Informatics theory

1. Purpose and main features of MathCAD package in the most general sense, you can think of MathCAD as a combination of: a powerful technical computing environment centred on real math notation a flexible, full-featured technical word processor. This means that with MathCad the tasks of performing computations and documenting them are integrated into one seamless process, resulting in substantial increases in productivity. What you can do with Mathcad. Mathcad combines the live document interface of a spreadsheet with the WYSIWYG interface of a word processor. In addition, Mathcad’s computational abilities range from adding up a column of numbers to evaluating integrals and derivatives, solving systems of equations and more. You can place equations, text, and graphics anywhere in the Mathcad worksheet. The equations are WYSIWYG and live. That is, equations appear as you're used to seeing them on blackboards or in reference books, and as soon as you make a change anywhere in your worksheet, Mathcad updates results and redraws graphs. This makes it easy keep track of the most complex calculations. After creating a presentation-quality document, you can share your work with others by printing the worksheet exactly as it appears on the screen, emailing it, or posting it on the web. 2.The MathCAD main screen and objects When you start Mathcad, you will see:An untitled Mathcad worksheet ,The Resource Center window,The menu bar ,The Math toolbar ,The Standard toolbar ,The Formatting toolbar. To conserve screen space, you can show or hide these and other toolbars using the View menu options. If you prefer to have these elements elsewhere on the screen, you can move them around your window. When you exit and re-open Mathcad, the elements are positioned as they were when you exited. 3.Built-in string functions The following functions are useful when working with strings: concat(S1,S2) :Concatenates string S2 to the end of S1. Returns a string. error(S) :Returns the string S as an error message. IsString(x):Returns 1 if x is a string, otherwise returns 0. strlen(S) :Determines the number of characters in the string S. Returns an integer. substr(S,n,m):Extracts a substring of S starting with the character in position n and having at most m characters. The arguments m and n must be integers. search(S,SubS,x):Finds the starting position of the substring SubS in S, beginning from position x in S. str2num(S) :Converts a string of numbers S into a constant. num2str(x) :Converts the number x into a string. str2vec(S) :Converts a string S to a vector of ASCII codes. vec2str(v) :Converts a vector of ASCII codes to a string. Data You can enter data directly into Mathcad and assign it to a Mathcad variable by using an input table. When you create an input table, you’re actually creating an array with the name you entered into the placeholder. Once you’ve created an array using an input table, you can manipulate the array using Mathcad’s built-in functions and operators. Components are specialized OLE objects in your Mathcad worksheet. They allow you to exchange data with other applications or sources and to build user interface controls. Application components allow you to access functions and data from other computational applications such as Excel, SmartSketch, and MATLAB. Mathcad provides components to exchange data between Mathcad and other applications. A component communicates with the mathematical equations in Mathcad, linking your Mathcad computations to the rest of your computing environment. This link allows data to flow dynamically between the Mathcad worksheet and a data source or application. Some components are used to import data, some to export data, and application components, such as Excel, Axum, and MATLAB, allow you to communicate with other applications installed on your computer. 4. Calculation of expressions in MathCAD Any calculation Mathcad can perform with single values, it can also perform with arrays of values. There are two ways of doing this: By iteration over each element using range variables as subscripts. By using the vectorize operator which allows Mathcad to perform the same operation efficiently on each element of a vector or matrix. 5.Creating vectors and matrices The easiest way to create an array is to create an array of empty placeholders and just fill them in. For arrays in which there exists a formula relating the value of an array element to its indices, it is easier to use range variables and subscripts. Displaying vector or matrix results There are two ways of displaying a vector or matrix: If an array has fewer than ten rows and columns, you'll see it displayed in matrix form. If an array has more than nine rows or columns, you'll see a portion of it displayed as a scrolling output table. Graphing one vector against another is useful for plotting data points. Enter the x-values in one vector and the y-values in another. There are three functions for sorting arrays and one for reversing the order of their elements: sort(v) :Returns a vector with the values from v sorted in ascending order. If v contains complex elements, the imaginary part is ignored. csort(A,n):Returns an array formed by rearranging rows of A until column n is in ascending order. If A contains complex elements, the imaginary part is ignored. rsort(A,n) :Returns an array formed by rearranging columns of A until row n is in ascending order. If A contains complex elements, the imaginary part is ignored. reverse(v) :Returns a vector in which the elements of v are in reverse order. If v contains complex elements, the imaginary part is ignored. 6. Solving of equations in MathCAD Functions for equation solving Find(x,y,...):Solves a system of equations. Minerr(x,y,...):Approximate solution to a system of equations. root(f(x),x,a,b):Solves one equation in one unknown. lsolve(M,v):Solves a system of equations. polyroots(v):Solves for the roots of the polynomial whose coefficients are in v. Mathcad will solve for the variable and paste the result into your worksheet. If the equation has more than one solution, you'll see a vector having as many elements as there are solutions. If your equation includes numbers with decimal points, you'll see a decimal answer. Otherwise, you'll see an exact solution (if one is available). Mixed Integer Programming refers to the ability to solve equations or optimize functions such that the variables are forced to be integers or binary numbers. 7.Solving and optimizing overview Mathcad allows you to numerically solve a variety of optimization problems using various built-in functions. You can solve one equation for an unknown value using the root function. You also solve a system of equations using the Find or Minerr function. Use Find when you want to find an exact solution and Minerr when a close solution is sufficient Function optimization minimize(f, var1, var2,...):Finds the values at which a function takes on its minimum value. maximize(f, var1, var2,...):Finds the values at which a function takes on its maximum value. Interpolation Mathcad provides three interpolation methods and one linear prediction method: Linear interpolation: For connecting points with a straight line. Cubic spline interpolation: For connecting points with a cubic section. B-spline interpolation: For connecting points with polynomials of a specified degree at given knots. Multivariate cubic spline interpolation: For creating a surface which passes through a grid of points. Cubic spline interpolation Cubic spline interpolation lets you pass a curve through a set of points in such a way that the first and second derivatives of the curve are continuous across each point. This curve is assembled by taking three adjacent points and construction a cubic polynomial passing through those points. These cubic polynomials are then strung together to form the completed curve. In linear interpolation, Mathcad connects the existing datapoints with straight lines and interpolates for a particular value. Multivariate cubic spline interpolation Two dimentional cubic spline interpolation lets you pass a surface through a grid of points in such a way that the first and second derivatives of the curve are continuous across each point. This surface corresponds to a cubic polynomial in x and y in which the first and second partial derivatives are continuous in the corresponding direction across each grid point. 8. MathCAD graphs 2D You can graph several curves on one graph by typing a comma between the arguments on each axis. MathCAD matches up the expressions in pairs. It then draws a trace for each pair. Each matching pair of expressions should use the same range variable, but the range variable for one pair need not match the range variables for the other pairs. To graph several y-axis (or radial axis) expressions versus one x-axis (or angle axis) expression, enter one expression on the x-axis (or angle axis) and multiple expressions separated by commas on the y-axis (or radial axis). You can plot up to 16 y-axis arguments. 3D You can create the following kinds of plots to represent three-dimensional data: Surface, Parametric surface,Contour,3D Scatter,3D bar plot, Vector field When you create a surface plot, MathCAD visually represents a matrix of data as a surface in a three dimensional graph. You can format the graph in many ways to control its appearance. You can also change a surface plot into another type of 3D plot. MathCAD creates a surface plot of the function using default ranges and grids for the independent variables. MathCAD draws a perspective view of the matrix as a two-dimensional grid lying flat in three-dimensional space. Each matrix element is represented as a point at a specified height above or below this grid. If a point is complex or imaginary, MathCAD does not plot it. To plot the real or complex part of a point, use the Re and Im functions which pull off the real or imaginary parts. Alternatively you can create a surface plot from a set of x, y and z data points. First create three vectors: one containing the x values, one containing the y values, and one the z values. Create a surface plot region and type the names of the x, y and z vectors separated by commas into the placeholder. The surface plot MathCAD generates is the same as a 3D scatter plot changed into a surface plot. Parametric surface plots Parametric surface plots remove the restriction that surfaces be of the form z = f(x,y). With parametric surface plots, you can plot arbitrary surfaces. Contour plots Contour plots require a matrix of values, MathCAD linearly interpolates the values of the matrix to form level curves. Such level curves can represent isotherms, isobars, equipotentials, streamlines, and many other physical phenomena. MathCAD creates a contour plot of the function using default ranges and grids for the independent variables. MathCAD linearly interpolates the values of the matrix to form level curves in such a way that no two cross. MathCAD plots the matrix by rotating it so that the (0,0) element is at the lower-left corner. Thus the rows of the matrix correspond to the values on the x-axis, increasing to the right, and the columns correspond to the values along the y-axis, increasing toward the top. 3D Scatter Plots Mathcad creates a scatter plot of the function using default ranges and grids for the independent variables. create a 3D scatter plot using the x, y and z coordinates contained in three vectors. If a point is complex or imaginary, Mathcad does not plot it. Vector field plots A vector field can be thought of as a function which assigns to a point in the plane a vector which starts at a given point. You can create a two-dimensional vector field plot in Mathcad by creating a matrix of complex numbers. 9. Symbolic calculations in MathCAD One method of evaluating an expression symbolically is to use the commands from the Symbolics menu. Using the Symbolics menu all algebraic transformations work in fundamentally the same way: Select either all or part of an expression. Choose the appropriate menu command from the Symbolics menu. You'll see the transformed expression in your worksheet. Depending on how you've set your evaluation style, this transformed expression will either replace the expression you clicked on or place it below or to the right of the existing one. If the symbolic transformation was unsuccessful, the new expression will be identical to the old one. 10. DB main features. Data base is a large group of stored integrated data elements. Those elements can be retrieved and manipulated with great flexibility to produce information. DB is used when it’s needed to store an information about various related objects. Ex.: library keeps info about books, educational DB keeps info about students, professors, examinations. Composed in logical level: Data base; File (contains data about one group of objects at records); Record (contains data about one object of a group); Field (contains data about one object’s characteristic). Composed in physical level: Word; Byte; Bit. Main system includes set of software program that provide necessary capabilities for building, containing data base files, extracting the needed info, preparing reports. Requirements for DB MS: 1) Make data independent of application program being used. Can be used with different application prog. And structure mustn’t effect the application prog. 2) It must establish relationships among records in different files. The user must obtain all data relative to the data elements. 3) It must dominate data redundancy. It means that it’s not needed to store the same data in different files. 4) It must define the characteristics of data, manage access and data security. The system must maintain integrity. Each DB management system includes: 1) Dialog system (used for data entering & retrieving); 2) query language – specific language which allows to formulate the requirements; 3) Report writer (defines how selected data will appear in printed report. Controls data location); 4) Data manipulation language (specific high level programming language, which allows to create application progr. for specific data in DB usage); 5) Network support (security system, which enables to use the same data base in a local network for many users). 11. DB models. 1) Hierarchical model. This model consists of records organises like a family tree: R 1 R 11 R 12 R 13 Children can have only one parent, but parents can have many children. Consists of several branches which aren’t related and each branch stands like a root record. When you want to store or retrieve data, management system must begin from root record. Positive features: 1) Clearness of relations among records. 2) Easiness with which data can be stored and retrieved. 3) Ensures higher access speed. Negative features: 1) Records in separate branches can’t be relatively directed. 2) When parent is deleted, all all children are deleted. 3) Updating is complicated. 4) Data redundancy is great. 2) Network model. R 1 R 2 R 3 R 4 R 5 R 6 R 7 R 8 Each child can have many parents. It allows to establish relationship of records at different branches. The relationship syst. is many to many. Positive features: 1) Reduced data redundancy. 2) There are links among data in separate branches. Negative features: 1) Increased complexity. 2) Increased maintenance difficulties. 3) Complicated links recorded. 4) Links between records are prettified in DB structure. 3) Relational model. Is made of many tables in which relative data elements are stored. Tables are named as relations. Relations are similar in contest to files. A row is similar to record and column is similar to field. But table has no predity relation. The relation can be established in a very flexible manner. The relative tables must have fields of the same type. Such fields can be arbitrary introduced (as codes) and the serve as key codes of certain object. Possitive features: 1) Simplicity; 2) Flexibility; 3) Data independence; 4) Easiness of data updating; 5) Multiple relations; 6) Software isn’t complicated. Negative features: 1)Additionel fields; 2) Data search takes more time. This model is most wide spread. Only this model is used with microcomputers. All data base management systems are based on relational model. 12. ACCESS MAIN FEATURES. It includes: data definition, manipulation, control dealing with great amounts of information. ACC. includes all objects (tables, queries, forms, reports, macros, modules) related to the stored data. A TABLE is a collection of data about a specific topic. For each topic use separate table and enter new data only once, avoiding data entry errors. Tables organize data to columns (fields) and rows(records).Records keep data about one object from specified topic. Each field – about one characteristic of an object. QUERIES are used to view, change, analyze data in different ways. They can bring data from multiple tables and sort it in a particular order, perform various calculations on groups of record fields. FORMS can be used to enter data into table, create a dialog with a user, and carry out an action based on the dialog or input data. A REPORT is a good way to present data in a printed form, you have control on all your data and can display it as you want. MACROS include structured definition of operations to be performed in specified situations. They use standart macrocommands, and are used in application programs. MODULE is an object that includes procedures and functions written in MS Access Visual Basic. ACC. Support DDE(dynamic data exchange) and OLE(object linking and embedding) technologies .It means you can exchange data with any windows application that supports DDE.OLE objects are MS Word, Excel, pictures, sound. Embedding is inserting a copy of an object from another application. When an object is embedded, changes to it are not returned to the original object and vise versa. ACC. enables to process systems that support ODBC (open DB connectivity) standard. To search data in ACC. We use mouse using QBE (query by example) system. 13. CREATING & CHANGING DB. You have to create your own DB file structure: file-new-table/DBF-new or Create - File name. Create frame C:\ FoxproW; Y:\VVU-8\ginte\frame. Field types:1. Character (all type of char., also special symbol characters. Max. width-254 char.); 2.Numeric (numbers, decimal point & sign. Max. width 2); 3. Float (numbers analogical to numeric); 4. Date (YYYYMMDD. To input MM/DD/YY); 5. Logical (width 1,T or F, Y or N); 6. Memo (width is not limited, can include any char. From keyboard. This field is saved in separate file, with the same name, but different extension(.FPT). DB file has extension .DBF); 7.General(includes invalid objects(which have their own files-graph, pictures)-Excel, Paint-brush. So the field saves only object’s file name);8.Picture (is used to directly include pictures. It can be used only with Apple Macintosh comp.). Tag column is used for indexing. When the structure is created, appears an additional window. You can input data immediately or not. When DB is filled, you can display it in Browse mode. Database-Browse. You can change data in Browse mode. If you want to access memo field, simply click twice this field. To delete some records, at first you have to select them (click the left upper corner of record, it becomes dark. If mouse doesn’t operate, go with arrows, select and press Ctlr + T. Actual deleting appears if you go: Database-Pack or type Pack). Data can be analysed : 1.Change mode. 2. Browse mode. To change mode: Browse-Change or Browse-Browse. To add new records: Record-Append or type Append. To change DB structure: Database-Setup-Modify or type Modify Structure. To exit: File-Exit or type Quit. To begin work with existing DB: File-Open-yours file name. 3.Application of Command Window. 1st step: command. Commands can include 4 specific sections.They are denoted between brackets:[scope], [For cond.1], [While cond.2],[options]. Rest-the command will be applied from default record to the end of file. Next n-comm.’ll be applied to the next n records from default. Record n- comm.’ll be applied to record number n. [FOR condition1]-condition1 shows records for which comm. Will be executed. [WHILE condition2]-condition2 shows when to stop execution of comm. [Options] -includes specific additional options. The relational operations are denoted the same as in Pascal (=,,=>,). Logical operations-not, or, and. String operations: ‘john’ = ’j’ true; ‘j’ = ‘john’ false. To change a default record: Record-Goto-Top/Bottom /Record/Strip; Record-go to some rec.(must know its no.); Skip-skips name records(input, how many). 14.SORTING DB. To find record, which satisfies some conditions: Record-Locate(a dialog wind. appears) Browse[fields]. For operation realises vertical sorting. When data is selected it is needed to print it: LIST [Fields] [For..] [While..] [To printer/To file file name] .To file-a text file will be created. Data Base Sort-Sort to file name on field1[Ascending/Descending]. 15. DB TABLE EDITING. Open Database-Tables window. To copy table structure or table with data must select needed table icon and use: edit-copy, edit-paste. It opens a dialog window, to put data there from two alternatives; Structure Only, Structure and data, Append data to Existing Table. Table can be deleted or renamed: edit-delete, edit-rename. To modify table use Design View window. To insert a new field, select the first existing field before which the new field is to be inserted: insert-rows. Selected field or can be deleted using: edit-delete rows. It mistake, then correct it: edit-undo delete. Copy field: edit-copy, insert field: edit-paste. To move field, click row selector and drag it up or down. Table row and column width are corrected using: format-row height, format-column width. To hide column: format-hide columns to unhide: format-unhide columns. 16.ACCESS EXPRESIONS AND FUNCTIONS. Expressions are any combinations of operators, constants, literal values, functions, names of fields and properties that evaluates to a single value. We can use expressions as settings for many arguments to define calculated fields in queries. Arithmetic operations:+-*/,rising to a power ^,rounded integer division \,MOD remainder from division of rounded numbers, relational operators: IN, BETWEEN, LIKE, AND, OR, NOT. LIKE can include codes:*-any symbol,?-one symbol,#-one digit. Field names in expressions must be in brackets[].Text values are enclosed such “text”, date/time such #value#. MS Access has many functions divided into 16groups.Mathematical group: Abs, Exp, Log(Ln), Sin, Cos, Tan, Sqr. SQL Aggregate group: Avg, Count, Max, Min, StDev ,Sum, Var. Functions of time/date group; Day-(1-31),Month-(1-12),Year-(100-9999),Weekday-(1-7),Hour-(0-23),Date()-current date .Functions of program flow group: IIF(expr, True-value, False-value). Choose (numb, choise-1,choise-2,.)-(1

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