E fx-570MS fx-991MS User’s Guide 2 (Additional Functions) http://world.casio.
Important! Please keep your manual and all information handy for future reference. CASIO ELECTRONICS CO., LTD. Unit 6, 1000 North Circular Road, London NW2 7JD, U.K.
Contents Before getting started... .......................... 3 kModes .................................................................... 3 Mathematical Expression Calculations and Editing Functions ............................ 4 kReplay Copy .......................................................... 4 kCALC Memory ....................................................... 5 kSOLVE Function .................................................... 5 Scientific Function Calculations ............
Vector Calculations ............................... 18 kCreating a Vector ................................................. kEditing Vector Elements ....................................... kAdding and Subtracting Vectors .......................... kCalculating the Scalar Product of a Vector .......... kCalculating the Inner Product of Two Vectors ...... kCalculating the Outer Product of Two Vectors ..... kDetermining the Absolute Value of a Vector ........ 19 19 19 20 20 21 21 Metric Conversions .........
Before getting started... k Modes Before starting a calculation, you must first enter the correct mode as indicated in the table below. • The following table shows the modes and required operations for the fx-570MS and fx-991MS.
• Mode indicators appear in the upper part of the display, except for the BASE indicators, which appear in the exponent part of the display. • Engineering symbols are automatically turned off while the calculator is the BASE Mode. • You cannot make changes to the angle unit or other display format (Disp) settings while the calculator is in the BASE Mode. • The COMP, CMPLX, SD, and REG modes can be used in combination with the angle unit settings.
about using multi-statements, see “Multi-statements” in the separate “User’s Guide.” • Only the expressions in replay memory starting from the currently displayed expression and continuing to the last expression are copied. Anything before the displayed expression is not copied. COMP k CALC Memory CMPLX • CALC memory lets you temporarily store a mathematical expression that you need to perform a number of times using different values.
B AC – (B?) (A?) (C?) (D?) (A?) 1 DC 2 2 p2pup1-pk, R1\2T-ph-pkK AI 14 = ] 2= 9l8= [[ AI • Since the SOLVE function uses Newton’s Method, certain initial values (assumed values) can make it impossible to obtain solutions. In this case, try inputting another value that you assume to be near the solution and perform the calculation again. • The SOLVE function may be unable to obtain a solution, even though a solution exists.
• To turn engineering symbols on and off, press the F key a number of times until you reach the setup screen shown below. Disp 1 • Press 1. On the engineering symbol setting screen that appears, press the number key ( 1 or 2) that corresponds to the setting you want to use. 1(Eng ON): Engineering symbols on (indicated by “Eng” on the display) 2(Eng OFF): Engineering symbols off (no “Eng” indicator) • The following are the nine symbols that can be used when engineering symbols are turned on.
AP J Complex Number Calculations 0.9 9 ⫼1 m 900. CMPLX Use the F key to enter the CMPLX Mode when you want to perform calculations that include complex numbers. CMPLX ........................................................... F 2 • The current angle unit setting (Deg, Rad, Gra) affects CMPLX Mode calculations. You can store an expression in CALC memory while in the CMPLX Mode. • Note that you can use variables A, B, C, and M only in the CMPLX Mode.
k Absolute Value and Argument Calculation Supposing the imaginary number expressed by the rectangular form z = a + bi is represented as a point in the Gaussian plane, you can determine the absolute value (r) and argument ( ) of the complex number. The polar form is r⬔. • Example 1: To determine the absolute value (r) and argument () of 3+4i (Angle unit: Deg) (r = 5, = 53.13010235°) Imaginary axis Real axis (r 5 ) ( 53.
• You select rectangular form (a+bi) or polar form (r⬔ ) for display of complex number calculation results. F... 1(Disp) r 1(a+bi):Rectangular form 2(r⬔): Polar form (indicated by “r⬔ ” on the display) k Conjugate of a Complex Number For any complex number z where z = a+bi, its conjugate (z) is z = a – bi. • Example: To determine the conjugate of the complex number 1.23 + 2.34i (Result: 1.23 – 2.
• You can use the following logical operators between values in Base-n calculations: and (logical product), or (logical sum), xor (exclusive or), xnor (exclusive nor), Not (bitwise complement), and Neg (negation). • The following are the allowable ranges for each of the available number systems.
• Example 4: To convert the value 2210 to its binary, octal, and hexadecimal equivalents. (101102 , 268 , 1616 ) tb 0. b l l l 1(d) 22 = 10110. b Octal mode: o 26. o Hexadecimal mode: h 16. H Binary mode: • Example 5: To convert the value 51310 to its binary equivalent. tb 0. l l l 1(d) 513 = Ma t h ERROR Binary mode: b b • You may not be able to convert a value from a number system whose calculation range is greater than the calculation range of the resulting number system.
• Input a value from 1 to 4 to select the probability distribution calculation you want to perform. P(t) Q(t) R(t) • Example: To determine the normalized variate (→ t) for x = 53 and normal probability distribution P(t) for the following data: 55, 54, 51, 55, 53, 53, 54, 52 (→t = 0.284747398, P(t) = 0.38974 ) 55 S 54 S 51 S 55 S 53 S S 54 S 52 S 53 A D 4(→t) = A D 1( P( ) D 0.28 F = Differential Calculations COMP The procedure described below obtains the derivative of a function.
• You can omit input of ∆x, if you want. The calculator automatically substitutes an appropriate value for ∆x if you do not input one. • Discontinuous points and extreme changes in the value of x can cause inaccurate results and errors. • Select Rad (Radian) for the angle unit setting when performing trigonometric function differential calculations. Integration Calculations COMP The procedure described below obtains the definite integral of a function.
Matrix Calculations MAT The procedures in this section describe how to create matrices with up to three rows and three columns, and how to add, subtract, multiply, transpose and invert matrices, and how to obtain the scalar product, determinant, and absolute value of a matrix. Use the F key to enter the MAT Mode when you want to perform matrix calculations. MAT .....................................................
k Editing the Elements of a Matrix Press A j 2(Edit) and then specify the name (A, B, or C) of the matrix you want to edit to display a screen for editing the elements of the matrix. k Matrix Addition, Subtraction, and Multiplication Use the procedures described below to add, subtract, and multiply matrices.
(Matrix C 2 2) A j 1 (Dim) 3(C) 2 = 2 = (Element input) 2=D1=D5=3=t 3 - A j 3(Mat) 3(C) = (3 MatC) k Obtaining the Determinant of a Matrix You can use the procedure below to determine the determinant of a square matrix.
k Inverting a Matrix You can use the procedure below to invert a square matrix. • Example: To invert Matrix C = ([ –0.4 1 –0.8 –1.5 0.5 –1.5 –0.8 0 –0.6 ]) [ –3 6 –11 3 –4 6 4 –8 13 ] (Matrix C 3 3) A j 1(Dim) 3(C) 3 = 3 = (Element input) D 3 = 6 = D 11 = 3 = D 4 = 6 = 4 = D 8 = 13 = t A j 3(Mat) 3(C) a = (MatC –1) • The above procedure results in an error if a non-square matrix or a matrix for which there is no inverse (determinant = 0) is specified.
Use the F key to enter the VCT Mode when you want to perform vector calculations. VCT ..................................................... F F F 3 Note that you must create one or more vector before you can perform vector calculations. • You can have up to three vectors, named A, B, and C, in memory at one time. • The results of vector calculations are stored automatically into VctAns memory. You can use the matrix in VctAns memory in subsequent vector calculations.
• Example: To add Vector A = (1 –2 3) to Vector B = (4 5 –6). (Result: (5 3 –3) ) (3-dimensional Vector A) (Element input) (3-dimensional Vector B) (Element input) (VctA + VctB) A z 1(Dim) 1(A) 3 = 1=D2=3=t A z 1(Dim) 2(B) 3 = 4=5=D6=t A z 3(Vct) 1(A) + A z 3(Vct) 2(B) = • An error occurs in the above procedure if you specify vectors of different dimensions. k Calculating the Scalar Product of a Vector Use the procedure shown below to obtain the scalar product (fixed multiple) of a vector.
k Calculating the Outer Product of Two Vectors Use the procedure described below to obtain the outer product for two vectors. • Example: To calculate the outer product of Vector A and Vector B (Result: (–3, 18, 13) ) A z 3(Vct) 1(A) A z 3(Vct) 2(B) = (VctA VctB) • An error occurs in the above procedure if you specify vectors of different dimensions. k Determining the Absolute Value of a Vector Use the procedure shown below to obtain the absolute value (size) of a vector.
(Ans (AbsVctA AbsVctB)) \ R A A A z 3(Vct) 1(A) - A A A z 3(Vct) 2(B) T = (cos–1Ans) (Result: 108.4349488 °) AVg= (VctA VctB) A z 3(Vct) 1(A) A z 3(Vct) 2(B) = (AbsVctAns) A A A z 3(Vct) 4(Ans) = (VctAns Ans) (Result: (– 0.666666666 0.333333333 – 0.666666666) ) A z 3(Vct) 4(Ans) \ g = Metric Conversions COMP Use the F key to enter the COMP Mode when you want to perform metric conversions. COMP ............................................................
u Conversion Pair Table Based on NIST Special Publication 811 (1995).
• Simply input the number that corresponds to the scientific constant you want to look up and it appears instantly on the display. • See the Scientific Constant Table for a complete list of available constants. • Example: To determine how much total energy a person weighing 65kg has (E = mc2 = 5.841908662 × 1018 ) 65 L 28 K = 65 Co 2 5.841908662 18 28 is the “speed of light in vacuum” constant number. u Scientific Constant Table Based on ISO Standard (1992) data and CODATA recommended values (1998).
To select this constant: molar volume of ideal gas (Vm) molar gas constant (R) speed of light in vacuum (C 0) first radiation constant (C 1) second radiation constant (C 2) Stefan-Boltzmann constant (σ) electric constant (ε 0) magnetic constant (µ 0) magnetic flux quantum (φ 0) standard acceleration of gravity (g) conductance quantum (G 0) characteristic impedance of vacuum (Z 0) Celsius temperature (t) Newtonian constant of gravitation (G) standard atmosphere (atm) Input this scientific constant number: 2
u To replace the battery Screw Screw 1 Remove the five screws that hold the back cover in place and then remove the back cover. 2 Remove the old battery. 3 Wipe off the sides of new battery with a dry, soft cloth. Load it into the unit with the positive k side facing up (so you can see it). 4 Replace the back cover and secure it in place with the five screws. 5 Press 5 to turn power on. Be sure not to skip this step. fx-570MS This calculator is powered by single G13 Type (LR44) button battery.
5 Replace the battery cover and secure it in place with the screw. 6 Press 5 to turn power on. Auto Power Off Calculator power automatically turns off if you do not perform any operation for about six minutes. When this happens, press 5 to turn power back on. Specifications Power Supply: fx-570MS: Single G13 Type button battery (LR44) fx-991MS: Solar cell and a single G13 Type button battery (LR44) Battery Life: fx-570MS: Approximately 9,000 hours continuous display of flashing cursor.
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