Matcad training. Interactive MathCad tutorial
1.2. Introduction to Mathcad
In this section, looking ahead a little, we will show how to quickly start working with Mathcad, learn how to enter mathematical expressions and get the first results of calculations.
Rice. 1.1. Mathcad 11 window with a new document
After Mathcad 11 is installed on the computer and launched, the main application window appears, shown in Fig. 1.1. It has the same structure as most Windows applications. From top to bottom there is the window title, menu bar, toolbars (standard and formatting) and a worksheet or worksheet. A new document is created automatically when you start Mathcad. At the very bottom of the window is the status bar. Keeping in mind the similarity of the Mathcad editor to ordinary text editors, you will intuitively understand the purpose of most of the buttons on the toolbars.
In addition to the controls typical of a typical text editor, Mathcad is equipped with additional tools for entering and editing mathematical symbols, one of which is the Math toolbar (Fig. 1.1). Using this, as well as a number of auxiliary dial panels, it is convenient to enter equations.
To perform simple calculations using formulas, do the following:
- determine the place in the document where the expression should appear by clicking the mouse at the corresponding point in the document;
- enter the left side of the expression;
- enter an equal sign<=>.
Let's leave for now the conversation about more reliable ways to enter mathematical symbols and give an example of the simplest calculations. To calculate the sine of a number, just enter an expression like sin(1/4)= from the keyboard. After you press the equal sign key, the result appears on the right side of the expression, as if by magic (Listing 1.1).
Listing 1.1.Calculation of a simple expression
In a similar way, you can carry out more complex and cumbersome calculations, while using the entire arsenal of special functions that are built into Mathcad. It is easiest to enter their names from the keyboard, as in the example with calculating the sine, but to avoid possible errors in their writing, it is better to choose a different path. To introduce a built-in function into an expression:
- Determine where in the expression you want to insert the function.
- Click the button labeled f(x) on the standard toolbar (the cursor points to it in Fig. 1.2).
- From the Function Category list in the Insert Function dialog box that appears, select the category to which the function belongs—in this case, the Trigonometric category.
- From the Function Name list, select the name of the built-in function as it appears in Mathcad (sin). If you have difficulty choosing, follow the hint that appears when you select a function in the lower text field of the Insert Function dialog box.
- Click OK - the function will appear in the document.
- Fill in the missing arguments of the entered function (in our case it is 1/4).
The result will be the introduction of the expression from Listing 1.1, to obtain the value of which all that remains is to enter the equal sign.
Most of the numerical methods programmed in Mathcad are implemented as built-in functions. Scroll through the lists in the Insert Function dialog box at your leisure to get an idea of the special functions and numerical methods you can use in your calculations.
Of course, not every character can be entered from the keyboard. For example, it is not obvious how to insert an integral or differentiation sign into a document. For this purpose, Mathcad has special toolbars, very similar to the tools of the Microsoft Word formula editor. As noted earlier, one of them - the Math toolbar - is shown in Fig. 1.1. It contains tools for inserting mathematical objects (operators, graphs, program elements, etc.) into documents. This panel is shown in larger view in Fig. 1.3 already against the background of the document being edited.
The panel contains nine buttons, pressing each of which leads, in turn, to the appearance of another toolbar on the screen. These nine additional panels allow you to insert a variety of objects into Mathcad documents. In Fig. 1.3, as you can easily see, on the Math panel, when pressed, there are the first two buttons from the top left (the mouse pointer is located above the left one). Therefore, there are two more panels on the screen - Calculator and Graph. It's easy to guess what objects are inserted when you click the buttons on these panels.
Rice. 1.2. Inserting an Inline Function
More details about the purpose of these and other toolbars are described below (see section 1.3).
For example, you can enter the expression from Listing 1.1 solely using the Calculator panel. To do this, you must first press the sin button (the very first one from the top). The result of this action is shown in Fig. 1.3 (expression in box). Now all that remains is to type the expression 1/4 inside the brackets (in the placeholder indicated by the black rectangle). To do this, press buttons 1, - and 4 in sequence on the Calculator panel and then, on it, the button - to get the answer (of course, the same as in the previous line of the document).
As you can see, you can insert math symbols into documents in different ways, just like in many other Windows applications. Depending on experience with Mathcad and computer habits, the user can choose any of them.
Rice. 1.3. Using the Math Toolbar
If you are just starting to master the Mathcad editor, I strongly recommend that you enter formulas wherever possible using the toolbars and the described procedure for inserting functions using the Insert Function dialog. This will avoid many possible mistakes.
The described steps demonstrate the use of Mathcad as a regular calculator with an expanded set of functions. For a mathematician, it is of interest, at a minimum, to be able to define variables and operations with user functions. There is nothing simpler - in Mathcad these actions, like most others, are implemented according to the principle “as is customary in mathematics, so is entered.” Therefore, we will give relevant examples (Listings 1.2 and 1.3), without wasting time on comments (if you have problems understanding the listings, please refer to the relevant sections of this chapter for clarification). Notice only the assignment operator that is used to set the values of the variables in the first line of Listing 1.2. It, like all other characters, can be entered using the Calculator panel. An assignment is denoted by the symbol ":=" to emphasize its difference from an evaluation operation.
Listing 1.2. Using Variables in Calculations
Listing 1.3. Defining the user function and calculating its value at point x=1
The last listing defines the function f(x). Its graph is shown in Fig. 1.4. To build it, you should click on the Graph panel the button with the desired type of graph (the mouse pointer is hovering over it in the figure) and in the graph template that appears, determine the values that will be plotted along the axes. In our case, we needed to enter x in the placeholder near the x-axis and f (x) - near the Y-axis.
Rice. 1.4. Graphing a function (Listing 1.3)
Compare the contents of Listing 1.3 and Fig. 1 4. This style of presentation will be maintained throughout the book. Listings are snippets of document workspaces that run without any additional code (unless specifically noted). You can enter the contents of any listing into a new (blank) document and it will work exactly the same as in the workbook. To avoid cluttering the listings, the graphs are shown in separate figures. Unlike Fig. 1.4, in the following figures the listing code is not duplicated, and if there is a link to the listing in the caption, this means that this graph can be inserted into the document after the mentioned listing.
One of the most impressive features of Mathcad is symbolic calculations, which allow you to solve many problems analytically. In fact, according to the author, Mathcad "knows" mathematics, at least at the level of a good scientist. Skillful use of the intelligence of the Mathcad symbolic processor will save you from a huge number of routine calculations, for example, integrals and derivatives (Listing 1.4). Pay attention to the traditional form of writing expressions, the only peculiarity is the need to use the symbolic calculation symbol -> instead of the equal sign. By the way, it can be entered in the Mathcad editor from any of the Evaluation or Symbolic panels, and the integration and differentiation symbols can be entered from the Calculus panel.
Listing 1.4. Symbolic calculations
In this section, only a small part of the computing capabilities of the Mathcad system was considered. However, the few examples given here give a good idea of its purpose. It is even possible that by prematurely talking about the simplicity with which mathematical calculations can be carried out, the author lost some of the most impatient readers who had already moved on to solving their problems. I would like to advise them to use the second and third parts of the book as a reference, and for the best presentation of the results, use the fourth part. Below, in this and subsequent chapters of this part, the basics of Mathcad are covered in more detail.
The book is devoted to working in the 14th version of the popular mathematical package Mathcad.
The publication has a training course format and consists of four parts. The first part contains the information necessary to get started with Mathcad and solve most practical problems. The second part is devoted to the capabilities of the program; here, specific examples are used to discuss the features of using built-in functions, basic techniques and methods of calculations. The third part discusses the possibilities of preparing Mathcad documents, and the fourth contains a list of examples of solving engineering problems in Mathcad.
This training course is designed for beginner users of Mathcad and will be useful, first of all, to students of technical universities.
Editing Mathcad objects.
Editing entered expressions is done in the usual way for all Windows applications:
The corner of the cursor is moved around the screen using the arrow keys or by clicking the left mouse button at the desired location on the screen.
To highlight one character with the cursor corner, you need to set the blue cursor corner so that it covers the desired character on the left or right.
To expand the selection to part of an expression or the entire expression, use the arrow keys or the space bar. To exit the "tenacious" operator, it is preferable to use the spacebar. The corner of the cursor must cover the entire expression or the entire part of it on which some action must be performed.
To select part of an expression or the entire expression, click the mouse at the beginning or end of the selected part of the expression and move the cursor to the other edge without releasing the left mouse button. You can use the key combination Shift + ← or Shift + →. The selected part of the expression has a black background. Selection in Mathcad is used to cut or copy parts of an expression, change the font, and perform symbolic calculations on parts of expressions.
Table of contents
Preface
About the CD
Part I. Getting started with Mathcad
Chapter 1. Constructing expressions and graphs in Mathcad
Chapter 2. Some features of Mathcad
Part II. Calculations in Mathcad
Chapter 3. Solving equations
Chapter 4. Working with vectors and matrices
Chapter 5. Symbolic Computation
Chapter 6. Solving differential equations
Chapter 7. Processing of experimental data
Chapter 8. Mathematical statistics
Part III. Additional features of Mathcad
Chapter 9. Programming
Chapter 10. Animation
Chapter 11. Accounting for dimensions
Chapter 12. Additional Mathcad Built-in Functions
Chapter 13. Working with Mathcad documents
Chapter 14. Working with text
Chapter 15. Working with graphs
Chapter 16. Reference information in Mathcad
Chapter 17. Creating eBooks
Chapter 18. Working with an e-book
Part IV. Examples of engineering calculations in Mathcad.
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This chapter describes valid Mathcad variable and function names, predefined variable likes, and number representations.
Mathcad operates with complex numbers just as easily as with real numbers. Mathcad variables can take complex values, and most built-in functions are defined for complex arguments. This chapter describes the use of complex numbers in Mathcad.
This chapter describes discrete arguments and shows how to use them to perform iterative calculations, display tables of numbers, and make it easier to enter many numeric values into a table.
Mathcad uses regular operators like + and /, as well as operators specific to matrices, such as transpose and determinant operators, and special operators such as integrals and derivatives.This chapter contains a list of Mathcad operators and describes how to enter and use special operators.
This chapter lists and describes many of Mathcad's built-in functions. Mathcad statistical functions are described in the Chapter “Statistical Functions”. The functions used to work with vectors and matrices are described in the Chapter “Vectors and Matrices”. This chapter provides a list and description of the built-in functions of the Mathcad package. These functions perform a wide range of computational tasks, including statistical analysis, interpolation, and regression analysis. Mathcad PLUS allows you to write programs. A program in Mathcad is an expression, in turn, consisting of other expressions. Mathcad programs contain constructs that are in many ways similar to programming constructs in programming languages: conditional transfers of control, looping statements, variable scope, the use of subroutines and recursion.Writing programs in Mathcad allows you to solve problems that are impossible or very difficult to solve in any other way.
This chapter describes how to solve equations and systems of equations using Mathcad. You can solve both one equation with one unknown and systems of equations with several unknowns. The maximum number of equations and unknowns in the system is fifty. This chapter describes how to solve real-valued ordinary differential equations (ODEs) and partial differential equations using Mathcad. Mathcad contains a wide range of functions for solving differential equations. Some of these functions use specific properties of a particular differential equation to provide sufficient speed and accuracy in finding a solution. Others are useful when you need not only to obtain a solution to a differential equation, but also to plot a graph of the desired solution. This chapter describes symbolic transformations in Mathcad. Mathcad reads and writes data files- ASCII files containing numeric data. By reading data files, you can take data from various sources and analyze it in Mathcad. By writing data files, you can export Mathcad results to word processors, spreadsheets, and other application programs.Mathcad includes two sets of functions for reading and writing data. READ, WRITE And APPEND read or write one numeric value at a time. READPRN, WRITEPRN And APPENDPRN read the entire matrix from a file with rows and columns of data or write a matrix from Mathcad as such a file.
Mathcad graphs are both versatile and easy to use. To create a graph, click where you want to insert the graph, select Cartesian graph from the menu Graphic arts and fill in the empty fields. You can format the graphs in every possible way, changing the appearance of the axes and the outline of the curves and using different labels. In some cases, when constructing graphs, it is more convenient to use polar rather than Cartesian coordinates. Mathcad allows you to build polar plots. Mathcad working documents can include, along with two-dimensional and three-dimensional graphics. Unlike 2D plots, which use discrete arguments and functions, 3D plots require a matrix of values. This chapter shows how a matrix can be represented as a surface in three-dimensional space.This chapter covers creating, using, and formatting surfaces in 3D space. Subsequent chapters describe how to work with other types of charts.
The graphs described in this chapter allow you to display level lines. These are lines along which the magnitude of a function defined on a plane of two variables remains constant. In Mathcad, you can create a level line map in the same way as a surface plot: by defining a function as a matrix of its values, in which each row and column corresponds to specific argument values. This chapter describes how a matrix can be represented as a map of level lines. 3D histograms provide additional data visualization capabilities. With their help, a matrix of numbers can be represented as a set of columns of different heights. You can show the bars either where they are in the matrix, or by placing one above the other, or by placing them along one line. When using other types of 3D graphs, it is necessary to form a matrix in which the rows and columns correspond to the values x And y, and the value of the matrix element determines the coordinate z. When constructing a scatter plot, you can directly determine the coordinates x, y And z any collection of points. Therefore, this type of graph is useful for drawing parametric curves or for observing collections (clusters) of data in three-dimensional space. This chapter shows how three vectors can be used to create a scatter plot. This chapter describes how to create a two-dimensional vector field by representing two-dimensional vectors as complex numbers.If you have only heard about the almost limitless possibilities of the popular engineering design software called MathCAD, this tutorial will certainly become your faithful assistant in its detailed study. Very soon you will be able to use it for your fruitful work.
You will be presented with interactive lessons with professional voice acting, thanks to which you will be able to directly participate in the educational process, which will allow you to quickly and effectively learn the basic and additional features of MathCAD.
If you are only interested in one specific lesson, you can always launch the Main Menu and select exactly what you need from the list.
In each lesson you can see several topics discussed for a more detailed introduction to the MathCAD system. The scroll bar will help you move through a given lesson in any direction as required by the user. Playback control is carried out through a special control panel. After each section switching, a splash screen with the highlighted topic will be displayed on the working screen.
During the lesson playback, the user can follow the current instructions and complete the speaker’s tasks by pressing the appropriate keys or selecting the required documents. In this case, the involved fragments will be highlighted in red. If the object no longer requires any manipulation, it will glow blue.
The MathCAD 14 self-instruction manual was developed specifically for people studying at technical institutes with the goal of obtaining an engineering specialty in the future. With the help of such a new course, the process of solving various technical problems will significantly speed up and become more efficient. Thanks to the section called "Quick Start", users can easily become familiar with the most common graphs and mathematical expressions.
The book, entitled “Calculations in Mathcad,” consists of approximately 100 files that contain detailed information about all the available capabilities of the software, so it will be much easier for the user to understand them. In addition, you will be able to master the methods of building personal software components much faster by using a complex of existing fragments in a software tool.
In addition, the storage space contains at least 50 examples of design calculations in a variety of mathematical areas, including calculations of material strength, strength and dynamics of equipment, and finite element calculations. There shouldn't be any problems with navigation either.
The disk contains the following information:
- ReadMe text document - a detailed description of installing an e-book within Mathcad.
- A section called “Calculations in Mathcad”, as an integral part of the Mathcad shell, containing more than 100 additional fragments. The e-book includes a whole set of examples and special software components for solving problems of varying complexity and subject matter.
- Table of contents of the tutorial in pdf.
- "Quick start in Mathcad" - key data used to solve problems using Mathcad tools.
- "Examples of engineering calculations in Mathcad" - detailed explanations for all of the above examples.
- "Appendices to the book" - reference information on Mathcad (in pdf).
MINISTRY OF EDUCATION AND SCIENCE OF THE RUSSIAN FEDERATION
State educational institution of higher professional education
ST. PETERSBURG STATE UNIVERSITY
AEROSPACE INSTRUMENT ENGINEERING
A. I. Panferov, A. V. Loparev, V. K. Ponomarev
Tutorial
St. Petersburg 2004
UDC 681.3.068 BBK 32.973
Panferov A. I., Loparev A. V., Ponomarev V. K.
P16 Application of Mathcad in engineering calculations : Textbook. allowance / SPbGUAP. St. Petersburg, 2004. 88 p.: ill.
The tutorial contains a description of the main capabilities of the Mathcad 2000 application package with detailed recommendations for its use in engineering calculations. Algorithms for solving standard problems, examples and necessary information from the course of higher mathematics are given.
The manual is intended for students of technical specialties 1812, 1903, 1310.
Reviewers:
Department of Automation and Control Processes, St. Petersburg State Electrotechnical University; Candidate of Technical Sciences S. G. Kucherkov (SSC RF - Central Research Institute "Electropribor")
Approved by the University's Editorial and Publishing Council
as a teaching aid
Educational edition
Panferov Alexander Ivanovich Loparev Alexey Valerievich Ponomarev Valery Konstantinovich
APPLICATION OF MATHCAD IN ENGINEERING CALCULATIONS
Tutorial
Editor A. V. Podchepaeva
Computer typing and layout by N. S. Stepanova
Delivered for recruitment 06/04/04. Signed for publication on 10/08/04. Format 60×84 1/16. Offset paper. Offset printing. Conditional oven l. 5.2. Conditional cr.-ott. 5.3. Academic ed. l. 5.6. Circulation 100 copies. Order No. 444
Editorial and publishing department Department of electronic publications and bibliography of the library
Department of operational printing of St. Petersburg State University of Aviation Administration
190000, St. Petersburg, B. Morskaya St., 67
© State Educational Institution of Higher Professional Education "St. Petersburg State University of Aerospace Instrumentation", 2004
Preface........................................................ ........................................... | |
1. INTRODUCTION TO MATHCAD .................................................... ................... | |
1.1. Mathcad window .................................................... ........................... | |
1.2. Examples of simple actions........................................................ ... | |
1.3. Charts........................................................ ........................................ | |
1.4. Text areas........................................................ ............. | |
2. VECTORS AND MATRICES.................................................... .................... | |
2.1. Specifying arrays........................................................ ................... | |
2.2. Vector and matrix operators and functions.................. | |
2.3. Discrete arguments................................................... .......... | |
3. OPERATORS................................................... ....................................... | |
4. BUILT-IN FUNCTIONS.................................................... ............... | |
4.1. Trigonometric functions................................................... | |
4.2. Logarithmic and exponential functions.................................... | |
4.3. Special and truncation functions................................... | |
4.4. Discrete Fourier transform.................................................... | |
4.5. Fourier transform in the real domain......... | |
4.6. Alternative forms of the Fourier transform................................. | |
4.7. Piecewise continuous functions.................................................... | |
4.8. Statistical functions................................................... ...... | |
4.9. Probability distribution densities......................................... | |
4.10. Distribution functions................................................... ...... | |
4.11. Interpolation and prediction functions................................... | |
4.12. Regression functions................................................... .............. | |
5. SOLUTION OF EQUATIONS.................................................... ............... | |
5.1. Numerical solution of an equation with one unknown...... | |
5.2. Finding the roots of a polynomial......................................................... | |
5.3. Solving systems of equations................................................................... .... | |
5.4. Solving differential equations................................... | |
6. SYMBOLIC COMPUTATIONS.................................................... ...... | |
6.1. Calculations......................................................... ................................... | |
6.2. Fourier and Laplace transforms.................................................. | |
6.3. Direct and inverse z-transforms................................................. | |
7. PROGRAMMING.................................................... ................... | |
Bibliography................................................................ ............... |
PREFACE
The effective work of an engineer is currently unthinkable without personal computers (PCs) and developed telecommunications. The operation of the PC itself is ensured by the operating system (for example, MS-DOS, OS/2, Be OS, Linux, Windows, etc.), and special application software packages are used to solve applied problems.
Naturally, a qualified user who has sufficient knowledge of one of the programming languages (for example, C, Pascal, Fortran, Lisp, Prolog, etc.) can independently develop and debug a separate program or a set of programs that allows him to implement the algorithm of his task on a PC. Moreover, in some cases, a highly specialized program developed by the user can work significantly faster than a program from a software package. However, this approach usually requires large labor costs for programming, debugging and testing of each program, significantly reducing the share of creative work to solve a specific technical problem.
To reduce programming time, a large number of application packages have been created, the areas of use of which largely overlap. For the most effective use of computer technology, it is necessary to correctly select the best software package at the earliest stage of solving an application problem.
The most well-known application software packages currently used in engineering calculations are Mathcad, Matlab, Derive, Maple V, Mathematica, VisSim from well-known foreign companies and packages from Russian manufacturers open source software Dynamics and CLASSIC (developed by SPGETU).
When studying automatic control systems and computational mathematical problems, it is most effective to use the Matlab software system with extensive subject-specific
digital libraries (toolbox) and the visual modeling tool Simulink. For visual modeling and simulation in conjunction with real equipment, VisSim is most convenient, a free academic version of which is available at the university. For the analysis and synthesis of linear control systems, CLASSIC is most convenient.
Analytical transformations can be performed by many software packages, for example Mathcad, Matlab, Mathematica, but the Maple V package is considered the most powerful tool for automating analytical calculations. A simpler specialized package for analytical transformations is Derive.
All of the above packages are supported and developed by large companies. There are a sufficient number of pages on the Internet where, by the name of the package, you can find libraries of freely distributed programs, tutorials, additions and corrections to new versions of programs (patch), and links to newsgroups.
This tutorial introduces the popular Mathcad software package and contains a large number of examples. When studying the manual, it is recommended to do all the examples on a PC.
1. INTRODUCTION TO MATHCAD
Mathcad is extremely easy to use and easy to learn. Most of the actions required to manage the program are intuitive, and it takes two to three hours for a person who has previously worked in the Windows environment to master its basic capabilities.
The Mathcad system has the following features:
The usual method of mathematical notation is used everywhere. If there is a generally accepted way to represent an equation, mathematical operation, or graph, then Mathcad uses it;
The principle “What you see is what you get” (WYSIWYG) is used. There is no hidden information, everything is shown on the screen. The printed result looks exactly the same as on the display screen;
simple expressions are typed on the keyboard using standard keys. Special palettes are provided for special operators (sum signs, integrals, matrices, etc.);
a large number of well-tested numerical algorithms greatly facilitate the solution of applied problems;
in addition to numerical calculations, symbolic transformations are possible,
has extensive graphic capabilities for analyzing calculation results and allows you to create animations;
fully supports OLE and DDE technologies, allowing connections with other Windows applications;
convenient help system. By highlighting a statement, function, or error message and pressing , you can display explanatory help information on the screen. Help contains step-by-step explanations on a specific topic and illustrative examples;
in the window, you can use scroll bars, as in any Windows program. Like other Windows programs, Mathcad contains a menu bar. To call up a menu, just click on it with the mouse or press a key along with the underlined character.
To use the symbol palette buttons, place the cursor at the selected location in the working document and click the left mouse button. A small cross will appear in the working document. Then place the cursor on the desired symbol palette button and press the left mouse button again and select the desired element (equal signs, ratios, two- or three-dimensional graph, integral, program structure, etc.). The selected element will appear in place of the cross in the working document.
Below the strip of symbol palette buttons are toolbar buttons that duplicate the main menu commands. When you place the pointer over a button, text appears that describes what the button does. Directly below the toolbar is the font panel, which allows you to change the size and other characteristics of fonts in formulas and text. To save screen space, each of these components can be displayed or hidden using the corresponding command from the Window menu. All pictures in this tutorial show the working document only.
1.2. Examples of simple actions
Click anywhere on the screen with the left mouse button and enter the line using the keyboard
After typing the equal sign, Mathcad evaluates the expression and displays the result
15 − 8 = 14.923
This example demonstrates the features of Mathcad.
Mathcad displays formulas exactly as they are printed in books or written on the board - across the entire screen area. Mathcad sizes fractions, parentheses, and other mathematical symbols so that they appear on the screen as they would normally appear on paper.
Mathcad understands which operation to perform first. In the example above, Mathcad "knew" that the division needed to be done before the calculation and displayed the expression accordingly.
The expression on the screen can be edited by placing the pointer in the desired place and replacing old characters with new ones. After setting the pointer to a free field or other expression, the new result will be calculated automatically.
Let's type the following lines on the keyboard:
b:0.1 x(t):exp(–b t) sin(t) x(t)=
After clicking outside the equality for x(t), the working document will look like this:
t:= 0.5,0.6..20 b:= 0.1
x(t):= exp(–b t) sin(t) x(t)=
The first line provides sequential assignment of the numbers 0.5 to the argument t; 0.6; 0.7, etc. up to 20. It should be noted that the colon [:] on the screen is automatically replaced by the assignment sign [:=], and the period with
comma [;] – sign [..]. The third line introduces the function definition. The fourth line displays the function value for the given argument values in table form. The default screen displays the first 16 rows of the table. To view subsequent elements, you can click anywhere in the table with the mouse and use the scroll bar that appears or “stretch” the table.
Mathcad can set the format for displaying numbers, i.e., change the number of decimal places displayed, change the exponential representation of numbers to a regular notation with a decimal point, and so on. This is done as follows:
Left-click on the table to highlight it with a solid contour line;
select Result from the Format menu; In the dialog box that appears, set the necessary parameters.
For example, the default "Threshold" is 3. This means that numbers greater than 103 and less than 10–3 are displayed in scientific notation. To replace 3 with 6, you need to click to the right of 3, press the key and type 6, or use the incrementing buttons.
1.3. Charts
Mathcad can build two-dimensional graphs in Cartesian and polar coordinates, pictures of level lines, depict surfaces and display a number of other three-dimensional graphs.
Let's consider creating a simple two-dimensional plot that displays the function introduced in the previous section. To create a graph in Mathcad, you need to click on the free space where you want to place it and select Graph - X-Y Dependency from the Insert menu. An empty graph will appear with input fields for data. In the field under the middle of the x-axis you need to enter the name of the variable t. Now you need to click in the field opposite the middle of the y-axis and enter x(t) here. The remaining fields are intended for entering boundaries on the axes - the maximum and minimum values plotted on the axes. If you leave them empty, Mathcad will automatically fill them in when creating the graph. After clicking outside the graph, Mathcad calculates and plots the points on the graph, as shown in Fig. 2.
