HP HP 33s - Manuals

Contents 3 3. Storing Data into Variables Storing and Recalling Numbers ........................................... 3–2 Viewing a Variable without Recalling It ................................. 3–3 Reviewing Variables in the VAR Catalog ............................... 3–3 Clearing Variables ...........

4 Contents Factorial .................................................................. 4–14 Gamma................................................................... 4–14 Probability ............................................................... 4–14 Parts of Numbers ..................................

Contents 5 Editing and Clearing Equations ........................................... 6–7 Types of Equations............................................................. 6–9 Evaluating Equations.......................................................... 6–9 Using ENTER for Evaluation ...................

6 Contents Using Complex Numbers in Polar Notation........................... 9–5 10. Base Conversions and Arithmetic Arithmetic in Bases 2, 8, and 16....................................... 10–2 The Representation of Numbers......................................... 10–4 Negative Numbers................

8 Contents Selecting a Base Mode in a Program ......................... 12–22 Numbers Entered in Program Lines ............................ 12–23 Polynomial Expressions and Horner's Method ................... 12–23 13. Programming Techniques Routines in Programs ........................................

Contents 9 15. Mathematics Programs Vector Operations ........................................................... 15–1 Solutions of Simultaneous Equations ................................. 15–12 Polynomial Root Finder ................................................... 15–20 Coordinate Transformatio...

10 Contents Resetting the Calculator ..................................................... B–2 Clearing Memory ............................................................. B–3 The Status of Stack Lift ....................................................... B–4 Disabling Operations ....................

Contents 11 Underflow ......................................................................D–14 E. More about Integration How the Integral Is Evaluated .............................................. E–1 Conditions That Could Cause Incorrect Results ....................... E–2 Conditions That Prolon...

Getting Started 1–1 1 Getting Started v Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in RPN mode and must be performed differently in ALG mode. Appendix C explains how to use your calculator in ALG mode. Important Preliminaries Turning the Calculator On an...

1–2 Getting Started Highlights of the Keyboard and Display Shifted Keys Each key has three functions: one printed on its face, a left–shifted function (Green), and a right–shifted function (Purple). The shifted function names are printed in green and purple above each key. Press the appropriate shif...

Getting Started 1–3 Pressing { or | turns on the corresponding ¡ or ¢ annunciator symbol at the top of the display. The annunciator remains on until you press the next key. To cancel a shift key (and turn off its annunciator), press the same shift key again. Alpha Keys Rig h t - s hi f t e dfu nct i...

1–4 Getting Started Silver Paint Keys Those eight silver paint keys have their specific pressure points marked in blue position in the illustration below. To use those keys, make sure to press down the corresponding position for the desired function. Backspacing and Clearing One of the first things ...

Getting Started 1–7 Using Menus There is a lot more power to the HP 33s than what you see on the keyboard. This is because 14 of the keys are menu keys. There are 14 menus in all, which provide many more functions, or more options for more functions. HP 33s Menus Menu N a m e Menu Description Chapte...

Getting Started 1–9 Example: 6 ÷ 7 = 0.8571428571… Keys: Display: 6 ‘ 7 q  % ({ }) ( or š — ‘ ) ) . Menus help you execute dozens of functions by guiding you to them with menu choices. You don't have to remember the names of the functions built into the calculator nor search through the names printe...

1–10 Getting Started RPN and ALG Keys The calculator can be set to perform arithmetic operations in either RPN (Reverse Polish Notation) or ALG (Algebraic) mode. In Reverse Polish Notation (RPN) mode, the intermediate results of calculations are stored automatically; hence, you do not have to use pa...

Getting Started 1–11 The Display and Annunciators Fi r s t L i n e S e c o n d L i n e A n n u n c i a t o r s The display comprises two lines and annunciators . The first line can display up to 255 characters. Entries with more than 14 characters will scroll to the left. However, if entries are mor...

1–14 Getting Started Keying in Numbers You can key in a number that has up to 12 digits plus a 3–digit exponent up to ±499. If you try to key in a number larger than this, digit entry halts and the ¤ annunciator briefly appears. If you make a mistake while keying in a number, press b to backspace an...

Getting Started 1–15 Keying in Exponents of Ten Use a ( exponent ) to key in numbers multiplied by powers of ten. For example, take Planck's constant, 6.6261 × 10 –34 : 1. Key in the mantissa (the non –exponent part) of the number. If the mantissa is negative, press ^ af ter keying in its digits. Ke...

1–16 Getting Started Keys: Display: Description: 123 _ Digit entry not terminated: the number is not complete. If you execute a function to calculate a result , the cursor disappears because the number is complete — digit entry has been terminated. # ) Digit entry is terminated. Pressing ‘ terminate...

Getting Started 1–17 One–Number Functions To use a one–number function (such as , # , ! , { @ , { $ , | K , { , Q or ^ ) 1. Key in the number. ( You don't need to press ‘ .) 2. Press the function key. (For a shifted function, press the appropriate { or | shift key first.) For example, calculate 1/32...

1–18 Getting Started For example, To calculate: Press: Display: 12 + 3 12 ‘ 3 › ) 12 – 3 12 ‘ 3 … ) 12 × 3 12 ‘ 3 z ) 12 3 12 ‘ 3 8) Percent change from 8 to 5 8 ‘ 5 | T .) The order of entry is important only for non –commutative functions such as … , q , , { F , | D , , { \ , { _ , Q , | T . If yo...

Getting Started 1–19 Number of Decimal Places All numbers are stored with 12–digit precision, but you can select the number of decimal places to be displayed by pressing   (the display menu). During some complicated internal calculations, the calculator uses 15–digit precision for intermediate resul...

1–20 Getting Started Engineering Format ({ }) ENG format displays a number in a manner similar to scientific notation, except that the exponent is a multiple of three (there can be up to three digits before the " ) " or " 8 " radix mark). This format is most useful for scientific and...

Getting Started 1–21 For example, in the number 14.8745632019, you see only "14.8746" when the display mode is set to FIX 4, but the last six digits ("632019") are present internally in the calculator. To temporarily display a number in full precision, press |  . This shows you the ...

Getting Started 1–23 Displaying Fractions Press {‹ to switch between Fraction–display mode and the c urrent decimal display mode. Keys: Display: Description: 12  3  8 + _ Displays characters as you key them in. ‘ ) Terminates digit entry; displays the number in the current display format. { ‹ + Di...

1–24 Getting Started Calculator Memory The HP 33s has 31KB of memory in which you can store any combination of data (variables, equations, or program lines). Checking Available Memory Pressing { Y displays the following menu: # 8 Where 8 is the number of bytes of memory available. Pressing the { # }...

RPN: The Automatic Memory Stack 2–1 2 RPN: The Automatic Memory Stack This chapter explains how calculations take place in the automatic memory stack in RPN mode. You do not need to read and understand this material to use the calculator , but understanding the material will greatly enhance your use...

2–2 RPN: The Automatic Memory Stack T 0.00 00 "O ld e st " nu m b er Z Y X D i sp l aye d 0.00 00 0.00 00 0.00 00 D i sp l aye d The most "recent" number is in the X–register: this is the number you see in the second line of the display. In programming, the stack is used to perform c...

RPN: The Automatic Memory Stack 2–3 Reviewing the Stack R ¶ (Roll Down) Th e (roll down) key lets you review the entire contents of the stack by "rolling" the contents downward, one register at a time. You can see each number when it enters the X–register. Suppose the stack is filled with 1,...

2–4 RPN: The Automatic Memory Stack Exchanging the X– and Y–Registers in the Stack Another key that manipulates the stack contents is [ ( x exchange y ). This key swaps the contents of the X– and Y–registers without affecting the rest of the stack. Pressing [ twice restores the original order of the...

RPN: The Automatic Memory Stack 2–5 3. The stack drops. „ Notice that when the stack lifts, it replaces the contents of the T– (top) register with the contents of the Z–register, and that the former contents of the T–register are lost. You can see, therefore, that the stack's memory is limited to fo...

2–6 RPN: The Automatic Memory Stack Using a Number Twice in a Row You can use the replicating feature of ‘ to other advantages. To add a number to itself, press ‘ › . Filling the stack with a constant The replicating effect of ‘ together with the replicating effect of stack drop (from T into Z) allo...

RPN: The Automatic Memory Stack 2–7 „ During program entry, b deletes the currently–displayed program line and ‡ cancels program entry. „ During digit entry, b backspaces over the displayed number. „ If the display shows a labeled number (such as /) ), pressing ‡ or b cancels that display and shows ...

2–8 RPN: The Automatic Memory Stack 2. Reusing a number in a calculation. See appendix B for a comprehensive list of the functions that save x in the LAST X register. Correcting Mistakes with LAST X Wrong One–Number Function If you execute the wrong one–number function, use {  to retrieve the numbe...

RPN: The Automatic Memory Stack 2–9 Example: Suppose you made a mistake while calculating 16 × 19 = 304 There are three kinds of mistakes you could have made: Wrong Calculation: Mistake: Correction: 16 ‘ 19 … Wrong function {  ›{  z 15 ‘ 19 z Wrong first number 16 {  z 16 ‘ 18 z Wrong second numb...

RPN: The Automatic Memory Stack 2–11 9.5 a 15 ) _ Speed of light, c . z ) Meters to R. Centaurus. 8.7 {  ) Retrieves c . z ) Meters to Sirius. Chain Calculations in RPN mode In RPN mode, the automatic lifting and dropping of the stack's contents let you retain intermediate results without storing o...

RPN: The Automatic Memory Stack 2–13 Exercises Calculate: 0000 . 181 05 . 0 ) 5 3805 . 16 ( = x Solution: 16.3805 ‘ 5 z # .05 q Calculate: 5743 . 21 )] 9 8 ( ) 7 6 [( )] 5 4 ( ) 3 2 [( = + × + + + × + Solution: 2 ‘ 3 › 4 ‘ 5 › z # 6 ‘ 7 › 8 ‘ 9 › z # › Calculate: (10 – 5) ÷ [(17 – 12) × 4] = 0.2500 ...

2–14 RPN: The Automatic Memory Stack This method takes one additional keystroke. Notice that the first intermediate result is still the innermost parentheses (7 × 3). The advantage to working a problem left–to–right is that you don't have to use [ to reposition operands for nomcommutaiive functions ...

3–2 Storing Data into Variables Each black letter is associated with a key and a unique variable. The letter keys are automatically active when needed. (The A..Z annunciator in the display confirms this.) Note that the variables, X , Y , Z and T are different storage locations from the X–register, Y...

Storing Data into Variables 3–3 Viewing a Variable without Recalling It The | Š function shows you the contents of a variable without putting that number in the X–register. The display is labeled for the variable, such as: /) In Fraction–display mode ( { ‹ ), part of the integer may be dropped. This...

3–4 Storing Data into Variables Clearing Variables Variables' values are retained by Continuous Memory until you replace them or clear them. Clearing a variable stores a zero there; a value of zero takes no memory. To clear a single variable: Store zero in it: Press 0 I variable . To clear selected ...

Storing Data into Variables 3–5 A 15 A 12 Res ul t: 1 5 3 tha t i s, A x T t T t Z z Z z Y y Y y X 3 X 3 Recall Arithmetic Recall arithmetic uses L › , L … , L z , or L q to do arithmetic in the X–register using a recalled number and to leave the result in the display. Only the X–register is affecte...

3–6 Storing Data into Variables Keys: Display: Description: 1 I D 2 I E 3 I F ))) Stores the assumed values into the variable. 1 I › D I › E I › F ) Adds1 to D , E , and F . | Š D /) Displays the current value of D . | Š E /) | Š F /) b ) Clears the VIEW display; displays X-register again. Suppose t...

Real–Number Functions 4–1 4 Real–Number Functions This chapter covers most of the calculator's functions that perform computations on real numbers, including some numeric functions used in programs (such as ABS, the absolute–value function): „ Exponential and logarithmic functions. „ Quotient and Re...

4–2 Real–Number Functions To Calculate: Press: Natural logarithm (base e ) Common logarithm (base 10) { Natural exponential Common exponential (antilogarithm) { Quotient and Remainder of Division You can use { F and | D to produce either the quotient or remainder of division operations involving two...

Real–Number Functions 4–3 In RPN mode, to calculate a number y raised to a power x , key in y ‘ x , then press . (For y > 0, x can be any number; for y < 0, x must be an odd integer; for y = 0, x must be positive.) To Calculate: Press: Result: 15 2 15 ! ) 10 6 6 { 88) 5 4 5 ‘ 4 ) 2 –1.4 2 ‘ 1....

4–4 Real–Number Functions Setting the Angular Mode The angular mode specifies which unit of measure to assume for angles used in trigonometric functions. The mode does not convert numbers already present (see "Conversion Functions" later in this chapter). 360 degrees = 2 π radians = 400 grad...

4–6 Real–Number Functions Hyperbolic Functions With x in the display: To Calculate: Press: Hyperbolic sine of x (SINH). { O Hyperbolic cosine of x (COSH). { R Hyperbolic tangent of x (TANH). { U Hyperbolic arc sine of x (ASINH). { { M Hyperbolic arc cosine of x (ACOSH). { { P Hyperbolic arc tangent ...

4–8 Real–Number Functions Physics Constants There are 40 physics constants in the CONST menu. You can press | ž to view the following items. CONST Menu Items Description Value { F } Speed of light in vacuum 299792458 m s –1 { J } Standard acceleration of gravity 9.80665 m s –2 { } Newtonian constant...

Real–Number Functions 4–9 Items Description Value { TH } Classical electron radius 2.817940285 × 10 –15 m { ' µ } Characteristic impendence of vacuum 376.730313461 Ω { λ F } Compton wavelength 2.426310215 × 10 –12 m { λ FQ } Neutron Compton wavelength 1.319590898 × 10 –15 m { λ FR } Proton Compton w...

4–10 Real–Number Functions Coordinate Conversions The function names for these conversions are y , x Æ θ , r and θ , r Æ y , x . Polar coordinates ( r , θ ) and rectangular coordinates ( x , y ) are measured as shown in the illustration. The angle θ uses units set by the current angular mode. A calc...

4–12 Real–Number Functions R C R X c _ 36.5 o 77. 8 oh m s θ Keys: Display: Description: Ÿ { } Sets Degrees mode. 36.5 ^ ‘ . ) Enters θ , degrees of voltage lag. 77.8 ) _ Enters r , ohms of total impedance. | s ) Calculates x , ohms resistance, R . [ . ) Displays y , ohms reactance, X C . For more s...

Real–Number Functions 4–13 | u ) Equals 8 minutes and 34.29 seconds.   { % } 4 ) Restores FIX 4 display format. Angle Conversions When converting to radians, the number in the x–register is assumed to be degrees; when converting to degrees, the number in the x–register is assumed to be radians. To c...

4–14 Real–Number Functions Probability Functions Factorial To calculate the factorial of a displayed non-negative integer x (0 ≤ x ≤ 253), press { (the left–shifted key). Gamma To calculate the gamma function of a noninteger x , Γ ( x ), key in ( x – 1) and press { . The x ! function calculates Γ ( ...

4–16 Real–Number Functions Parts of Numbers These functions are primarily used in programming. Integer part To remove the fractional part of x and replace it with zeros, press | " . (For example, the integer part of 14.2300 is 14.0000.) Fractional part To remove the integer part of x and replace...

Real–Number Functions 4–17 Names of Functions You might have noticed that the name of a function appears in the display when you press and hold the key to execute it. (The name remains displayed for as long as you hold the key down.) For instance, while pressing O , the display shows . "SIN"...

5–2 Fractions If you didn't get the same results as the example, you may have accidentally changed how fractions are displayed. (See "Changing the Fraction Display" later in this chapter.) The next topic includes more examples of valid and invalid input fractions. You can type fractions only...

Fractions 5–3 Entered Value Internal Value Displayed Fraction 2 3 / 8 2.37500000000 + 14 15 / 32 14.4687500000 + 54 / 12 4.50000000000 + 6 18 / 5 9.60000000000 + 34 / 12 2.83333333333 + T 15 / 8192 0.00183105469 + S 12345678 12345 / 3 (Illegal entry) ¤ 16 3 / 16384 (Illegal entry) ¤ Accuracy Indicat...

5–4 Fractions This is especially important if you change the rules about how fractions are displayed. (See "Changing the Fraction Display" later.) For example, if you force all fractions to have 5 as the denominator, then 2 / 3 is displayed as + c because the exact fraction is approximately ...

Fractions 5–5 „ You can select one of three fraction formats. The next few topics show how to change the fraction display. Setting the Maximum Denominator For any fraction, the denominator is selected based on a value stored in the calculator. If you think of fractions as a b/c , then /c corresponds...

5–6 Fractions To select a fraction format, you must change the states of two flags . Each flag can be "set" or "clear," and in one case the state of flag 9 doesn't matter. Change These Flags: To Get This Fraction Format: 8 9 Most precise Clear — Factors of denominator Set Clear Fixed...

Fractions 5–7 Number Entered and Fraction Displayed Fraction Format ¼ 2 2.5 2 2 / 3 2.9999 2 16 / 25 Most precise 2 2 1/2 2 2/3 S 3 T 2 9/14 T Factors of denominator 2 2 1/2 2 11/16 T 3 T 2 5/8 S Fixed denominator 2 0/16 2 8/16 2 11/16 T 3 0/16 T 2 10/16 S ¼ For a / c value of 16. Example: Suppose a...

5–8 Fractions In an equation or program, the RND function does fractional rounding if Fraction–display mode is active. Example: Suppose you have a 56 3 / 4 –inch space that you want to divide into six equal sections. How wide is each section, assuming you can conveniently measure 1 / 16 –inch increm...

Fractions 5–9 Fractions in Programs When you're typing a program, you can type a number as a fraction — but it's converted to its decimal value. All numeric values in a program are shown as decimal values — Fraction–display mode is ignored. When you're running a program, displayed values are shown u...

Entering and Evaluating Equations 6–1 6 Entering and Evaluating Equations How You Can Use Equations You can use equations on the HP 33s in several ways: „ For specifying an equation to evaluate (this chapter). „ For specifying an equation to solve for unknown values (chapter 7). „ For specifying a f...

6–2 Entering and Evaluating Equations L ¾ Begins a new equation, turning on the " ¾ " equation–entry cursor. L turns on the A..Z annunciator so you can enter a variable name. V | d #/¾ L V types # and moves the cursor to the right. .25 #/) _ Digit entry uses the "_" digit–entry curso...

Entering and Evaluating Equations 6–3 Summary of Equation Operations All equations you create are saved in the equation list. This list is visible whenever you activate Equation mode. You use certain keys to perform operations involving equations. They're described in more detail later. Key Operatio...

6–4 Entering and Evaluating Equations Entering Equations into the Equation List The equation list is a collection of equations you enter. The list is saved in the calculator's memory. Each equation you enter is automatically saved in the equation list. To enter an equation: 1. Make sure the calculat...

Entering and Evaluating Equations 6–5 Numbers in Equations You can enter any valid number in an equation except fractions and numbers that aren't base 10 numbers. Numbers are always shown using ALL display format, which displays up to 12 characters. To enter a number in an equation, you can use the ...

6–6 Entering and Evaluating Equations Parentheses in Equations You can include parentheses in equations to control the order in which operations are performed. Press | ] and | ` to insert parentheses. (For more information, see "Operator Precedence" later in this chapter.) Example: Entering ...

Entering and Evaluating Equations 6–7 „ ! ! if there are no equations in the equation list or if the equation pointer is at the top of the list. „ The current equation (the last equation you viewed). 2. Press ™ or š to step through the equation list and view each equation. The list "wraps around...

Entering and Evaluating Equations 6–9 Keys: Display: Description: | H /ºº 1!.2 Shows the current equation in the equation list. b º 1!.2-¾ Turns on Equation–entry mode and shows the " ¾ " cursor at the end of the equation. b b /ºº 1!.2¾ Deletes the number 25. ‘ /ºº 1!.2 Shows the end of edit...

6–10 Entering and Evaluating Equations Because many equations have two sides separated by "=", the basic value of an equation is the difference between the values of the two sides. For this calculation, "=" in an equation essentially treated as " ಥ ". The value is a measure o...

Entering and Evaluating Equations 6–11 The evaluation of an equation takes no values from the stack — it uses only numbers in the equation and variable values. The value of the equation is returned to the X–register. The LAST X register isn't affected. Using ENTER for Evaluation If an equation is di...

6–12 Entering and Evaluating Equations a 6 q ) Changes cubic millimeters to liters (but doesn't change V ). Using XEQ for Evaluation If an equation is displayed in the equation list, you can press X to evaluate the equation. The entire equation is evaluated, regardless of the type of equation. The r...

Entering and Evaluating Equations 6–13 „ To change the number, type the new number and press g . This new number writes over the old value in the X–register. You can enter a number as a fraction if you want. If you need to calculate a number, use normal keyboard calculations, then press g . For exam...

Entering and Evaluating Equations 6–15 Equation Functions The following table lists the functions that are valid in equations. Appendix G, "Operation Index" also gives this information. LN LOG EXP ALOG SQ SQRT INV IP FP RND ABS x! SGN INTG IDIV RMDR SIN COS TAN ASIN ACOS ATAN SINH COSH TANH ...

6–16 Entering and Evaluating Equations 01.%(.2 01%(1.&22 Eleven of the equation functions have names that differ from their equivalent operations: Operation Equation function x 2 SQ x SQRT e x EXP 10 x ALOG 1/x INV X y XROOT y x ^ INT÷ IDIV Rmdr RMDR x 3 CB 3 x CBRT Example: Perimeter of a Trape...

Entering and Evaluating Equations 6–17 S i n g l e l e t te r n a m e N o i m p l i e d m u l ti p l ic a t io n D ivis io n i s do n e b e fo re a d d i ti on Pa ren th ese s us e d to g ro u p it e m s P = A + B + H x ( 1 SI N ( T )+ 1 SI N( F) ) Ί Ί Th e next equation also obeys the syntax rules....

6–18 Entering and Evaluating Equations Syntax Errors The calculator doesn't check the syntax of an equation until you evaluate the equation and respond to all the prompts — only when a value is actually being calculated. If an error is detected, # is displayed. You have to edit the equation to corre...

Solving Equations 7–1 7 Solving Equations In chapter 6 you saw how you can use ‘ to find the value of the left–hand variable in an assignment –type equation. Well, you can use SOLVE to find the value of any variable in any type of equation. For example, consider the equation x 2 – 3 y = 10 If you kn...

Solving Equations 7–5 g #O/) Stores 297.1 in T ; solves for P in atmospheres. A 5–liter flask contains nitrogen gas. The pressure is 0.05 atmospheres when the temperature is 18°C. Calculate the density of the gas ( N × 28/ V , where 28 is the molecular weight of nitrogen). Keys: Display: Description...

7–6 Solving Equations When SOLVE evaluates an equation, it does it the same way X does — any "=" in the equation is treated as a " – ". For example, the Ideal Gas Law equation is evaluated as P × V – ( N × R × T ). This ensures that an equality or assignment equation balances at the ...

Solving Equations 7–7 Interrupting a SOLVE Calculation To halt a calculation, press ‡ or g . The current best estimate of the root is in the unknown variable; use | Š to view it without disturbing the stack. Choosing Initial Guesses for SOLVE The two initial guesses come from: „ The number currently...

Solving Equations 7–11 For More Information This chapter gives you instructions for solving for unknowns or roots over a wide range of applications. Appendix D contains more detailed information about how the algorithm for SOLVE works, how to interpret results, what happens when no solution is found...

Integrating Equations 8–1 8 Integrating Equations Many problems in mathematics, science, and engineering require calculating the definite integral of a function. If the function is denoted by f(x) and the interval of integration is a to b , then the integral can be expressed mathematically as ³ = b ...

8–2 Integrating Equations Integrating Equations ( ³ FN) To integrate an equation: 1. If the equation that defines the integrand's function isn't stored in the equation list, key it in (see "Entering Equations into the Equation List" in chapter 6) and leave Equation mode. The equation usually...

Integrating Equations 8–3 Find the Bessel function for x– values of 2 and 3. Enter the expression that defines the integrand's function: cos ( x sin t ) Keys: Display: Description: { c { } { & } Clears memory. | H Current equation or ! ! Selects Equation mode. R L X 1%¾ Types the equation. z O 1...

Integrating Equations 8–5 Keys: Display: Description: | H The current equation or ! ! Selects Equation mode. O L X 1%¾ Starts the equation. | ` 1%2¾ The closing right parenthesis is required in this case. q L X 1%2ª%¾ ‘ 1%2ª% Terminates the equation. |  // Checksum and length. ‡ Leaves Equation mod...

8–6 Integrating Equations Specifying Accuracy The display format's setting (FIX, SCI, ENG, or ALL) determines the precision of the integration calculation: the greater the number of digits displayed, the greater the precision of the calculated integral (and the greater the time required to calculate...

Operations with Complex Numbers 9–1 9 Operations with Complex Numbers The HP 33s can use complex numbers in the form x + iy . It has operations for complex arithmetic (+, –, × , ÷ ), complex trigonometry (sin, cos, tan), and the mathematics functions – z , 1/ z , 2 1 z z , ln z , and e z . (where z ...

9–2 Operations with Complex Numbers Since the imaginary and real parts of a complex number are entered and stored separately, you can easily work with or alter either part by itself. y 1 Z 1 x 1 Compl ex fun ction y 2 y ima gi na r y p ar t Z 2 x 2 x re al pa r t Compl ex i np ut z or z 1 an d z 2 C...

Operations with Complex Numbers 9–3 Functions for One Complex Number, z To Calculate: Press: Change sign, –z { G ^ Inverse, 1/z { G Natural log, ln z { G Natural antilog, e z { G Sin z { G O Cos z { G R Tan z { G U To do an arithmetic operation with two complex numbers: 1. Enter the first complex nu...

Operations with Complex Numbers 9–5  2  3 ^ ‘ .) .) Enters imaginary part of second complex number as a fraction. 3 { G z .) ) Completes entry of second number and then multiplies the two complex numbers. Result is 11.7333 – i 3.8667. Evaluate 2 − z e , where z = (1 + i ). Use { G to evaluate z –2...

Base Conversions and Arithmetic 10–1 10 Base Conversions and Arithmetic The BASE menu ( { x ) lets you change the number base used for entering numbers and other operations (including programming). Changing bases also converts the displayed number to the new base. BASE Menu Menu label Description { ...

10–4 Base Conversions and Arithmetic The Representation of Numbers Although the display of a number is converted when the base is changed, its stored form is not modified, so decimal numbers are not truncated — until they are used in arithmetic calculations. When a number appears in hexadecimal, oct...

Base Conversions and Arithmetic 10–5 Range of Numbers The 36-bit word size determines the range of numbers that can be represented in hexadecimal (9 digits), octal (12 digits), and binary bases (36 digits), and the range of decimal numbers (11 digits) that can be converted to these other bases. Rang...

10–6 Base Conversions and Arithmetic Windows for Long Binary Numbers The longest binary number can have 36 digits — three times as many digits as fit in the display. Each 12–digit display of a long number is called a window . 36 - bi t nu m b er High e st wi ndow Lowe st wi n d ow ( d i s pl aye d )...

Statistical Operations 11–1 11 Statistical Operations The statistics menus in the HP 33s provide functions to statistically analyze a set of one– or two–variable data: „ Mean, sample and population standard deviations. „ Linear regression and linear estimation ( x ˆ and y ˆ ). „ Weighted mean ( x we...

11–2 Statistical Operations Entering One–Variable Data 1. Press { c { Σ } to clear existing statistical data. 2. Key in each x –value and press . 3. The display shows n , the number of statistical data values now accumulated. Pressing actually enters two variables into the statistics registers becau...

11–4 Statistical Operations Statistical Calculations Once you have entered your data, you can use the functions in the statistics menus. Statistics Menus Menu Key Description L.R. | The linear–regression menu: linear estimation { º ˆ } { ¸ ˆ } and curve–fitting { T } { P } { E }. See ''Linear Regres...

11–6 Statistical Operations Sample Standard Deviation Sample standard deviation is a measure of how dispersed the data values are about the mean sample standard deviation assumes the data is a sampling of a larger, complete set of data, and is calculated using n – 1 as a divisor. „ Press | { Uº } fo...

Statistical Operations 11–7 Example: Population Standard Deviation. Grandma Hinkle has four grown sons with heights of 170, 173, 174, and 180 cm. Find the population standard deviation of their heights. Keys: Display: Description: { c { ´ } Clears the statistics registers. 170 173 174 180 ) Enters d...

Statistical Operations 11–9 x 0 2 0 40 60 8 0 8 .50 7.50 6.50 5.50 4 .50 r = 0 . 9880 m = 0 .0387 b = 4 . 8560 (70, y ) y X What if 70 kg of nitrogen fertilizer were applied to the rice field ? Predict the grain yield based on the above statistics. Keys: Display: Description: ‡ 70 ) _ Enters hypothe...

11–10 Statistical Operations Normalizing Close, Large Numbers The calculator might be unable to correctly calculate the standard deviation and linear regression for a variable whose data values differ by a relatively small amount. To avoid this, normalize the data by entering each value as the diffe...

Statistical Operations 11–11 If you've entered statistical data, you can see the contents of the statistics registers. Press { Y { # }, then use ™ and š to view the statistics registers. Example: Viewing the Statistics Registers. Use to store data pairs (1,2) and (3,4) in the statistics registers. T...

Simple Programming 12–3 Designing a Program The following topics show what instructions you can put in a program. What you put in a program affects how it appears when you view it and how it works when you run it. Selecting a Mode Programs created and saved in RPN mode can only be edited and execute...

12–4 Simple Programming When a program finishes running, the last RTN instruction returns the program pointer to ! , the top of program memory. Using RPN, ALG and Equations in Programs You can calculate in programs the same ways you calculate on the keyboard: „ Using RPN operations (which work with ...

Simple Programming 12–5 For output, you can display a variable with the VIEW instruction, you can display a message derived from an equation, or you can leave unmarked values on the stack. These are covered later in this chapter under "Entering and Displaying Data." Entering a Program Pressi...

12–6 Simple Programming 5. End the program with a return instruction, which sets the program pointer back to ! after the program runs. Press | – . 6. Press ‡ (or { e ) to cancel program entry. Numbers in program lines are stored as precisely as you entered them, and they're displayed using ALL or SC...

Simple Programming 12–7 Function Names in Programs The name of a function that is used in a program line is not necessarily the same as the function's name on its key, in its menu, or in an equation. The name that is used in a program is usually a fuller abbreviation than that which can fit on a key...

Simple Programming 12–9 Running a Program To run or execute a program, program entry cannot be active (no program–line numbers displayed; PRGM off). Pressing ‡ will cancel Program–entry mode. Executing a Program (XEQ) Press X label to execute the program labeled with that letter. If there is only on...

Simple Programming 12–11 Entering and Displaying Data The calculator's variables are used to store data input, intermediate results, and final results. (Variables, as explained in chapter 3, are identified by a letter from A through Z or i , but the variable names have nothing to do with program lab...

Simple Programming 12–13 For example, see the " Coordinate Transformations" program in chapter 15. Routine D collects all the necessary input for the variables M, N, and T (lines D0002 through D0004) that define the x and y coordinates and angle θ of a new system. To respond to a prompt: Whe...

12–14 Simple Programming „ Pressing { c clears the contents of the displayed variable. Press g to continue the program, If you don't want the program to stop, see "Displaying Information without Stopping" below. For example, see the program for "Normal and Inverse–Normal Distributions...

12–16 Simple Programming Keys: (In RPN mode) Display: Description: | Š V #$ # Displays volume. | Š S #$ Displays surface area. | – ! Ends program. { Y { } / Displays label C and the length of the program in bytes. |  / / Checksum and length of program. ‡ ‡ Cancels program entry. Now find the volume...

Simple Programming 12–17 The display is cleared by other display operations, and by the RND operation if flag 7 is set (rounding to a fraction). Press | f to enter PSE in a program. The VIEW and PSE lines — or the equation and PSE lines — are treated as one operation when you execute a program one l...

12–18 Simple Programming To see the line in the program containing the error–causing instruction, press { e . The program will have stopped at that point. (For instance, it might be a ÷ instruction, which caused an illegal division by zero.) Editing a Program You can modify a program in program memo...

Simple Programming 12–19 2. Press b . This turns on the " ¾ " editing cursor, but does not delete anything in the equation. 3. Press b as required to delete the function or number you want to change, then enter the desired corrections. 4. Press ‘ to end the equation. Program Memory Viewing P...

12–20 Simple Programming Memory Usage If during program entry you encounter the message & " , then there is not enough room in program memory for the line you just tried to enter. You can make more room available by clearing programs or other data. See "Clearing One or More Programs"...

Simple Programming 12–21 To clear all programs from memory: 1. Press { e to display program lines ( PRGM annunciator on). 2. Press { c { } to clear program memory. 3. The message @ & prompts you for confirmation. Press { & }. 4. Press { e to cancel program entry. Clearing all of memory ( { c...

12–22 Simple Programming Nonprogrammable Functions The following functions of the HP 33s are not programmable: { c { } { V   { c { } { V  label nnnn b { Y š , ™ , ˜ , — |  { e | H { h , {j { ‹ Programming with BASE You can program instructions to change the base mode using { x . These settings w...

Simple Programming 12–23 Numbers Entered in Program Lines Before starting program entry, set the base mode. The current setting for the base mode determines the base of the numbers that are entered into program lines. The display of these numbers changes when you change the base mode. Program line n...

Programming Techniques 13–1 13 Programming Techniques Chapter 12 covered the basics of programming. This chapter explores more sophisticated but useful techniques: „ Using subroutines to simplify programs by separating and labeling portions of the program that are dedicated to particular tasks. The ...

Programming Techniques 13–3 Nested Subroutines A subroutine can call another subroutine, and that subroutine can call yet another subroutine. This "nesting" of subroutines — the calling of a subroutine within another subroutine — is limited to a stack of subroutines seven levels deep (not co...

13–4 Programming Techniques In RPN mode, Starts subroutine here. "! Enters A . "! Enters B . "! Enters C. "! Enters D. Recalls the data. º A 2 . % € M A 2 + B 2 . N € % € O A 2 + B 2 + C 2 P € % € Q A 2 + B 2 + C 2 + D 2 R € º 2 2 2 2 D C B A + + + ! Returns to main routine.  MOQ Ne...

Programming Techniques 13–5 A Programmed GTO Instruction The GTO label instruction (press { V label ) transfers the execution of a running program to the program line containing that label, wherever it may be. The program continues running from the new location, and never automatically returns to it...

13–6 Programming Techniques „ To ! : { V   . „ To a line number: { V  label nnnn ( nnnn < 10000). For example, { V  A0005. „ To a label: { V label —but only if program entry is not active (no program lines displayed; PRGM off). For example, { V A. Conditional Instructions Another way to alter...

Programming Techniques 13–7 „ Flag tests. These check the status of flags, which can be either set or clear. „ Loop counters. These are usually used to loop a specified number of times. Tests of Comparison (x ? y, x ? 0) There are 12 comparisons available for programming. Pressing { n or | o display...

13–8 Programming Techniques Example: The "Normal and Inverse–Normal Distributions" program in chapter 16 uses the x < y ? conditional in routine T: Program Lines: (In RPN mode) Description . . . ! ª Calculates the correction for X guess . ! !- % Adds the correction to yield a new X guess ...

Programming Techniques 13–9 „ Flag s 0, 1, 2, 3, and 4 have no preassigned meanings. That is, their states will mean whatever you define them to mean in a given program. (See the example below.) „ Flag 5, when set, will interrupt a program when an overflow occurs within the program, displaying #$ an...

Programming Techniques 13–11 Annunciators for Set Flags Flags 0, 1, 2, 3 and 4 have annunciators in the display that turn on when the corresponding flag is set. The presence or absence of 0 , 1 , 2 , 3 or 4 lets you know at any time whether any of these five flags is set or not. However, there is no...

13–16 Programming Techniques Use the above program to see the different forms of fraction display: Keys: (In ALG mode) Display: Description: X F #@ value Executes label F ; prompts for a fractional number ( V ). 2.53 g @ value Stores 2.53 in V; prompts for denominator (D). 16 g ) Stores 16 as the /c...

13–20 Programming Techniques Indirectly Addressing Variables and Labels Indirect addressing is a technique used in advanced programming to specify a variable or label without specifying beforehand exactly which one . This is determined when the program runs, so it depends on the intermediate results...

Solving and Integrating Programs 14–1 14 Solving and Integrating Programs Solving a Program In chapter 7 you saw how you can enter an equation — it's added to the equation list — and then solve it for any variable. You can also enter a program that calculates a function, and then solve it for any va...

14–6 Solving and Integrating Programs Using SOLVE in a Program You can use the SOLVE operation as part of a program. If appropriate, include or prompt for initial guesses (into the unknown variable and into the X–register) before executing the SOLVE variable instruction. The two instructions for sol...

Solving and Integrating Programs 14–7 Program Lines: (In RPN mode) Description: % % Setup for X . % Index for X . % ! Branches to main routine. Checksum and length: 4800 21 & & Setup for Y . & Index for Y . & ! Branches to main routine. Checksum and length: C5E1 21 Main routine. ! L ...

Solving and Integrating Programs 14–9 Example: Program Using Equation. The sine integral function in the example in chapter 8 is ³ = t 0 dx ( Si(t) ) x x sin This function can be evaluated by integrating a program that defines the integrand: Defines the function. 1%2ª% The function as an expression....

Solving and Integrating Programs 14–11 Restrictions on Solving and Integrating The SOLVE variable and ³ FN d variable instructions cannot call a routine that contains another SOLVE or ³ FN instruction. That is, neither of these instructions can be used recursively. For example, attempting to calcula...

Mathematics Programs 15–1 15 Mathematics Programs Vector Operations This program performs the basic vector operations of addition, subtraction, cross product, and dot (or scalar) product. The program uses three–dimensional vectors and provides input and output in rectangular or polar form. Angles be...

Mathematics Programs 15–9 N (y ) S W E (x ) An te n na Tra n s m it t er 7.3 1 5.7 Keys: (In ALG mode) Display: Description: Ÿ { } Sets Degrees mode. X R %@ value Starts rectangular input/display routine. 7.3 g &@ value Sets X equal to 7.3. 15.7 g '@ value Sets Y equal to 15.7. .76 ^ g @) Sets Z...

15–12 Mathematics Programs 125 g @) Sets T equal to 125. 63 g @) Sets P equal to 63. X D /) Calculates dot product. g /) Calculates angle between resultant force vector and lever. g @) Gets back to input routine. Solutions of Simultaneous Equations This program solves simultaneous linear equations i...

15–20 Mathematics Programs g @.) Displays next value. g @) Displays next value. g @) Displays next value. X I ) Inverts inverse to produce original matrix. X A @) Begins review of inverted matrix. g @) Displays next value, ...... and so on. . . . . . . Polynomial Root Finder This program finds the r...

Mathematics Programs 15–21 b 0 = a 0 (4 a 2 – a 3 2 ) – a 1 2 . Let y 0 be the largest real root of the above cubic. Then the fourth–order polynomial is reduced to two quadratic polynomials: x 2 + ( J + L ) x + ( K + M ) = 0 x 2 + ( J – L ) x + ( K – M ) = 0 where J = a 3 /2 K = y 0 /2 L = 0 2 2 y a...

Mathematics Programs 15–29 Because of round–off error in numerical computations, the program may produce values that are not true roots of the polynomial. The only way to confirm the roots is to evaluate the polynomial manually to see if it is zero at the roots. For a third– or higher–order polynomi...

Mathematics Programs 15–31 Example 2: Find the roots of 4 x 4 – 8 x 3 – 13 x 2 – 10 x + 22 = 0. Because the coefficient of the highest–order term must be 1, divide that coefficient into each of the other coefficients. Keys: (In RPN mode) Display: Description: X P @ value Starts the polynomial root f...

15–32 Mathematics Programs Example 3: Find the roots of the following quadratic polynomial: x 2 + x – 6 = 0 Keys: (In RPN mode) Display: Description: X P @ value Starts the polynomial root finder; prompts for order. 2 g @ value Stores 2 in F ; prompts for B . 1 g @ value Stores 1 in B ; prompts for ...

Statistics Programs 16–1 16 Statistics Programs Curve Fitting This program can be used to fit one of four models of equations to your data. These models are the straight line, the logarithmic curve, the exponential curve and the power curve. The program accepts two or more ( x , y ) data pairs and t...

16–2 Statistics Programs y x y B M x = + S t r a i g h t L i n e F i t S y x y B e M x = E x po n e n t i a l C u r v e F i t E y x y B M I n x = + L o g a r i t h m i c C u r v e F i t L y x y B x M = Pow er C u r ve Fi t P To fit logarithmic curves, values of x must be positive. To fit exponential...

16–8 Statistics Programs 5. Repeat steps 3 and 4 for each data pair. If you discover that you have made an error after you have pressed g in step 3 (with the &@ value prompt still visible), press g again (displaying the %@ value prompt) and press X U to undo (remove) the last data pair. If you d...

Statistics Programs 16–11 Logarithmic Exponential Power To start: X L X E X P R 0.9965 0.9945 0.9959 M –139.0088 51.1312 8.9730 B 65.8446 0.0177 0.6640 Y ( y ˆ when X =37) 98.7508 98.5870 98.6845 X ( x ˆ when Y =101) 38.2857 38.3628 38.3151 Normal and Inverse–Normal Distributions Normal distribution...

Statistics Programs 16–17 55 g @) Stores 55 for the mean. 15.3 g ) Stores 15.3 for the standard deviation. X D %@ value Starts the distribution program and prompts for X . 90 g /) Enters 90 for X and calculates Q ( X ). Thus, we would expect that only about 1 percent of the students would do better ...

Miscellaneous Programs and Equations 17–1 17 Miscellaneous Programs and Equations Time Value of Money Given any four of the five values in the "Time–Value–of–Money equation" (TVM), you can solve for the fifth value. This equation is useful in a wide variety of financial applications such as ...

17–2 Miscellaneous Programs and Equations Equation Entry: Key in this equation: ºº1.1-ª2:.2ª-º1-ª2:.- Keys: (In RPN mode) Display: Description: | H ! ! or current equation Selects Equation mode. L P z 100 º _ Starts entering equation. z | ] 1 … ºº1.¾ | ] 1 › ºº1.1-¾ L I q 100 º1.1-ª _ | ` 1.1-ª2:¾ …...

17–6 Miscellaneous Programs and Equations g @) Retains P ; prompts for I . g @ ) Retains 0.56 in I ; prompts for N. 24 g @8) Stores 24 in N ; prompts for B . g #/.8) Retains 5750 in B ; calculates F , the future balance. Again, the sign is negative, indicating that you must, pay out this money.   { ...

Support, Batteries, and Service A–1 A Support, Batteries, and Service Calculator Support You can obtain answers to questions about using your calculator from our Calculator Support Department. Our experience shows that many customers have similar questions about our products, so we have provided the...

A–2 Support, Batteries, and Service A: You must clear a portion of memory before proceeding. (See appendix B.) Q: Why does calculating the sine (or tangent) of π radians display a very small number instead of 0 ? A: π cannot be represented exactly with the 12–digit precision of the calculator. Q: Wh...

A–4 Support, Batteries, and Service Warning Do not mutil ate, puncture, or dispose of bat teries in fire. The bat teries can burst or explode, releasing hazardous chemicals. 5. Insert a new CR2032 lithium battery, making sure that the positive sign (+) is facing outward. Replace the plate and push i...

Support, Batteries, and Service A–5 „ If the calcul ator responds to keystrokes but you suspect th at it is malfunctioning: 1. Do the self–test described in the next section. If the calculator fails the self test, it requires service. 2. If the calculator passes the self–test, you may have made a mi...

A–6 Support, Batteries, and Service Warranty HP 33s Scientific Calculator; Warranty period: 12 months 1. HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified a...

Support, Batteries, and Service A–7 7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLU...

Support, Batteries, and Service A–9 N.America Country : Telephone numbers USA 1800-HP INVENT Canada (905)206-4663 or 800-HP INVENT ROTC = Rest of the country Please logon to http://www.hp.com for the latest service and support information. Regulatory Information This section contains information tha...

A–10 Support, Batteries, and Service File name 33s-English-Manual-050427-Publication(Edition 3) Page : 387 Printed Date : 2005/4/27 Size : 13.7 x 21.2 cm Japan この装置は、情報処理装置等電波障害自主規制協議会 (VCCI) の基準 に基づく第二情報技術装置です。この装置は、家庭環境で使用することを目的としていま すが、この装置がラジオやテレビジョン受信機に近接して使用されると、受信障害を引き 起こすことがあります。 取扱説明書に従って正...

User Memory and the Stack B–1 B User Memory and the Stack This appendix covers „ The allocation and requirements of user memory, „ How to reset the calculator without affecting memory, „ How to clear (purge) all of user memory and reset the system defaults, and „ Which operations affect stack lift. ...

B–2 User Memory and the Stack 2. If necessary, scroll through the equation list (press ™ or š ) until you see the desired equation. 3. Press |  to see the checksum (hexadecimal) and length (in bytes) of the equation. For example, / / . To see the total memory requirements of specific programs: 1. P...

User Memory and the Stack B–3 Clearing Memory The usual way to clear user memory is to press { c { }. However, there is also a more powerful clearing procedure that resets additional information and is useful if the keyboard is not functioning properly. If the calculator fails to respond to keystrok...

B–4 User Memory and the Stack Memory may inadvertently be cleared if the calculator is dropped or if power is interrupted. The Status of Stack Lift The four stack registers are always present, and the stack always has a stack–lift status . That is to say, the stack lift is always enabled or disabled...

B–6 User Memory and the Stack File name 33s-English-Manual-041129-Publication(Edition 3) Page : 388 Printed Date : 2004/12/8 Size : 13.7 x 21.2 cm The Status of the LAST X Register The following operations save x in the LAST X register: +, –, × , ÷ x , x 2 , 3 x , x 3 e x , 10 x LN, LOG y x , X y I/...

ALG: Summary C–1 C ALG: Summary About ALG This appendix summarizes some features unique to ALG mode, including, „ Two–number arithmetic „ Chain calculation „ Reviewing the stack „ Coordinate conversions „ Operations with complex numbers „ Integrating an equation „ Arithmetic in bases 2, 8, and 16 „ ...

C–2 ALG: Summary Doing Two–number Arithmetic in ALG This discussion of arithmetic using ALG replaces the following parts that are affected by ALG mode. One-number functions (such as # ) work the same in ALG and RPN modes. Two–number arithmetic operations are affected by ALG mode: „ Simple arithmetic...

ALG: Summary C–3 To Calculate: Press: Display: 12 3 12 3 ‘ :/8) 64 1/3 (cube root) 3 64 ‘ º / ) Percentage Calculations The Percent Function. The Q key divides a number by 100. Combined with › or … , it adds or subtracts percentages. To Calculate: Press: Display: 27% of 200 200 z 27 Q ‘ º0/) 200 les...

C–4 ALG: Summary Example: Suppose that the $15.76 item cost $16.12 last year. What is the percentage change from last year's price to this year's ? Keys: Display: Description: 16.12 | T 15.76 ‘ )0) /.) This year's price dropped about 2.2% from last year's price. Permutations and Combinations Example...

ALG: Summary C–5 File name hp 33s_user's manual_English_E_HDPM20PIE30.doc Page : 409 Printed Date : 2005/10/17 Size : 13.7 x 21.2 cm Parentheses Calculations In ALG mode, you can use parentheses up to 13 levels. For example, suppose you want to calculate: 9 12 85 30 × − If you were to key in 30 ¯ 85...

C–8 ALG: Summary š 8 ´ ¸8º &/) Displays y . If you want to perform a coordinate conversion as part of a chain calculation, you need to use parentheses to impose the required order of operations. Example: If r = 4.5, θ = π 3 2 , what are x, y ? Keys: Display: Description: Ÿ { } Sets Radians mode....

C–12 ALG: Summary File name hp 33s_user's manual_English_E_HDPM20PIE30.doc Page: 409 Printed Date : 2005/10/18 Size : 13.7 x 21.2 cm 100 8 ÷ 5 8 = ? 100 ¯ 5 Ï   Integer part of result. 5A0 16 + 10011000 2 = ? ¹ ¶ {  } 5A0 Ù   Set base 16; HEX annunciator on. ¹ ¶ {  } 1001...

More about Solving D–1 D More about Solving This appendix provides information about the SOLVE operation beyond that given in chapter 7. How SOLVE Finds a Root SOLVE first attempts to solve the equation directly for the unknown variable. If the attempt fails, SOLVE changes to an iterative(repetitive...

D–2 More about Solving f ( x ) x a f ( x ) b x f ( x ) x c f ( x ) x d F u n c t i o n W h o s e R o o t s C a n B e Fo u n d In most situations, the calculated root is an accurate estimate of the theoretical, infinitely precise root of the equation. An "ideal" solution is one for which f(x)...

More about Solving D–3 Interpreting Results The SOLVE operation will produce a solution under either of the following conditions: „ If it finds an estimate for which f(x) equals zero. (See figure a, below.) „ If it finds an estimate where f(x) is not equal to zero, but the calculated root is a 12–di...

D–4 More about Solving Keys: Display: Description: | H Select Equation mode. 2 ^z L X 3 › 4 z L X 2 … 6 zL X › 8 ‘ .º%:-º%:. º Enters the equation. |  // Checksum and length. ‡ Cancels Equation mode. Now, solve the equation to find the root: Keys: Display: Description: 0 I X 10 _ Initial guesses fo...

D–6 More about Solving f ( x ) x a f ( x ) x b S p e c i a l C a s e : A D i s c o n t i n u i t y a n d a Po l e Example: Discontinuous Function. Find the root of the equation: IP( x ) = 1.5 Enter the equation: Keys: Display: Description: | H Selects Equation mode. | " L X | ` | ’ 1.5 ‘ 1%2/) E...

D–8 More about Solving Now, solve to find the root. Keys: Display: Description: 2.3 I X 2.7 ) _ Your initial guesses for the root. | H %ª1%:. 2. Selects Equation mode; displays the equation.  X ! No root found for f(x) . 8 8 8) f(x) is relatively large. When SOLVE Cannot Find a Root Sometimes SOLVE...

More about Solving D–9 f ( x ) x a f ( x ) x b f ( x ) x c C a s e W h e r e N o R o o t I s F o u n d Example: A Relative Minimum. Calculate the root of this parabolic equation: x 2 – 6 x + 13 = 0. It has a minimum at x = 3. Enter the equation as an expression: Keys: Display: Description: | H Selec...

More about Solving D–13 ¶ ! Checksum and length: B956 75 You can subsequently delete line J0003 to save memory. Solve for X using initial guesses of 10 –8 and –10 –8 . Keys: (In RPN mode) Display: Description: a 8 ^ I X 1 ^ a 8 ^ . . _ Enters guesses. | W J .) . Selects program "J" as the fu...

More about Integration E–1 E More about Integration This appendix provides information about integration beyond that given in chapter 8. How the Integral Is Evaluated The algorithm used by the integration operation, ³ Gº , calculates the integral of a function f(x) by computing a weighted average of...

E–2 More about Integration As explained in chapter 8, the uncertainty of the final approximation is a number derived from the display format, which specifies the uncertainty for the function. At the end of each iteration, the algorithm compares the approximation calculated during that iteration with...

E–6 More about Integration Note that the rapidity of variation in the function (or its low–order derivatives) must be determined with respect to the width of the interval of integration. With a given number of sample points, a function f(x) that has three fluctuations can be better characterized by ...

More about Integration E–7 In many cases you will be familiar enough with the function you want to integrate that you will know whether the function has any quick wiggles relative to the interval of integration. If you're not familiar with the function, and you suspect that it may cause problems, yo...

F–4 Messages # The calculator is solving an equation or program for its root. This might take a while. !12 Attempted to calculate the square root of a negative number. !! Statistics error: „ Attempted to do a statistics calculation with n = 0. „ Attempted to calculate s x s y , x ˆ , y ˆ , m , r , o...

Operation Index G–1 G Operation Index This section is a quick reference for all functions and operations and their formulas, where appropriate. The listing is in alphabetical order by the function's name. This name is the one used in program lines. For example, the function named FIX n is executed a...

Operation Index G–7 Name Keys and Description Page ¼ CMPLX × { G z Complex multiplication . Returns ( z 1x + i z 1y ) × ( z 2x + i z 2y ). 9–2 CMPLX ÷ { G q Complex division . Returns ( z 1x + i z 1y ) ÷ ( z 2x + i z 2y ). 9–2 CMPLX1/ x { G Complex reciprocal . Returns 1/(z x + i z y ). 9–2 CMPLXCOS...

Operation Index G–11 Name Keys and Description Page ¼ ( i ) L ” I ” Indirect . Value of variable whose letter corresponds to the numeric value stored in variable i. 6–4 13–21 2 € IN | ‚ Converts centimeters to inches. 4–13 1 IDIV { F Produces the quotient of a division operation involving two intege...

Index– 1 File name 33s-English-Manual-050502-Publication(Edition 3) Page : 388 Printed Date : 2005/5/2 Size : 13.7 x 21.2 cm Index Special Characters , 6–5 ∫ FN. See integration % functions, 4–6  . See equation–entry cursor ~ . See backspace key " . See integration z , 1–14 â , 1–23 π , 4–3, A–...