E fx-570MS fx-991MS User's Guide 2 (Additional Functions) http://world.casio.com/edu_e/ CA 310030-001V08 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 ............ 6 kInputting Engineering Symbols .............................. 6 Complex Number Calculations .............. 8 kAbsolute Value and Argument Calculation ............. 9 kRectangular Form Polar Form Display .............. 9 kConjugate of a Complex Number ........................ 10 Base-n Calculations .............................. 10 Statistical Calculations ......................... 12 Normal Distribution .................................................. 12 Differential Calculations ....................... 13 Integration Calculations ....................... 14 Matrix Calculations ............................... 15 kCreating a Matrix ................................................. kEditing the Elements of a Matrix .......................... kMatrix Addition, Subtraction, and Multiplication ... kCalculating the Scalar Product of a Matrix ........... kObtaining the Determinant of a Matrix ................. kTransposing a Matrix ........................................... kInverting a Matrix ................................................. kDetermining the Absolute Value of a Matrix ......... 15 16 16 16 17 17 18 18 E-1 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 ............................... 22 Scientific Constants .............................. 23 Power Supply ........................................ 25 Specifications ........................................ 27 See the "fx-95MS/fx-100MS/fx-115MS/fx-570MS/fx-991MS User's Guide" for details about the following items. Removing and Replacing the Calculator's Cover Safety Precautions Handling Precautions Two-line Display Before getting started... (except for "Modes") Basic Calculations Memory Calculations Scientific Function Calculations Equation Calculations Statistical Calculations Technical Information E-2 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. fx-570MS and fx-991MS Modes To perform this type of calculation: Basic arithmetic calculations Complex number calculations Standard deviation Regression calculations Base-n calculations Solution of equations Matrix calculations Vector calculations Perform this key operation: To enter this mode: COMP CMPLX SD REG BASE EQN MAT VCT F1 F2 FF1 FF2 FF3 FFF1 FFF2 FFF3 · Pressing the F key more than three times displays additional setup screens. Setup screens are described where they are actually used to change the calculator setup. · In this manual, the name of the mode you need to enter in order to perform the calculations being described is indicated in the main title of each section. Example: Complex Number Calculations CMPLX Note! · To return the calculation mode and setup to the initial defaults shown below, press A B 2(Mode) =. Calculation Mode: Angle Unit: Exponential Display Format: Complex Number Display Format: Fraction Display Format: Decimal Point Character: E-3 COMP Deg Norm 1, Eng OFF a+b i a b/c Dot · 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. · Be sure to check the current calculation mode (SD, REG, COMP, CMPLX) and angle unit setting (Deg, Rad, Gra) before beginning a calculation. Mathematical Expression Calculations and Editing Functions COMP Use the F key to enter the COMP Mode when you want to perform mathematical expression calculations or edit expressions. COMP ............................................................ F 1 k Replay Copy Replay copy lets you recall multiple expressions from replay so they are connected as a multi-statement on the screen. · Example: Replay memory contents: 1+1 2+2 3+3 4+4 5+5 6+6 Multi-statement: 4 + 4:5 + 5:6 + 6 Use [ and ] to display the expression 4 + 4. Press A [(COPY). · You can also edit expressions on the display and perform other multi-statement operations. For more details E-4 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. k CALC Memory COMP CMPLX · CALC memory lets you temporarily store a mathematical expression that you need to perform a number of times using different values. Once you store an expression, you can recall it, input values for its variables, and calculate a result quickly and easily. · You can store a single mathematical expression, with up to 79 steps. Note that CALC memory can be used in the COMP Mode and CMPLX Mode only. · The variable input screen shows the values currently assigned to the variables. · Example: Calculate the result for Y = X2 + 3X ­ 12 when X = 7 (Result: 58 ), and when X = 8 (Result: 76). (Input the function.) p y p u p x K + 3 p x , 12 C (Input 7 for X? prompt.) 7= (Input 8 for X? prompt.) C8= (Store the expression.) · Note that the expression you store is cleared whenever you start another operation, change to another mode, or turn off the calculator. k SOLVE Function The SOLVE function lets you solve an expression using variable values you want, without the need to transform or simply the expression. · Example: C is the time it would take for an object thrown straight up with initial velocity A to reach height B. Use the formula below to calculate initial velocity A for a height of B = 14 meters and a time of C = 2 seconds. Gravitational acceleration is D = 9.8 m/s2. (Result: A = 16.8) E-5 B AC ­ 1 DC 2 2 (B?) (A?) (C?) (D?) (A?) 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. · Due to certain idiosyncrasies of Newton's method, solutions for the following types of functions tend to be difficult to calculate. Periodic functions (i.e. y = sin x) Functions whose graph produce sharp slopes (i.e. y = ex, y = 1/x) Discontinuous functions (i.e. y = x ) · If an expression does not include an equals sign (=), the SOLVE function produces a solution for expression = 0. Scientific Function Calculations COMP Use the F key to enter the COMP Mode when you want to perform scientific function calculations. COMP ............................................................ F 1 k Inputting Engineering Symbols COMP EQN CMPLX · Turning on engineering symbols makes it possible for you to use engineering symbols inside your calculations. E-6 · 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. To input this symbol: Perform this key operation: Ak k (kilo) M (Mega) AM G (Giga) Ag T (Tera) At m (milli) Am µ (micro) AN n (nano) An p (pico) Ap f (femto) Af Unit 103 106 109 1012 10­3 10­6 10­9 10­12 10­15 · For displayed values, the calculator selects the engineering symbol that makes the numeric part of the value fall within the range of 1 to 1000. · Engineering symbols cannot be used when inputting fractions. · Example: 9 Ö10 = 0.9 m (milli) Eng F ..... 1(Disp) 1 9 \ 10 = 9 1 0. m 900. When engineering symbols are turned on, even standard (non-engineering) calculation results are displayed using engineering symbols. E-7 AP J 9 1 0.9 m 900. Complex Number Calculations 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. Variables D, E, F, X, and Y are used by the calculator, which frequently changes their values. You should not use these variables in your expressions. · The indicator "RI" in the upper right corner of a calculation result display indicates a complex number result. Press A r to toggle the display between the real part and imaginary part of the result. · You can use the replay function in the CMPLX Mode. Since complex numbers are stored in replay memory in the CMPLX Mode, however, more memory than normal is used up. · Example: (2 3i) (4 5i) (Real part 6) (Imaginary part 8 i) 6 8i 2+3i+4+5i= Ar E-8 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) 53.13010235°) AAR3+4iT= AaR3+4iT= · The complex number can also be input using the polar form r . · Example 2: 2 45 1 i (Angle unit: Deg) L 2 A Q 45 = Ar k Rectangular Form Polar Form Display You can use the operation described below to convert a rectangular form complex number to its polar form, and a polar form complex number to its rectangular form. Press A r to toggle the display between the absolute value (r) and argument ( ). · Example: 1 (Angle unit: Deg) i 1.414213562 45 1+iAY=Ar L 2 A Q 45 A Z = A r E-9 · 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 ­ 2.34i ) A S R 1 l 23 + 2 l 34 i T = Ar Base-n Calculations BASE Use the F key to enter the BASE Mode when you want to perform calculations using Base-n values. BASE ........................................................ F F 3 · In addition to decimal values, calculations can be performed using binary, octal and hexadecimal values. · You can specify the default number system to be applied to all input and displayed values, and the number system for individual values as you input them. · You cannot use scientific functions in binary, octal, decimal, and hexadecimal calculations. You cannot input values that include decimal part and an exponent. · If you input a value that includes a decimal part, the unit automatically cuts off the decimal part. · Negative binary, octal, and hexadecimal values are produced by taking the two's complement. E-10 · 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 ...