Casio fx-570ES manuale d’uso

http://world.casio.com/edu/ RCA502107-001V01 E User's Guide fx-570ES[...]

CASIO Europe GmbH Bornbarch 10, 22848 Norderstedt, Germany[...]

E-1 About this Manual • The MA TH mark indicates an example that uses Math f ormat, while the LINE mark indicates Linear format. For details about input/output f or mats, see “Specifying the Input/Output F ormat”. •K e ycap mar kings indicate what a ke y inputs or what function it performs. Example: 1 , 2 , + , - , ! , A , etc. •P ressing[...]

E-2 • The follo wing shows an example of ho w a key oper ation to select an on-screen menu item is represented in this User’ s Guide. Example: 1 (Setup) Indicates the menu item that is selected b y the number ke y operation ( 1 ) bef ore it. Note that this is not part of the actual ke y operation you perf orm. • The cursor key is mark ed with[...]

E-3 Safety Precautions Be sure to read the f ollowing safety precautions bef ore using this calculator . K eep this manual handy for later ref erence. Caution This symbol is used to indicate inf or mation that can result in personal injury or mater ial damage if ignored. Battery •A fter removing the battery from the calculator, put it in a saf e [...]

E-4 Handling Precautions •B e sure to press the O ke y before using the calculator f or the first time. •E ven if the calculator is operating normally , replace the battery at least once every tw o years. A dead battery can leak, causing damage to and malfunction of the calculator . Nev er leav e a dead battery in the calculator. • The batter[...]

E-5 Befor e Using the Calculator k Removing the Har d Case Bef ore using the calculator, slide its hard case do wnwards to remov e it, and then affix the hard case to the bac k of the calculator as shown in the illustration below . k T urning P ower On and Off •P ress O to turn on the calculator. •P ress 1A (OFF) to turn off the calculator. k A[...]

E-6 k About the Display Y our calculator has a 31-dot × 96-dot LCD screen. Example: k Display Indicator s Sample Display: This Means this: indicator: The keypad has been shifted b y pressing the 1 ke y. The ke ypad will unshift and this indicator will disappear when you press a k ey . The alpha input mode has been entered by pressing the S ke y. T[...]

E-7 Important! •F or a very complex calculation or some other type of calculation that takes a long time to e xecute, the displa y ma y show only the abov e indicators (without any value) while it perf orms the calculation internally . Calculation Modes and Calculator Setup k Calculation Modes When you want to perf orm this type of Select this op[...]

E-8 •S ee “Adjusting Displa y Contrast” f or information about how to use “ ] CONT ' ”. Specifying the Input/Output Format For this input/output format: P erf orm this key operation: Math 1N 1 (MthIO) Linear 1N 2 (LineIO) •M ath format causes fractions, irrational n umbers, and other e xpressions to be displa yed as the y are writt[...]

E-9 •N orm: Selecting one of the tw o availab le settings (Nor m1, Norm2) determines the range in which results will be display ed in non- e xponential format. Outside the specified r ange, results are display ed using exponential f ormat. Norm1: 10 –2 >  x  ,  x  > 10 10 Norm2: 10 –9 >  x  ,  x  > 10 10 Ex[...]

E-10 k Initializing the Calculation Mode and Other Settings P erf or ming the follo wing procedure initializes the calculation mode and other setup settings as shown belo w . 1 9 (CLR) 1 (Setup) = (Y es) This setting: Is initialized to this: Calculation Mode COMP Input/Output Format MthIO Angle Unit Deg Display Digits Norm1 Fr action Display F orma[...]

E-11 Example: sin 30 = LINE s 30)= Pressing s inputs “sin(”. •N ote that the input procedure is different if y ou want to use Math fo rm at. For more inf ormation, see “Inputting with Math Format”. Omitting the Multiplication Sign Y ou can omit the multiplication sign ( × ) in any of the f ollowing cases . •B efore an open parentheses [...]

E-12 •N ormally the input cursor appears as a straight ver tical ( I ) or horizontal ( ) flashing line on the displa y screen. When there are 10 or fe wer bytes of input remaining in the current e xpression, the cursor changes shape to I to let you know . If the I cursor appears, terminate the expression at a con venient point and calculate the r[...]

E-13 Deleting a Character or Function Example: To correct the expression 369 × × 12 so it becomes 369 × 12 LINE Inser t Mode: 369**12 dd Y Ov erwrite Mode: 369**12 ddd Y Correcting a Calculation Example: To correct cos(60) so it becomes sin(60) LINE Inser t Mode: c 60) ddd Y s Ov erwrite Mode: c 60) dddd s Inserting Input into a Calculation Alwa[...]

E-14 k Displaying the Location of an Err or If an error message (lik e “Math ERROR” or “Syntax ERR OR”) appears when you press = , press d or e . This will display the part of the calculation where the error occurred, with the cursor positioned at the error location. Y ou can then mak e necessar y corrections. Example: When you input 14 ÷ [...]

E-15 Functions and Symbols Supported for Math Format Input • The “Bytes” column shows the n umber of bytes of memory that are used up by input. Function/Symbol Ke y Operation Bytes Improper F raction ' 9 Mixed F r action 1 ' ( ( )1 3 log(a,b) (Logarithm) & 6 10^ x (P ower of 10) 1l ( $ )4 e^ x (P ower of e ) 1i ( % )4 Square Roo[...]

E-16 Example 3: To input (1 + ) 2 × 2 = MA TH (1+ ' 2 c 5 e ) Math w *2= •W hen you press = and obtain a calculation result using Math fo rm at, par t of the expression y ou input can be cut off as shown in the Example 3 screen shot. If you need to vie w the entire input e xpression again, press A and then press e . Incorporating a V alue i[...]

E-17 Original Expression: Function Ke y Operation Resulting Expression Integral 7 Derivative 1 7 ( F ) Σ Calculation 1 & ( 8 ) Y ou can also incor porate v alues into the following functions. 1l ( $ ), 1i ( % ), ! , 6 , 1 ! ( # ), 1w (Abs) Displaying Calculation Results in a Form that Includes ' ' ' ' ' 2, π , etc. (I[...]

E-18 Example 2: sin (60) = (Angle Unit: Deg) MA TH s 60= Math Example 3: sin –1 (0.5) = π (Angle Unit: Rad) MA TH 1 s (sin –1 ) 0.5= Math • The follo wing are the calculations for which ' fo rm (form that includes ' within irrational number display) results can be display ed. a. Arithmetic calculations of values with square root sy[...]

E-19 The follo wing shows the range f or each of the coefficients ( a , b , c , d , e , f ). 1 < a < 100, 1 < b < 1000, 1 < c < 100 0 < d < 100, 0 < e < 1000, 1 < f < 100 Example: The underlined areas in the abov e examples indicate what caused decimal f or m to be used. Reasons why the results of the e xamples a[...]

E-20 • If a term is encountered during the calculation cannot be displayed as a root ( ' ) form or a fraction, the calculation result is displa yed in decimal f or m. Example: log3 + ' 2 = 1.891334817 Basic Calculations (COMP) This section e xplains how to perform arithmetic, fraction, percent, and sexagesimal calculations . All calcula[...]

E-21 Omitting a Final Closed P arenthesis Y ou can omit any closed parenthesis ( ) ) immediately preceding operation of the = ke y at the end of a calculation. This is true only in the case of Linear format. Example: (2 + 3) × (4 – 1) = 15 LINE (2+3)* (4-1= k Fraction Calculations How y ou should input fractions depends on the input/output forma[...]

E-22 Switching between Fraction and Decimal Format • The f or mat of the fraction depends on the currently selected fraction display f ormat setting (improper fraction or mixed fraction). •Y ou cannot switch from decimal f ormat to mixed fraction f or mat if the total number of digits used in the mix ed fraction (including integer , numerator ,[...]

E-23 Sexa gesimal Calculations •P erforming the following types of se xagesimal calculations produces a se xagesimal result. -A ddition or subtraction of two se xagesimal values -M ultiplication or division of a sexagesimal v alue and a decimal value Appendix <#012> 2 ° 20´30˝ + 39´30˝ = 3 ° 00´00˝ Con verting V alues between Sexage[...]

E-24 Using Calculation History Memory and Replay Calculation history memor y maintains a record of each calculation e xpression y ou input and e xecute, and its result. Modes that suppor t calculation history memor y: COMP ( N 1 ), CMPLX ( N 2 ), BASE-N ( N 4 ) Recalling Calculation History Memory Contents Press f to back-step through calculation h[...]

E-25 Using Calculator Memory Memory Name Description An sw er Memo ry Stores the last calculation result obtained. Calculation results can be added to or sub- Independent tracted from independent memory . The “M” Memory display indicator indicates data in independent memory . Va r iables Six variab les named A, B, C, D , X, and Y can be used fo[...]

E-26 Inputting Answer Memory Contents into an Expression Example: To perform the calculations shown below: LINE 123+456= 789- G = k Independent Memory (M) Y ou can add calculation results to or subtract results from independent memory . The “M” appears on the display when independent memory contains a value. Independent Memory Overview • The [...]

E-27 Calculation Examples Using Independent Memory • If the “M” indicator is on the displa y , perform the procedure under “Clearing Independent Memor y” before perf orming this example. Example: 23 + 9 = 32 23+9 m 53 – 6 = 47 53-6 m –) 45 × 2 = 90 45*2 1m (M–) 99 ÷ 3 = 33 99/3 m (T otal) 22 tm (M) Clearing Independent Memory Pres[...]

E-28 Using CALC The CALC feature lets y ou input a calculation e xpression that contains v ar iab les, and then assign values to the v ariables and perf or m the calculation. Y ou can use CALC in the COMP Mode ( N 1 ) and in the CMPLX Mode ( N 2 ). k Expressions Suppor ted b y CALC The f ollowing describes the types of expressions that can be used [...]

E-29 s (or = ) 10= •T o exit CALC , press A . • If the expression y ou are using contains more than one variable , an input prompt appears for each one . Appendix <#016> Cal culate a n +1 = a n + 2 n (a 1 = 1) as the value of a n changes from a 2 to a 5 . (Results: a 2 = 3, a 3 = 7, a 4 = 13, a 5 = 21) *1 Assigns 1 to a 1 .* 2A ssigns 1 t[...]

E-30 •A n error (V ariable ERR OR) occurs when the solution variable is not included in the expression being solv ed. k Example SOL VE Operation Example: To solve y = ax 2 + b for x when y = 0, a = 1, and b = –2. MA TH S f (Y) Ss (=) S y (A) S ) (X) w + S e (B) Math 1 ) (,) S ) (X) 1s (SOL VE) Math Prompts for input of a v alue f or Y . Current[...]

E-31 • SOL VE may not be ab le to deter mine the correct solution, e ven when one exists . • SOL VE uses Newton’ s Method, so e ven if there are multiple solutions, only one of them will be returned. •N ew ton’s Method can ha ve prob lems obtaining solutions for the f ollowing types of functions. -A per iodic function ( y = sin( x ), etc.[...]

E-32 Function Calculations This section explains ho w to use the calculator’ s built-in functions. The functions av ailable to you depends on the calculation mode y ou are in. The e xplanations in this section are mainly about the functions that are av ailable in all calculation modes. All of the e xamples in this section sho w operation in the C[...]

E-33 k Con verting an Input V alue to the Calculator’ s Default Angle Unit After inputting a value , press 1G (DRG ' ) to displa y the angle unit specification menu shown belo w . Press the number ke y that corresponds to the angle unit of the input value . The calculator will automatically conv er t it to the calculator’ s default angle u[...]

E-34 k Po wer Functions and P ower Root Functions •P ower functions and power root functions can be used in the COMP , ST A T , EQN, MA TRIX, T ABLE, and VECTOR calculation modes . •T he X 2 , X 3 , X –1 functions can be used in complex number calculations in the CMPLX Mode, and comple x number arguments are suppor ted. • The X ^ , ' ([...]

E-35 Tips on Impr oving Integration V alue Accuracy •W hen a periodic function or integration interval results in positive and negative f ( x ) function values P erf or m separate integrations f or each cycle, or f or the positive part and the negative par t, and then combine the results. P ositive P art Negative P art ( S P ositive) ( S Negative[...]

E-36 k Differential Calculations Y our calculator performs differential calculations b y approximating the derivativ e based on centered difference appro ximation. d / dx ( f ( x ), a , tol ) f ( x ): Function of X (All non-X v ariables are treated as constants.) a : Input a value to specify the point f or which the derivativ e should be obtained ([...]

E-37 k Σ Calculations With Σ (, you can obtain the sum of an input f ( x ) e xpression for a specific range . Σ calculations are perf ormed using the follo wing for m ula. Σ ( f ( x ), a , b ) = f ( a ) + f ( a + 1) + .... + f ( b ) f ( x ): Function of X (All non-X v ariables are treated as constants.) a :C alculation range start point b :C al[...]

E-38 • If you perf or m coordinate con version inside of an e xpression instead of a stand-alone operation, the calculation is performed using only the first value (either the r -v alue or the X-value) produced b y the conv ersion. Example: P ol ( ' 2, ' 2) + 5 = 2 + 5 = 7 Appendix <#036> to <#037> k Other Functions This sec[...]

E-39 Rounding Function (Rnd) This function rounds the value or the result of the e xpression in the function’ s argument to the number of significant digits specified by the number of displa y digits setting. Display Digits Setting: Norm1 or Nor m2 The mantissa is rounded to 10 digits. Display Digits Setting: F ix or Sci The value is rounded to t[...]

E-40 k Practical Examples Appendix <#042> ∫ (sin X + cos X ) 2 dX = π 0 π ( tol : Not specified) <#043> Confirm that the two sides of the f ollowing equation are equal: e = Σ n ! 1 n = 0 ∞ Tr a n sfor ming Displayed Va l ues Y ou can use the procedures in this section to transform a displa yed va lue to engineer ing notation, or [...]

E-41 π : The f ollowing are the π fo rm s that are suppor ted. This is true only in the case of Math format. n π ( n is an integer .) c d π or c b π a (depending on fraction display format setting) •T r ansf ormation to a fractional π fo r m is limited to inverse trigonometric function results and values that are normally e xpressed in r ad[...]

E-42 k Inputting Complex Number s • In the CMPLX Mode, the W ke y changes function to become an imaginary number i input key . In this section, the W ke y is ref erred to as the i ke y. Use the i ke y when inputting a complex number of the format a + b i . The key oper ation below shows how to input 2 + 3 i , f or example. 2+3 i Math CMPLX •Y o[...]

E-43 Examples of Calculation Results Using P olar Coordinate Format ( r ∠ θ ) Example 1: 2 × ( ' 3 + i ) = 2 ' 3 + 2 i = 4 ∠ 30 (Angle Unit: Deg) MA TH 2*( ! 3 e + i )= Math CMPLX •W ith Linear format, the absolute value and argument are sho wn in two diff erent lines. Example 2: 1 + i = ' 2 ∠ 45 (Angle Unit: Deg) MA TH 1+ [...]

E-44 Statistical Calculation (ST A T) All calculations in this section are perf or med in the ST A T Mode ( N 3 ). Selecting a Statistical Calculation T ype In the ST A T Mode, display the statistical calculation type selection screen. k Statistical Calculation T ypes Key Menu Item Statistical Calculation 1 1-V AR Single-v ariable 2 A+BX Linear reg[...]

E-45 Y ou can use the FREQ column to specify the frequency (the number of times the same sample appears in the group of data) of each sample v alue. Rules for Inputting Sample Data on the ST A T Editor Screen •D ata you input is inserted into the cell where the cursor is located. Use the cursor keys to mo ve the cursor between cells . • The val[...]

E-46 Precautions Concerning Sample Data Stora ge Sample data you input is deleted automatically whene v er you change to another mode from the ST A T Mode or change the Statistical Displa y setting (which causes the FREQ column to be shown or hidden) on the calculator’ s setup screen. Editing Sample Data Replacing the Data in a Cell (1) On the ST[...]

E-47 k Using the ST A T Men u While the ST A T editor screen or ST A T calculation screen is on the display , press 1 1 (ST A T) to display the ST A T menu. The content to the ST A T menu depends on whether the currently selected statistical operation type uses a single v ariable or paired var i a bl e s . Single-variable Statistics Paired-v ariabl[...]

E-48 Single-v ariable (1-V AR) Statistical Calculation Commands The follo wing are the commands that appear on the sub-menus that appear when you select 4 (Sum), 5 (V ar), 6 (MinMax), or 7 (Distr) on the ST A T menu while a single-variable statistical calculation type is selected. See Appendix <#052> f or information about the calculation fo [...]

E-49 Standard Normal Distrib ution Appendix Single-variable Statistical Calculation <#053> Select single-variable (1-V AR) and input the f ollowing data: {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} (FREQ: ON) <#054> Edit the data to the f ollowing, using inser t and delete: {0, 1, 2, 3, 4, 5, 6, 7, 9, 10} (FREQ: ON) <#055> Edit the FREQ data [...]

E-50 Sum Sub-menu ( 1 1 (ST A T) 4 (Sum)) Select this When you want to obtain this: menu item: 1 Σ x 2 Sum of squares of the X-data 2 Σ x Sum of the X-data 3 Σ y 2 Sum of squares of the Y -data 4 Σ y Sum of the Y -data 5 Σ xy Sum of products of the X-data and Y -data 6 Σ x 3 Sum of cubes of the X-data 7 Σ x 2 y Sum of (X-data squares × Y -d[...]

E-51 Appendix Linear Regression Calculation: <#061> to <#064> •E xamples <#062> through <#064> all use the data input in Example <#061>. *1 Estimated V alue ( y = –3 → m = ? ) *2 Estimated V alue ( x = 2 → n = ? ) Commands when Quadratic Regression Calculation (_+CX 2 ) Is Selected With quadratic regression, re[...]

E-52 Statistical Calculation Model Equation Calculation T ype Formula ab Exponential Regression y = AB X <#071> (A•B^X) Po wer Regression (A•X^B) y = AX B <#072> Inverse Reg ression (1/X) y = A + X B <#073> Appendix Comparison of Regression Curves • The follo wing example uses the data input in Example <#061>. <#074[...]

E-53 • The initial def ault number base setting when you enter the BASE- N Mode is alwa ys decimal (DEC). Inputting V alues In the BASE-N Mode, y ou can input values using the currently selected number base . •A Syntax ERROR occurs if you input values that are not allo wed f or the currently selected number base (such as inputting 2 while binar[...]

E-54 The k ey operation below shows ho w to input a value of 3 using the decimal number base, f or example . Ab1 3 (BASE) c 1 (d) 3 The value y ou input here is decimal number base. Appendix <#080> Calculate 1 2 + 1 2 in binary . <#081> Calculate 7 8 + 1 8 in octal. <#082> Calculate 1F 16 + 1 16 in he xadecimal. <#083> Co nv[...]

E-55 Equation Calculations (EQN) All calculations in this section are perf or med in the EQN Mode ( N 5 ). k Equation T ypes An equation type menu appears when you press N 5 (EQN) and enter the EQN Mode. Key Men u Item Equation T ype Simultaneous Linear 1 a n X + b n Y = c n Equations with T wo Unknowns Simultaneous Linear 2 a n X + b n Y + c n Z =[...]

E-56 • The values and e xpressions you can input on the coefficient editor screen are the same as those you can input in the COMP Mode with Linear format. •P ressing A while inputting data clears y our current input. • After inputting data, press = . This registers the value and displa ys up to six of its digits in the currently selected cell[...]

E-57 Matrix Calculations (MA TRIX) Y ou can sav e matrices under the names “MatA”, “MatB”, and “MatC” in matrix memor y . Matrix calculation results are stored in a special Matrix Answer Memory named “MatAns”. All calculations in this section are perf or med in the MA TRIX Mode ( N 6 ). k Creating and Managing a Matrix Creating a Ma[...]

E-58 Copying the Contents of One Matrix to Another Matrix (1) Use the matr ix editor screen to display the matrix you w ant to copy , or display the Matrix Ans wer Memory screen. • If you w ant to copy Matrix A, f or example, press 1 4 (MA TRIX) 2 (Data) 1 (MatA). (2) Press 1t (ST O). • This causes the “STO” indicator to appear on the displ[...]

E-59 k Matrix Menu Items The follo wing are the menu items on the matrix menu that appears when you press 1 4 (MA TRIX). Select this When you want to do this: menu item: 1 Dim Select a matrix (MatA, MatB, MatC) and specify its dimension 2 Data Select a matrix (MatA, MatB, MatC) and display its data on the matrix editor screen 3 MatA Input “MatA?[...]

E-60 Generating a Number T able from a Function (T ABLE) All calculations in this section are perf ormed in the T ABLE Mode ( N 7 ). k Configuring a Number T ab le Generation Function The procedure below configures the number tab le generation function with the f ollowing settings. Function: f ( x ) = x 2 + Star t V alue: 1, End V alue: 5, Step V a[...]

E-61 (5) After specifying the end value, press = . • This displa ys the step value input screen. •S pecify the step value. •F or details about specifying the star t, end, and step values, see “Star t, End, and Step V alue Rules”. (6) After specifying the step value, press = . •P ressing the A ke y retur ns to the function editor screen.[...]

E-62 k Number T able Screen The number tab le screen shows x -values calculated using the specified Start, End, and Step values, as well as the v alues obtained when each x -value is substituted in the function f ( x ). •N ote that you can use the number tab le screen for vie wing values only . T able contents cannot be edited. •P ressing the A[...]

E-63 (4) Use the vector editor screen to input each element. •I nput is subject to the same r ules as those that gov ern the coefficient editor screen in the EQN Mode. F or more information, see “Rules for Inputting and Editing Coefficients”. • If you want to create another v ector , repeat this procedure from step (1). Copying the Contents[...]

E-64 Appendix <#106> Store VctA = (1, 2) and VctC = (2, –1, 2). <#107> Copy VctA = (1, 2) to VctB and then edit V ector B to VctB = (3, 4). • The follo wing examples use the v ectors input in Examples <#106> and <#107> (VctA, VctB, VctC). <#108> VctA + VctB (V ector Addition) <#109> 3 × VctA (V ector Scalar [...]

E-65 •T he values are based on ISO Standards (1992) and CODA T A Recommended V alues (1998). For details, see Appendix <#114>. Appendix <#115> and <#116> P erf or m all of these examples in the COMP Mode ( N 1 ). Metric Conversion The calculator’ s built-in metric conv ersion commands make it simple to conv er t values from on[...]

E-66 3. F ractions: a b / c 4. Prefix symbol: (–) (negative sign) d, h, b , o (base n symbol) 5. Metric conversion commands: cm ' in, etc. Statistical estimated value calculation: m , n , m 1 , m 2 6. P ermutations, combinations: n P r , n C r Complex polar f orm symbol: ∠ 7. Dot product: • (Dot) 8. Multiplication and division: × , ÷ M[...]

E-67 A Stack ERR OR occurs when the calculation you are perf orming causes the capacity of either stac k to be exceeded. Stack Issues to K eep in Mind for Each Mode •I n the CMPLX Mode, each input value uses two le vels of the numeric stack, regardless of whether the input v alue is a real number or a complex number . This means that the numeric [...]

E-68 Functions Input Range tanh x 0   x   9.999999999  10 99 tanh – 1 x 0   x   9.999999999  10 –1 log x /ln x 0  x  9.999999999  10 99 10 x –9.999999999  10 99  x  99.99999999 e x –9.999999999  10 99  x  230.2585092 ' x 0  x  1  10 100 x 2  x  1  10 50 1/ x [...]

E-69 k Error Messa g es The calculator will displa y an error message when a result exceeds the calculation r ange, when y ou attempt an illegal input, or whenev er any other similar problem occurs. When an error messa ge appears... The follo wing are general operations you can use when an y error message appears. •P r e ssing d or e displays to [...]

E-70 • Action •M a k e necessar y corrections. Dimension ERR OR (MA TRIX and VECT OR Modes only) • Cause • The matrix or vector you are trying to use in a calculation was input without specifying its dimension. •Y ou are trying to perform a calculation with matrices or vectors whose dimensions do not allow that type of calculation. • Ac[...]

E-71 (1) Check the calculation expression to mak e sure that it does not contain an y errors. (2) Make sure that you are using the correct mode f or the type of calculation you are trying to perform. (3) If the above steps do not correct y our problem, press the O key . This will cause the calculator to perf orm a routine that checks whether calcul[...]

E-72 Au t o Po wer Off Y our calculator will tur n off automatically if you do not perf orm any operation f or about six minutes. If this happens , press the O key to turn the calculator back on. Specifications Po wer Requirements: AAA-size battery: R03 (UM-4) × 1 Battery Life: Approximately 17,000 hours (continuous displa y of flashing cursor) Po[...]

CASIO COMPUTER CO. , L TD . 6-2, Hon-machi 1-chome Shibuya-ku, Tokyo 151-8543, Japan SA0411-A Printed in China[...]