m x+b.
Result operator (operator
"equal") in MathCAD has the form:
expression =

10. Numbers

MathCad
Expressions
Expressions can contain numbers, exchanges
variables, simple operators.
The simplest operators are
famous mathematical operations: + - * / and
etc.

11. Assignment and result operator

MathCad
Simplest operators
Operator
How to enter
Name
(x)
(x)
brackets
X!
X!
Factorial
xy
x^y
Degree
√x
\x
Root

12. Expressions

MathCad
Tips for recruiting operators
You can avoid having to remember key combinations by
corresponding to each operator. To enter operators you can
Operator palettes can be used. To open palettes
operators, use buttons on the toolbar,
located below the menu. Each button opens a palette
operators grouped by general purpose.

13. The simplest operators

MathCad
Simple calculations
To perform simple calculations,
like a calculator, enough
type the calculated expression with
sign = at the end of it and press the key
input ENTER .
After this, MathCad will calculate and output
result on screen
2+2=4MathCad
Math built-in functions
The following mathematical formulas can be used in expressions:
Features:
1) Trigonometric (argument in radians): sin(x), cos(x), tan(x)
2) Inverse trigonometric (result in radians): asin(x),
acos(x), atan(x)
3) Hyperbolic: sinh(x), cosh(x), tanh(x)
4) Inverse hyperbolic: asinh(x), acosh(x), atanh(x)
5) Others:
exp(x) exponent
ln(x) natural logarithm
log(x) decimal logarithm
Re(z) real part of z
Im(z) imaginary part of z
arg(z) argument of complex number z
floor(x) largest integer< x (x - вещест.)
ceil(x) smallest integer > x (x - real)
mod(x,y) remainder of x divided by y (x,y are real)
rnd(x) random number from between
Etc.

15. Simple calculations

MathCad
Function
A function is a rule according to which
evaluating some expression with arguments and
the resulting numeric value is displayed.
Defining and using a user function:
define all arguments (simple or discrete),
used in an expression to evaluate a function
type the name of the function with the name of the argument in parentheses,
then - the colon symbol
in the input field, type an expression with which
the value of the function is calculated
To get the result for an argument (simple or
discrete), in parentheses after the function name indicate the value
(or name) of this argument.

16. Math built-in functions

MathCad
Defining your own functions
To define your own function,
enter an equality of the form:
FuncName(arguments) := expression
Here FuncName is the name of the function,
arguments - list of elements separated
commas.
Function arguments can be variables or
function names. For example:
Setting a function
f(x):= cos(x) + 2
Appeal
f(1.8)
f(cos(3))

17. Function

MathCad
Changing Variables
In the MathCAD system you can specify with
limits of their change, which means
carrying out cyclic calculations.
For example:
x:=0..5 (x takes values ​​1, 2, 3, 4, 5)
To set.. (two dots) is used;
If you need to specify a fractional step
the following notation is used:
z:= 0,0.2..4

18. Defining your own functions

MathCad
Function tabulation
Tabulation
functions y=f(x)
means to receive
table at
change x by
given interval
with a given step.

19. Defining and using a user function

MathCad
Numerical and symbolic methods
Integration, differentiation,
solving algebraic equations,
approximation, etc. in MathCAD can
carried out by two methods: numerically and
symbolically. Using
numerical method results in
number. In this case, the result obtained
is an approximate number.
When using a symbolic solution
the result will be a symbolic
formula.

20. Changing Variables

MathCad
Approximate numbers
An approximate number a is a number that is insignificant
different from the exact A and replacing the latter in
calculations
Under the error or error Δa of the approximate number a
is understood:
Δa = A – a
In many cases the error sign is not known, then use
absolute error of the approximate number Δ
Δ = |Δa| = |A – a|
Relative error δ of the approximate number a
the ratio of the absolute error Δ of this number is called
to the modulus of this number A (A≠0)
δ = Δ / |A|

21. Tabulation of functions

MathCad
Numerical integration
Let us consider the work of numerical methods on
example of integrating the function f(x),
continuous on the segment.
Rectangle method
Numerical integration is based on the fact that
that the definite integral is numerically equal
area of ​​a curved trapezoid.
It is practically convenient to divide the segment into
equal parts. Then the length of all segments
calculated as:
Δxk = (b-a) / n = const

22. Numerical and symbolic methods

MathCad
Rectangle method
Let us denote yk = f(xk) then
b
a
b a
f(x)dx
(y0 y1 ... yn 1)
n
y
x0
x1
x2
x3
xn1
xn
x

23. Approximate numbers

MathCad
The trapezoidal method gives a more accurate result according to
compared with the rectangle method, with one and
the same number of partitions of the segment. The essence of the method
also consists in dividing the segment into n
parts. Then the length of all segments is calculated as:
Δxk = (b-a) / n = const
The arc of the graph of the function on the k segment is replaced by a chord.
We get a trapezoid whose area is equal to:
Sk= Δxk * (yk+yk+1)/2
y
xk
xk+1
x

24. Numerical integration

MathCad
Integration Accuracy
The accuracy of the result is affected by:
1. Selected numerical method.
There are much more accurate methods
than the rectangles method or the
trapezoid. For example, the parabola method
(Simpson), Adams method, Monte Carlo method, etc.
2. Number of partitions. The higher the number
partitions, the higher the accuracy, but
computation time increases.

25. Rectangle method

MathCad
Solving equations
IN general case equation with one unknown
can be reduced to the form f(x)=0. Any number ξ
(real or imaginary) on a segment
converting the equation into an identity f(ξ)=0
is called the root of the equation or its solution.
Solving the approximate solution problem
The equation consists of two stages:
1. Separation of roots consists of searching
intervals on the segment that contain
only one root of the equation. Or branch
roots is to find a value close to
decision. The first stage can be done by
function graph.
2. Clarification of roots consists in
directly calculating the values ​​of the roots on
found intervals with a given accuracy ε.

26.

MathCad
Half division method
Let's consider the simplest numerical method for refining the root
equations The method is based on dividing the segment into
which determines the root of the equation, in half. Algorithm
The method is as follows:
1. To find the root of the equation f(x)=0 on the segment, divide
segment bisected by point c. с = (a+b)/2
2. Consider the segments and [c, b] and select a segment on
the ends of which the function f(x) has opposite signs.
If f(a) f(c)<0 выбираем отрезок в ином случае
select the segment [c, b].
3. For the selected segment, repeat step 1 and step 2 until
until the value of the next segment becomes less than the specified one
accuracy ε.
y
a
c
b
x

27. Integration accuracy

MathCad
Chord method
The essence of the chord method is to replace f(x) with
segment with a chord passing through point A and point B. Point of intersection with the axis
x1 represents the approximation to the root
equations. Next we consider the segments and
[s, x1] and similar to the method in the division method
choose one of the segments in half. On the selected
segment again construct a chord and get x2 –
another approach to the root of the equation. Condition
end of calculations: |xi+1-xi|< ε
y
A
x x 2 x1
a
b
3
B
x

28. Solving equations

MathCad
Solving equations in MathCAD
To find the zeros of a function, as well as the roots of the equation
The built-in root function is used. Format
Features:
root(expression, variable_name)
To find the zero of a function (or the root of an equation):
1) set the initial guess value
unknown;
2) set the accuracy value TOL:=....;
3) use root function for solution.
For example, organize a search for the root of the equation
x3+x+1=0 can be done as follows:
x:=0.5 TOL:= 0.0001 res:= root (x3+x+1,x)

29. Half division method

MathCad
Solving a system of linear algebraic
equations (SLAE)
A-1– inverse matrix
Another way to get the solution
X:=lsolve(A,B)
lsolve(A, B) - standard function

30. Chord method

MathCad
An example of a SLAE solution

31. Solving equations in MathCAD

MathCad
Indexed Variables
In MathCAD you can use variables with
index. For a set of indexes, [ is used. If
index is complex; it is enclosed in brackets (in old
versions of MathCAD).
Kit
Result
u [(i, j)
u[(i+1)
u[i+1
ui,j
ui+1
ui+1
Variables with index make up vectors and
matrices. That is, to access the elements of the matrix
you can use a variable with an index.

32. Solving a system of linear algebraic equations (SLAE)

MathCad
Vectors and matrices
A vector or matrix is ​​specified by pressing
hotkeys ALT+M or from the toolbar
Matrix. Addition operations are possible on matrices,
subtraction, multiplication, squaring,
inversions, transpositions, definition
determinant.
C:= A-1 – obtaining the inverse matrix
C:= AT – obtaining a transposed matrix
N:= |A| - calculation of determinant

33. Example of solving SLAE

MathCad
Numerical and symbolic methods
Integration, differentiation, etc.
can be performed by two methods: numerical and
symbolic. When writing the original expressions
The symbolic calculation palette is used.
Dialing is completed by pressing keys
As a result of use
numerical method
it turns out to be approximate
number.
As a result of use
symbolic method in
the result is
symbolic (analytical)
expression.

34. Indexed Variables

MathCad
An example of solving an equation

35. Vectors and matrices

MathCad
Entering text
Text
Text in documents
MathCad is created in
text areas,
which may have
arbitrary width,
and are located in
anywhere
document.
For creating
text area
should be done
menu command
Text/Create Region
(Create text
region).

36. Creating and editing a vector or matrix - 1

MathCad
Example of plotting