Taylor Calculator Real 36

Mathematical Software. Mathematical Research. Mathematical Education. Tvalx Products.

 

Taylor Calculator Real 36 for Windows 98, Windows 2000, Windows Server (2000, 2003, 2008, 2012), Windows XP, Windows Vista, Windows 7, and Windows 8.

 

Quick Start

Type into Function textbox a mathematical function using keyboard or clicking buttons. Them click button 'calculate' or press key Enter. For example, type tan(x) and press Enter. The result

tan(α)+(tan(α)^2+1)/1!*(x-α)^1+(2*tan(α)^3+2*tan(α))/2!*(x-α)^2+(6*tan(α)^4+8*tan(α)^2+2)/3!*(x-α)^3+(24*tan(α)^5+40*tan(α)^3+16*tan(α))/4!*(x-α)^4+(120*tan(α)^6+240*tan(α)^4+136*tan(α)^2+16)/5!*(x-α)^5+(720*tan(α)^7+1680*tan(α)^5+1232*tan(α)^3+272*tan(α))/6!*(x-α)^6+(5040*tan(α)^8+13440*tan(α)^6+12096*tan(α)^4+3968*tan(α)^2+272)/7!*(x-α)^7+(40320*tan(α)^9+120960*tan(α)^7+129024*tan(α)^5+56320*tan(α)^3+7936*tan(α))/8!*(x-α)^8+(362880*tan(α)^10+1209600*tan(α)^8+1491840*tan(α)^6+814080*tan(α)^4+176896*tan(α)^2+7936)/9!*(x-α)^9+(3628800*tan(α)^11+13305600*tan(α)^9+18627840*tan(α)^7+12207360*tan(α)^5+3610112*tan(α)^3+353792*tan(α))/10!*(x-α)^10

 will appear in Taylor polynomial about α in symbolic form textbox. Although it is common to use letter "a" for "point about", we use letter alpha to facilitate syntax analysis .

Using keyboard type 0 into α textbox and click Calculate button. The result

+1*x^1+3.33333333333333333333333333333333333E-1*x^3+1.33333333333333333333333333333333333E-1*x^5+5.39682539682539682539682539682539683E-2*x^7+2.18694885361552028218694885361552028E-2*x^9

 will appear in the Taylor polynomial with numeric coefficients textbox. Also a Taylor polynomial with factorials +1/1!*x^1+2/3!*x^3+16/5!*x^5+272/7!*x^7+7936/9!*x^9 will be appended to History textbox. All calculations are reflected in History textbox.

Now type 0.5 for x in Numeric Value pane. Click button 'calculate' in Numeric Value pane. You will get function value 5.46302489843790513255179465780285385E-1 and Taylor polynomial value 5.46297674162257495590828924162257496E-1.

This calculator calculates Taylor polynomials of high orders in symbolic and numeric forms. Numerical coefficients and values are calculated with precision 36-45 digits. Obtained symbolic formula can be used with Graphing Calculator 2D Polar, Graphing Calculator 2D Parametric,  and Graphing Calculator 2D Numeric for drawing graphs. There is also possibility to use symbolic parameters ( for example, tan(a*x)+cos(b*x)), but then numeric values and graphs cannot be calculated, of course.

Lets continue. You can type into Edit Formula window a mathematical expression of any length and complexity. For example, type (1+scn(2+cos(3))+tan(4))/(ln(5)-tan(6)+atan(7)). Typing of such expression takes time. If you want to repeat such formula (after other calculations), go to Tab History. In the History rich-text-box find the formula and select it (pressing left button on mouse and dragging mouse). Right-Click and choose Copy from right-click menu. Return to Tab Formula. Right-click into Edit windows and from context-menu choose Paste. All text-boxes in the calculator have similar right-click menus.

 

 

Formula editing

The easiest way to edit formula is left-clicking buttons. It allows to keep brackets balanced, functions names correct and so on. Clicking the button "calculate" triggers calculation of entered formula. The result of calculation appears in the window (text-box) named Result.

The second way is to use keyboard (and keypad). All controls usual for editing are available. Pressing the key Enter triggers calculation. Before using keyboard don't forget to click inside text-box to get focus (blinking cursor).

After calculation the entered formula is not deleted from the Edit window allowing to modify formula. If you want to delete formula select it by mouse and delete. For selecting text you can use right-click menu "Select All" or left-click mouse dragging along the text. For deleting selected text use right-click menu "Cut" or "Delete".

Using right-click menu you can copy and paste text between Edit window and all other text-box windows.

For copying text from saved History file open saved History file (usually in WordPad, Notepad, or MS Word ), drag mouse along the text for selection and then choose Copy from right-click menu. Then go to Formula tab, right-click onto Edit window, select command Paste.

Apply the same procedure for copying text from History window or saved History file into variables windows in Variables tab.

Functions and operations have to be entered exactly as they appears by pressing buttons. Alternative names are not supported.

Numbers can be entered in wide variety of formats. But for exponent always use E, since "e" is reserved for "number e". Long numbers will be rounded for 36 digits. For example, 1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890 will become 1.234567890123467890123456890123457E+99.

 

Iterations

Calculation of high order derivatives can be long. For aborting calculation click Stop button. Calculation will stop at current iteration. Result of current iteration will be shown.

 

Precision

Numerical coefficients and values are calculated with precision 36-45 digits (45 digits for integer coefficients).

 

Variables

There is option to choose x0, x1, x2, x3, x4, x5, x6, x7, x8, x9, x, τ, or θ as variable. It is useful if you plan to plug derivative formula into calculators Precision series, Graphing Calculator 2D Numeric, Graphing Calculator 2D Parametric, or Graphing Calculator 2D Polar. You can use these variables in any combination, mixing them in one formula, but derivative is calculated only in respect to one variable. For example, D(sin(x)*cos(τ)) = cos(τ) * cos(x) by x and D(sin(x)*cos(τ)) = -sin(x)*sin(τ) by τ.

 

 

 

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