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Solution 2.0 SOLUTION TLB GROUP User`s Manual

1. to zoom out use navigation keys to move through the worksheet To view several functions on the same worksheet use More functions menu select this item and press navigation centre key You can change existing functions and add new ones to the same worksheet To learn more read the information below 12 SA SOLUTION 2 0 More Functions Menu wey Solution Functions to plot x sin x 2 sin 1 x x 2 Add new Use this utility to view several functions graphs on the same worksheet How to use Create new Select Add new item or use Options Edit Add new Enter the function in the appeared dialog Functions menu is available Change existing To change the function name or formula select it from the list left column using navigation keys Press navigation centre key or use Options Edit Change In the appeared dialog make the necessary changes To change the color of function s graph set the cursor over the right column in the list and press navigation centre key In the appeared dialog make the necessary changes Delete To delete function from the list select it any column and press C or use Options Edit Delete Order Functions are listed in the same order as they were saved To change cur rent position of function select it and call Options Edit Order Plot To plot all the functions use Options Plot 13 SA SOLUTION 2 0 Scientific Calculator This is pow
2. To change current position of function select it and call Options Edit Order 10 SA SOLUTION 2 0 Multidimensional function example Suppose you want to save the function fun x1 x2 sin x1 x2 Select Add new item and enter the function s name fun Enter the formula Functions Menu is available sin x1 x2 Press OK or press centre key twice To use new function select its name and press centre key In the parent dialog fun appears The comma separates arguments Enter the values for both arguments that can be numbers other functions variables or expressions and get the answer fun 0 1 provides 1 fun asin 1 1 provides 0 11 SA SOLUTION 2 0 Plot General Description More functions Xmax 5 Use this utility to create a linear plot of function F x in specified bounds Xmin Xmax Ymin Ymax Parameter A can be used in F x formula specify this value if necessary This utility also provides an opportunity to view sev eral graphs of functions on the same worksheet How to use For entering F x formula quicker press navigation centre key and use the appeared Functions Menu This menu provides quick access to standard and user defined functions and constants To learn more about Functions Menu read User s Interface chapter above When you finish entering data press navigation centre key two more times On the appeared worksheet you will see plot of F x function Press to zoom in and press
3. Examples If you need to solve a system of the three linear equations like the following one you should fill the coef ficients matrix as shown Linear system to be solved Then coefficients matrix is al a2 a3 C Eq1 2x y 3z 9 Eq1 2 13 9 Eq2 5x y z 0 Eq2 5 1 1 0 Eq3 2y z 1 Eq3 0 2 1 1 x is a1 y is a2 and z is a3 The elements of the first row are the coefficients of the first equation 2 x s coefficient 1 y s coef ficient 3 z s coefficient The last one 9 is the constant right part of the equation In the third equation the first variable x has a zero coefficient The answer is 1 2 3 which means that x 1 y 2 z 3 20 SA SOLUTION 2 0 ODE Solver Use this utility to solve initial value problems for ordinary differential equa tions ODEs Specified equation dy dx f x y where y x is scalar function depending on x is numerically solved in the specified interval x1 x2 using ODE 7 Euler method dy dx 2 abs x How to use For entering F x formula quicker press navigation centre key and use the appeared Functions Menu This menu provides quick access to standard and user defined functions and constants To learn more about Functions Menu call Options Help there Mind the special symbol y that represents the desired unknown function and can be used in equation When you finish entering data press navigation centre key two more times to get the answer The numerically
4. resolved answer is plotted in a new dialog Examples dy dx cos x x1 0 x2 6 3 y x1 0 sin x is plotted dy dx 2 y x1 0 x2 1 y x1 1 exp 2 x is plotted dy dx 2 abs x x1 1 X2 1 y x1 1 y x 2 for x gt 0 and y x 2 else is plotted 21 SA SOLUTION 2 0 More Conversions 2 1016 58B Number 25F1 10 2 10 8 10 16 2 10 8 10 1610 Answer 9713 You can use this utility for converting values between various numeration systems Conversions from decimal numeration system return the posi tive decimal numbers in a true representation the whole negative decimal numbers in a complement representation The fractional negative decimal numbers are not represented in the complement form for not creating con tradictions Also there are functions for converting values from binary octal or hexa decimal numeration to decimal These functions return the positive decimal numbers How to use Enter the number you want to convert to another notation press naviga tion centre key to enter letters and then use special buttons that represent six available operations In the first row there are decimal to binary form decimal to octal form decimal to hexadecimal form In the second row there are binary to decimal form octal to decimal form and hexadeci mal to decimal form Select the necessary operation and press navigation centre key Answer appears in the box
5. Add new item or use Options Edit Add new Enter the name and the value to be saved in the appeared dialogs Some of the names e g pi or e are not allowed Add new Ta Usage in formula To use saved constant in arbitrary formula set the cursor over constant s name in the list left column using navigation keys Press navigation centre key or use Options OK Change existing To change constant name or value set the cursor over the value of this constant in the list right column using navigation keys Press navigation centre key or use Options Edit Change In the appeared dialogs enter new name and then new value Delete To delete constant select it in the list any column and press C or use Options Edit Delete Order Constants are listed in the same order as they were saved To change current position of constant select it and call Options Edit Order More The last numerical result can be easily added to constants list It appears as special button in Constants menu There is also possibility to save the last result of any calculation directly to constants list Set the cursor over the Answer box in parent dialog and press navigation centre key twice SA SOLUTION 2 0 Custom Functions Menu s Use this utility to store any functions that are frequently used in calcula my Solution tions Give them unique names and use these names anywhere you need This menu shows the full list of user defined functions an
6. LB GROUP DISCLAIMS ALL WARRANTIES EITHER EXPRESS OR IMPLIED INCLUDING THE WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE NOBODY WILL BE LIABLE FOR DATA LOSS DAMAGES LOSS OF PROFITS OR ANY OTHER KIND OF LOSS WHILE USING OR MISUSING THIS SOFTWARE You may not distribute copy emulate clone rent lease sell modify decompile disassemble otherwise reverse engineer or transfer the program or any subset of the program except as provided for in this agreement Any such unauthorized use shall result in im mediate and automatic termination of this license and may result in criminal or civil prosecution All rights not expressly granted here are reserved by SOLUTION TLB GROUP SOLUTION TLB GROUP reserves the right to make exceptions to any of these conditions or alter these conditions at any time How ever you may always use these conditions instead of any altered version if you prefer note that this license explicitly applies only to one version of the program therefore if SOLUTION TLB GROUP make new conditions in connection with a future version you do not then have the right to apply these conditions to that version instead Installing or using the program signifies acceptance of these terms and conditions of the license If you do not agree with the terms of this license you must remove the program files from your storage devices and cease to use the program 25 SA SOLUTION 2 0 Disclaimer This document d
7. SOLUTION Solution 2 0 SOLUTION TLB GROUP User s Manual Table of Contents Introduction Quick Start User s Interface Main Menu Help Functions Menu Constants Menu Custom Functions Menu Plot General description Navigation More Functions Menu Scientific Calculator Supported functions Complex computations Analysis Limit Symbolic Differentiation Numeric Differentiation Integration Matrix Operations Solvers Non linear Equation solver Linear System Solver ODE Solver More Conversions History Settings Credits End User License Agreement Disclaimer 12 14 15 18 19 22 24 25 26 SA SOLUTION 2 0 Introduction Solution is the most powerful mathematical application for mobile devices running Symbian OS Nokia Series 60 3rd Edition Solution contains lots of different instruments and provides smart interface which makes using Solution quick and easy This document describes all the Solution features and abilities and the right way to use them In the 2nd chapter Quick Start you can find a detailed description of plotting exp x function This simple example will introduce the basic interface features In the 3rd chapter User s Interface the interface utilities that are used in the whole program are widely discussed The main idea of Solution interface is in fact this simply one to enter any data press navigation centre key first and look a
8. below Examples Number 4 5 Number 1 Number abcdef 10 gt 2 10 gt 2 16 gt 10 Answer 100 1 Answer 1111 Answer 11259375 Number 1000 Number 11001 10 gt 16 2 gt 10 Answer 3e8 Answer 25 22 SA SOLUTION 2 0 History This utility provides quick access to the last 30 performed actions How to use The first line of each history item represents utility used and the second line represents object function matrix etc upon which the action took place Cauchy problem gt abs x Select the necessary item using navigation keys and press navigation cen tre key The proper already filled dialog opens Linear system lt 1 2 12 1 245 1 L L 2 1 3 Linear system lt 1 2 1 2 1 3 gt lt 0 0 0 0 0 Additional Settings Reset colors sets default values to all graph colors Units of Angle changes the behavior of trigonometric functions You can choose between radians default and degrees computations Alpha Mode sets the F x editor mode Digits mode 123 is set by default letters mode Abc is recom mended for users of QWERTY keyboard 23 SA SOLUTION 2 0 Credits Alexander Taboriskiy Nadezhda Baldina Sergey Basheleyshvili Dmitriy Kuznetsov http www math solution com support math solution com 24 SA SOLUTION 2 0 End User License Agreement Solution is copyright C 2005 2008 SOLUTION TLB GROUP All rights reserved This license describes the conditions under whi
9. ch you may use version 2 0 of Solution the program If you are unable or unwilling to accept these conditions in full then notwithstanding the conditions in the remainder of this license you may not use the program at all You are granted a non exclusive license to use the program on one device at a time The program may not be rented leased or transferred Any use of the program which is illegal under international or local law is forbidden by this license Any such action is the sole respon sibility of the person committing the action The program is distributed AS IS and you assume full responsibility for determining the suitability of the program and for results obtained SOLUTION TLB GROUP makes no warranty that all errors have been or can be eliminated from the program software and with re spect thereto SOLUTION TLB GROUP shall not be responsible for losses damages costs or expenses of any kind resulting from using or misusing the program including without limitation any liability for business expenses machine downtime damages experi enced by you or any third person as a result of any deficiency defect bug error or malfunction SOLUTION TLB GROUP shall not be liable for any indirect special incidental or consequential damages relating to or arising out of the subject matter of this Agreement or actions taken hereunder NO WARRANTY OF ANY KIND IS EXPRESSED OR IMPLIED YOU USE THE PROGRAM AT YOUR OWN RISK SOLUTION T
10. d provides quick log2 Mialba rane access to them User defined functions can be multidimensional sinc2 x sinc 2 x sinc x sin x x How to use dist x1 x4 sqrt x1 x2 2 5 Create new Select Add new item or use Options Edit Add new Enter the unique name and the formula to be saved in the appeared dialog Some of the names e g sin or exp are not allowed To create multidimensional function use several independent variables the names of them should be x1 x2 etc See the example below for details The current function from parent dialog can be easily saved It appears as special button in Custom Func tions menu asin sin x1 x2 Add sin exp p Usage in formula To use saved function set the cursor over it s name in the list left column using navigation keys Press navi gation centre key or use Options OK If function is multidimensional it is added to parent dialog with brack ets and commas You should specify all the necessary arguments See the example below for details Change existing To change function name or formula set the cursor over the it s formula right column in the list using navigation keys Press navigation centre key or use Options Edit Change In the appeared dialog enter new name and then new formula Delete To delete function select it in the list any column and press C or use Options Edit Delete Order Functions are listed in the same order as they were saved
11. ently used Give them unique names and then use them in any formula To learn more about creation changing and using constants and custom functions open the appropriate menu and call Options Help there SA SOLUTION 2 0 Details Here are brief descriptions of every Functions Menu standard item x independent variable pi e constants sin cos tan ctg asin acos atan actg trigonometric functions sh ch th cth hyperbolic functions exp exponent In natural logarithm log logarithm of base 10 sqrt square root of a number abs absolute value i imaginary unity re im real and imaginary parts of a complex number arithmetic operations factorial function Ank n n k combinatorial function Cnk n k n k combinatorial function 0 brackets delimiter between arguments in multidimensional user defined function A numeric parameter in plotter E scientific notation sign e g 2E3 2 10 3 2000 Ans the last answer y desired function in Cauchy problem SA SOLUTION 2 0 Constants Menu Use this utility to store any constant values that are frequently used in cal my Solution culations Give them unique names and use these names in any formula you Constants like This menu contains the full list of saved constants and provides quick big 2E 21 access to them 245 cm 2 2 i How to use Add 0 54030 Create new Select
12. er F x Answer exp 2 x F x th x 2 exp 2 x Answer 1 th x 42 sin x exp x sin x exp x exp x cos x x sin x 1 In x cos x 1 sin x x x4 1 sin x 16 SA SOLUTION 2 0 Numeric Differentiation F x xA sin x 1 x0 1 k Answer 2 63014901 a 1 b Answer 3 62687166380633 1 Backi Numerically computes the first second or higher order derivative of the function F x with respect to variable x at specified point x0 Examples F x x0 Answer F x x0 Answer exp 2 x 1 k 4 118 224898 sin x exp x O k 3 2 F x x0 Answer F x x0 Answer x sin x 1 1 2 63014901 x 2 pi x 1 k 1 45 7616029 Numerically computes a definite integral of the function F x with respect to the variable x over the straight line from a to b finite numbers The numerical answers are carried out with accuracy up to the five decimal places Examples Answer F x a Answer exp 2 x 1 b 1 3 62687 166380 sin x exp x 0 b 3 11 8594882628 x sin x 1 1 b 0 Can t Do It x sin x 1 0 b 1 0 40824193777 17 SA SOLUTION 2 0 Matrix Operations Matrices a e Operations my Solution i Width 4 Height 4 2A 23 13 21 599 14 15 2 442 1 53 3 3 56 1 9 08 17 23 14 2 111 152 74 This utility provides the most widely used matrix operations such as A B component wise addition A B component wise subtraction AxB matrix multiplyi
13. erful scientific calculator with real and complex computations support Supported functions sin 2 pi sinc i 1 sqrt 2 dist 4 9 5 7 1E10 1 Standard functions with complex variable support sqrt x sin x cos x tan x ctg x arcsin x arccos x arctan x arcctg x exp x log x In x abs x re x im x sh x ch x th x cth x 2 Combinatorial calculus factorial A n k n n k C n k n k n k Answer 1 59E 11 3 User defined functions and constants Create your own functions pos sibly multidimensional and remember constants that are frequently used in calculations Complex computations All the standard functions support complex computations To enter a complex number use Function Menu item i that represents imaginary unity How to use For entering F x formula quicker press navigation centre key and use the appeared Functions Menu This menu provides quick access to standard and user defined functions and constants To learn more about Functions Menu call Options Help there When you finish entering data press navigation centre key two more times to get the answer that will appear in the Answer box below By default pressing causes entering symbol To switch to Alpha mode use More menu By default everything is calculated in radians To switch to degrees use More menu 14 SA SOLUTION 2 0 Analysis mF Limit Fix Differen
14. escribes the features and user interface of program Solution 2 0 by SOLUTION TLB GROUP This program is intended for mobile phones running Symbian OS Nokia Series 60 3rd Edition For complete list of supported devices please consult phone manufacturer s website However SOLUTION TLB GROUP makes no warranty that the program will work properly at all devices listed there The information contained in this document is for general information purposes only and should not be used or relied on for any other purpose whatsoever While SOLUTION TLB GROUP has taken great care in the preparation of this document it makes no warranty or guarantee about the suitability or accuracy of the information contained in this document No part of this material may be reproduced without the express written permission of SOLUTION TLB GROUP All registered trademarks mentioned in this document are property of their legal owners The program Solution is protected by copyright law and international treaties Unauthorized reproduction or distribution of this program or any portion of it may result in severe civil and criminal penalties and will be prosecuted to the maximum possible under the law 26
15. ess navigation centre key two more times to get the answer that will appear in the Answer box below Examples F x sin x exp x F x x 2 2 a 1 b 1 a O b 2 Answer 0 Answer 1 41421222686 F x In x tan x F x exp 2 x a 2 b 4 a 1 b 1 Answer 2 418229103088 Answer Can t Do It 19 SA SOLUTION 2 0 Linear System Solver Use this utility to find numerical solution to a system of linear equations for several unknowns The numeri cal answers are carried out with accuracy up to the five decimal places How to use y Solution Amount 5 The system of linear equations is presented in Linear Algebra terms It lt a3 a4 _ a5 means that there is a coefficients matrix that you should fill minding the Eg1 12 1 2451 1 sequence of unknown variables Select Coefficients button and press navigation centre key In a new dia log set the number of equations in the system to be solved in Amount field Eq3 Then fill in the matrix displayed with all the system coefficients select the Egal i necessary element and press navigation centre key Mind that the k column is for the k unknown value only and the n row for the coefficients in the n equation The last column represents the constant right part of equa tions See the example below for details The answer is a vector where the sequence of unknown variables is the same as it was in the coefficients matrix The answer appears in a new dialog Eq2 Eqs
16. in tool that makes using Solution quick smart nice and easy This menu is available nearly in every instrument dialog to call it just press navigation centre key The main idea is simple Func tions Menu indicates what you are able to do in the particular situation e g which function you can use and which one you can not For mobile phones it s a well known problem to enter formulas fast The main purpose of this utility is of course to make entering formulas as fast as possible using only navigation keys and numbers The principle To enter any data press navigation centre key first is something like Solution interface general rule Functions Menu also provides the very important opportunity creation of user defined functions and quick access to previously saved ones If ex pressions are big and frequently used in calculations it takes a lot of time to print them each time you need to So this is time for creating a custom function or save a constant To enter standard function or constant value select the necessary one using navigation keys and press the navigation centre key Any standard item that can t be used in the particular case is marked grey User defined items You can define your own constant function using Constants and Custom Functions menus respectively To call Constants menu press To call Custom Functions menu press Use these utilities to store any con stants and functions that are frequ
17. is precisely what we wanted So press navigation centre key two more times and get the first result exp x function s plot appears on the screen Press to zoom in and press to zoom out Use navigation keys to move Press back to return to Plot dialog Let s change the horizontal bounds Xmin and Xmax that specify the original position of function s graph to 10 and 2 respectively Select Xmin box us ing navigation keys press down three times To enter minus press naviga tion centre key select minus sign and press navigation centre key again Use number keys to enter 10 Then press navigation right key and change the value of Xmax from default 5 to 2 Press navigation centre key two times to view exp x function s plot again but now on the different interval To view help topic select the icon in the upper right corner and press navigation centre key Now you are ready to start using Solution To learn all the details concerning Solution instruments read the following chapters SA SOLUTION 2 0 User s Interface p Plot f 0 o 010 001 Matrix Doooo isi 5 Calculate i y 0 Solve Version 2 0 F X Analysis 0S More Main Menu In the Main Menu you see six icons that represent six main parts of Solution program The first item is Plot using this utility you can plot any functions quickly and easily You can view several graphs on the same
18. ng A 1 computing the inverse matrix IA computing the determinant of the given matrix How to use To fill A and B matrices set the cursor over A or B icon respectively Press navigation centre key In appeared dialog you can change the size and ele ments of matrix you ve chosen To enter element set the cursor over its position and press navigation centre key Change the value and press navigation centre key once more or use OK When you finish entering data press Save button To call the matrix op eration set the cursor over the operation s icon and press navigation centre key The answer will appear in a new dialog Examples A Width 3 Height 3 B Width 2 Height 3 1 2 3 1 2 1 1 2 3 1 1 2 2 4 5 6 2 3 4 3 7 8 9 3 5 6 AxB IAI Width 2 Height 3 Determinant 0 1 2 1 22 28 2 49 64 3 76 100 18 SA SOLUTION 2 0 Solvers Non linear Equation solver Use this utility to find numerical solution to a single equation f x 0 solved for a single unknown x over the straight line from a to b finite numbers The numerical answers are carried out with accuracy up to the five decimal places F x cos x How to use For entering F x formula quicker press navigation centre key and use the appeared Functions Menu This menu provides quick access to standard and user defined functions and constants To learn more about Functions Menu call Options Help there Xmin 0 Answer 1 57079458236694 When you finish entering data pr
19. t the appeared dialog if any In the 4th 8th chapters you can find full description and detailed how to use instructions for all the Solu tion instruments such as Plot Calculate Analysis Matrix and Solve In the 9th chapter More you can find descriptions of some more utilities and settings that can be used in Solution We hope that you would find Solution useful and worthwhile application Good luck SA SOLUTION 2 0 Quick Start How to plot exp x function The interface of Solution is simple and provides a lot of opportunities at the same time The best thing is just to try it on the simple example and get the main ideas So let s plot exp x function In the Main Menu you see six icons that represent six main parts of Solution program 285 i ooog F x e Sooo OOooG je ooon Calculate Analysis 100 x 0 010 oo k 0 i 0 Matrix Solve More Version 2 0 Select Plot icon using navigation keys Press navigation centre key to open Plot dialog More functions Xmax 5 SA SOLUTION 2 0 To enter new formula in F x box press navigation centre key and in the ap peared Functions Menu dialog select exp using navigation keys wy Solution Press navigation centre key and see exp added to F x box Press naviga tion centre key again This time select x symbol and add it to F x box by pressing navigation centre key Now formula in F x box is exp x and that
20. tiate ey F G Diff in point b Foddx Integrate This utility includes several function analysis tools such as Limit Symbolic and Numerical Differentiation and Numerical Integration The detailed de scription of each instrument is provided below How to use For entering F x formula in each of these instruments quicker press naviga tion centre key and use the appeared Functions Menu This menu provides quick access to standard and user defined functions and constants To learn more about Functions Menu read User s Interface chapter above When you finish entering data press navigation centre key two more times to get the answer that will appear in the Answer box below 15 SA SOLUTION 2 0 Limit lim F x XX 1 1fx x sin In x Answer cos In x 1 x Calculates the limiting value of F x function as x variable approaches speci fied limiting point x0 possibly infinity or infinity The limit is the real bidirectional limit except in the case where the bidirec tional limit does not exist In this case the limit is directional taken from the right and left respectively Examples F x x0 Answer F x x0 Answer sin x x F x 1 1 x x 0 x0 inf 1 Answer 2 7182804690 exp x 1 x 1 F x In x x 1 0 x0 0 2 718281828 Answer Right inf Left Error Computes the symbolic derivative of the function F x with respect to vari able x Examples F x Answer F x Answ
21. worksheet or vary functions using parametric dependencies The second item is Calculate you can evaluate any expression using this scientific calculator that supports even complex computations You may create your own functions and remember frequently used constants and then refer to them by name The third item is Analysis it includes several powerful mathematical instru ments concerning function analysis Solution can evaluate limiting values numerically integrate and differentiate functions and even find out symbolic derivatives The next item is Matrix this utility includes widely used matrix opera tions The next item is Solve this instrument will help you to solve non linear equations linear systems or ordinary differential equations quickly using numerical methods with high accuracy in calculations The last item is More there are several utilities and settings that could be used in Solution Help There is a help topic for each instrument of Solution program Help is available in any dialog To view help topic for an instrument plot cal culate etc open the necessary utility and select icon if it s available and press navigation centre key In some menus e g Functions Menu there is no such icon In this case use Options Help to open the related help topic SA SOLUTION 2 0 Functions Menu wy Solution E constants custom How to use Standard items Functions Menu is the ma

Solution 2.0 SOLUTION TLB GROUP User`s Manual

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