LP z LV ’ LN z LR z LT ‘ | HP 33s Scientific guide

Keys:	Display:	Description:
(In ALG mode)

WG
P	#@
	value
2 g	@
	value
.005 g	@
	value
.0821 g	!@
	value
24 273.1 !@
	)
g	#
	/
	)

Selects "G" — the program. SOLVE evaluates to find the value of the unknown variable. Selects P; prompts for V.

Stores 2 in V; prompts for N.

Stores .005 in N; prompts for R.

Stores .0821 in R; prompts for T.

Calculates T.

Stores 297.1 in T; solves for P. Pressure is 0.0610 atm.

Example: Program Using Equation.

Write a program that uses an equation to solve the "Ideal Gas Law."

Keys:	Display:	Description:
(In RPN mode)

{e{
V	!
{H
y{ }
1
H
LP z
LV
LN z
LR z
LT	º#/ºº

Selects Program–entry mode. Moves program pointer to top of the list of programs.

Labels the program.

Enables equation prompting.

Evaluates the equation, clearing flag 11. (Checksum and length: EDC8 9).

14–4Solving and Integrating Programs

Page 214

Image 214

HP 33s Scientific manual LP z LV ’ LN z LR z LT ‘, 14-4Solving and Integrating Programs, Example Program Using Equation

Contents

Hp 33s scientific calculator Printing History Contents RPN The Automatic Memory Stack Clearing the X-Register Storing Data into Variables Fractions in Programs How You Can Use Equations Summary of Equation Operations For More Information Complex Stack Complex Operations ContentsSolving an Equation Accuracy of Integration Programming 12-6 12-4Data Input and Output 12-4 Entering a Program 12-5 12-7 13-3 13-113-2 Branching GTO 13-4 Vector Operations 15-1 Managing Calculator Memory ContentsPart 3. Appendixes and Reference 15-12 Disabling Operations Neutral Operations Resetting the Calculator Clearing MemoryRound-Off Error Contents About ALG How the Integral Is Evaluated UnderflowConditions That Prolong Calculation Time Page Part Basic OperationPage Important Preliminaries Adjusting Display ContrastGetting Started Turning the Calculator On and Off Shifted Keys Highlights of the Keyboard and Display2Getting Started Alpha Keys Cursor Keys Backspacing and Clearing Silver Paint Keys4Getting Started Equation-entry mode Keyboard-entry modeAre described in Using Menus on page 1-7. If ¾ when number entry is complete 6Getting Started Programming Instructions Using MenusHP 33s Menus Chapter Name Numeric Functions Description Other functions8Getting Started To use a menu function Exiting Menus KeysDisplay To select ALG mode RPN mode ALG modeTo select RPN mode RPN and ALG Keys Display and Annunciators First Line Second Line 2 3 HP 33s Annunciators Meaning Chapter12Getting Started RAD or §,¨ Exponents of Ten Keying in NumbersMaking Numbers Negative Keys Display Description Keying in Exponents of Ten Understanding Digit EntryOther Exponent Functions Keys Display Doing ArithmeticRange of Numbers and Overflow 16Getting Started , \, , Qor T One-Number FunctionsTwo-Number Functions Key in the number. You dont need to press ‘ ‘3 z Controlling the Display FormatPeriods and Commas in Numbers D, , \, ,Q Fixed-Decimal Format % Number of Decimal PlacesScientific Format Engineering Format SHOWing Full 12-Digit Precision20Getting Started ALL Format Entering Fractions FractionsKeysDisplayDescription 22Getting Started Displaying Fractions MessagesDisplayDescription Clearing All of Memory Calculator MemoryChecking Available Memory 24Getting Started What the Stack Is RPN The Automatic Memory StackRPN The Automatic Memory Stack Clearing the X-Register X and Y-Registers are in the Display2RPN The Automatic Memory Stack ¶ Roll Down Reviewing the StackRµ Roll Up Exchanging the X- and Y-Registers in the Stack Arithmetic How the Stack Does It4RPN The Automatic Memory Stack How Enter Works Lost 6RPN The Automatic Memory Stack Using a Number Twice in a RowHow Clear x Works Filling the stack with a constant Last X Register 8RPN The Automatic Memory Stack Correcting Mistakes with Last, \, , Qor T Wrong One-Number Function Mistake Reusing Numbers with Last› 96.704 + 10RPN The Automatic Memory Stack Chain Calculations in RPN mode Work from the Parentheses Out 12RPN The Automatic Memory Stack Order of Calculation SolutionExercises 16.3805x5 = 181.0000 14RPN The Automatic Memory Stack More Exercises‘14 ‘ ⋅ 0.8 ⎟ 12.5 − 0.73 = Page Storing Data into Variables Storing Data into Variables To recall a copy of a number from a variable to the display Storing and Recalling Numbers2Storing Data into Variables Example Storing Numbers Reviewing Variables in the VAR Catalog Viewing a Variable without Recalling ItTo review the values at any or all non-zero variables Storage Arithmetic Clearing VariablesArithmetic with Stored Variables 4Storing Data into Variables Recall Arithmetic Result 3 That is, x LzE Exchanging x with Any Variable6Storing Data into Variables Variable Page Exponential and Logarithmic Functions Real-Number FunctionsReal-Number Functions To Calculate Press Power FunctionsQuotient and Remainder of Division 2Real-Number Functions Entering π TrigonometryTo Calculate Press Result Option Description Annunciator Setting the Angular ModeTrigonometric Functions 4Real-Number Functions NzR Programming Note 6Real-Number Functions Hyperbolic FunctionsPercentage Functions ‘x Q 16.12 ‘ 15.76 T . Const Menu Items Description Value Physics Constants8Real-Number Functions Items Description Value Conversion FunctionsTo insert a constant 10Real-Number Functions Coordinate ConversionsTo convert between rectangular and polar coordinates Example Polar to Rectangular Conversion Example Conversion with Vectors To convert between decimal fractions and minutes-seconds Time Conversions12Real-Number Functions Example Converting Time Formats To Convert Press Displayed Results Angle ConversionsUnit Conversions To convert an angle between degrees and radians Gamma Probability FunctionsFactorial Probability Example Combinations of People KeysDisplay Parts of Numbers 16Real-Number Functions Names of Functions Page Fractions Entering Fractions Display Rules Fractions in the Display2Fractions Accuracy Indicators Entered Value Internal Value Displayed Fraction Longer Fractions Changing the Fraction Display4Fractions Setting the Maximum Denominator Choosing a Fraction Format Fraction How 2.77 Is Displayed Format Examples of Fraction DisplaysTo Get This Fraction Format Change These Flags 6Fractions Fraction Number Entered and Fraction Displayed Format ¼ Rounding FractionsDenominator Fixed Fractions in Equations 8Fractions Fractions in Programs Page Entering and Evaluating Equations Entering and Evaluating EquationsHow You Can Use Equations Example Calculating with an Equation ZLL ZNz2Entering and Evaluating Equations Summary of Equation Operations Enters and leaves Equation modeKey Operation 4Entering and Evaluating Equations Entering Equations into the Equation ListVariables in Equations To enter an equation Numbers in Equations Functions in Equations LR d Displaying and Selecting EquationsParentheses in Equations ZLC z To view a long equation Editing and Clearing Equations——— To select an equation 8Entering and Evaluating Equations Types of Equations Evaluating Equations Fx ¼ Type of Equation Result for ‘10Entering and Evaluating Equations To evaluate an equation Using Enter for Evaluation Example Evaluating an Equation with Enter 12Entering and Evaluating Equations Using XEQ for EvaluationResponding to Equation Prompts Example Evaluating an Equation with XEQ ‘5 g Syntax of EquationsOperator Precedence „ To display digits hidden by the prompt, press Equations Meaning Order Operation Example14Entering and Evaluating Equations Equation Functions Σxy Example Perimeter of a Trapezoid Operation Equation function16Entering and Evaluating Equations Perimeter = a + b + h Example Area of a Polygon HLA ’.25 zLN zLD 2 zR NqLN `qONqLN `‘Cos π / n Area = 18Entering and Evaluating Equations Syntax ErrorsVerifying Equations Example Checksum and Length of an Equation Solving Equations Solving EquationsSolving an Equation Markup ⋅ Cost = Price 2Solving Equations LD dLVZLT › Example Solving the Equation of Linear Motion Value 4Solving Equations HL P zZL T Example Solving the Ideal Gas Law Equation LV q Understanding and Controlling Solve Verifying the Result 6Solving Equations Interrupting a Solve Calculation Choosing Initial Guesses for Solve Example Using Guesses to Find a Root 8Solving Equations H 40 ZL H 10Solving Equations For More Information Page Integrating Equations Integrating Equations J0 x = π1 ≥0π cos x sin t dt Integrating Equations ≥ FN2Integrating Equations ≥ 0π f t Value Example Sine Integral 4Integrating Equations= ≥ t Accuracy of Integration 6Integrating Equations Specifying AccuracyInterpreting Accuracy Example Specifying Accuracy Example Changing the Accuracy 8Integrating Equations Its uncertainty indicates + iy Operations with Complex NumbersComplex Stack To enter a complex number 2Operations with Complex Numbers Complex OperationsTo do an operation with one complex number Functions for One Complex Number, z To Calculate Press To do an arithmetic operation with two complex numbers 2 5 ‘ ‘2 ‘ ‘4 4Operations with Complex Numbers ‘2 Using Complex Numbers in Polar Notation2 3 ‘ 6Operations with Complex Numbers Example Vector Addition Operations with Complex Numbers Page Menu label Description Base Conversions and ArithmeticBase Menu Base Conversions and Arithmetic Arithmetic in Bases 2, 8, 10-2Base Conversions and Arithmetic Keys Display ˜˜ Representation of NumbersNegative Numbers 10-4Base Conversions and Arithmetic Range of Numbers 7FFFFFFFF Windows for Long Binary Numbers 10-6Base Conversions and Arithmetic Entering Statistical Data Statistical OperationsStatistical Operations Entering Two-Variable Data Correcting Errors in Data EntryEntering One-Variable Data 11-2Statistical Operations 400 Initial x, y Corrected x, y‘20 Statistics Menus Key Description Statistical CalculationsMean 11-4Statistical Operations Price per Part Example Weighted Mean Two Variables· Number of Parts y Uº Sample Standard DeviationPopulation Standard Deviation 11-6Statistical Operations Keys DisplayDescription Linear Regressionσº Linear Regression Menu Nitrogen Applied 11-8Statistical OperationsExample Curve Fitting Grain Yield Limitations on Precision of Data 70, y 11-10Statistical Operations Summation Values and the Statistics RegistersSummation Statistics Normalizing Close, Large Numbers Example Viewing the Statistics Registers Access to the Statistics RegistersStatistics Registers in Calculator Memory # ™ ´º¸/ ™ ´¸/ ™ ´º/ ™ ´¸/ ™ ´º/ ‡ 11-12Statistical Operations Programming Page Simple Programming RPN mode 5 !Nz ALG mode 5 !zN‘Simple Programming Example a Simple Program Display Description RPN mode ALG modeRPN mode 12-2Simple Programming Program Boundaries LBL and RTN Selecting a ModeDesigning a Program Program Labels Strengths of RPN Operations Using RPN, ALG and Equations in ProgramsData Input and Output ALG Operations Entering a Program To enter a program into memory 12-6Simple Programming Keys That ClearTo enter an equation in a program line Function Names in Programs RPN modeExample Entering a Labeled Program 12-8Simple Programming HN ZLR Example Entering a Program with an Equation Executing a Program XEQ Testing a ProgramRunning a Program NzX Example Testing a Program 12-10Simple Programming Entering and Displaying Data Using Input for Entering Data@ 12-12Simple Programming To use the Input function in a program Using View for Displaying Data To respond to a prompt 12-14Simple Programming Using Equations to Display MessagesExample INPUT, VIEW, and Messages in a Program ›p NzLR LR z › LH = 2π R2 + 2π RH = 2π R R + H Displaying Information without Stopping 12-16Simple Programming Programming a Stop or Pause STOP, PSE Error StopsStopping or Interrupting a Program Interrupting a Running Program To delete a program line Editing a Program12-18Simple Programming To insert a program line Program Memory Viewing Program Memory Clearing One or More Programs Memory UsageCatalog of Programs MEM 12-20Simple Programming Checksum To clear all programs from memory Programming with Base Selecting a Base Mode in a ProgramNonprogrammable Functions V Numbers Entered in Program Lines Decimal mode set Hexadecimal mode setPolynomial Expressions and Horners Method Ax4 + Bx3 + Cx2 + Dx + E ‰X Keys Display ALG mode12-24Simple Programming Checksum and length E41A Page Routines in Programs Programming TechniquesProgramming Techniques Calling Subroutines XEQ, RTN 13-2Programming Techniques Nested Subroutines Example a Nested Subroutine 13-4Programming Techniques Branching GTOA2 + B2 Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 13-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus 13-8Programming Techniques Program Lines Description RPN modeFlags !- % ! ! ! º¸@ ! Fraction-Control Flags Status Clear FlagSet 13-10Programming Techniques Flags Menu Menu Key Description Using FlagsAnnunciators for Set Flags Example Using Flags 13-12Programming Techniques Program Lines Description RPN mode$ @ $ $ @ $ 13-14Programming Techniques Example Controlling the Fraction Display Program Lines Description Loops 13-16Programming Techniques ! ! Conditional Loops GTO . ! º6¸@ ! #$ ! 13-18Programming Techniques Loops with Counters DSE, ISGLoop-Control Number $ ! $ $ $ Variable Indirectly Addressing Variables and Labels13-20Programming Techniques Indirect Address If i contains Then i will address Example Choosing Subroutines With Program Control with13-22Programming Techniques ! L - L & %1L2 If i holds Then XEQi callsProgram lines Example Loop Control With Equations with 13-24Programming Techniques L 1L2 Page Solving and Integrating Programs Solving and Integrating ProgramsSolving a Program To solve a programmed function 14-2Solving and Integrating Programs Example Program Using ALGV= N x R x T Pressure ⋅ volume. Pressure ⋅ volume LP z LV ’ LN z LR z LT ‘ Example Program Using Equation14-4Solving and Integrating Programs @ @ ‘10 !@ # / / label #variable Using Solve in a Program14-6Solving and Integrating Programs Example Solve in a Program Integrating a Program Program Lines In RPN modeTo integrate a programmed function 14-8Solving and Integrating Programs To write a program for ≥ FN Sin Using Integration in a Program/ label ≥ G variable 14-10Solving and Integrating ProgramsExample ≥ FN in a Program Restrictions on Solving and Integrating Page Mathematics Programs Mathematics ProgramsVector Operations = R cosP = arctan = XU + YV + ZW 15-2Mathematics ProgramsV1 = X i + Y j + Z k V2=U i + V j + W k X2 + Y2 + Z2 and P Program Listing Program Lines Description ALG mode 15-4Mathematics Programs Goes to the vector-addition routine 15-6Mathematics Programs Remarks Flags UsedProgram Instructions 15-8Mathematics Programs Variables Used XR 15-10Mathematics Programs@ 07 g !@ 125 g @ 15-12Mathematics Programs Solutions of Simultaneous EquationsAX + DY + GZ = J BX + EY + HZ = K CX + FY + IZ = L % 15-14Mathematics Programs Mathematics Programs 15-16Mathematics Programs Flags Used 15-18Mathematics Programs Scratch @ @ Polynomial Root Finder15-20Mathematics Programs @ @ X2 + J Lx + K M = Where J = a3/2 = y0 /2X2 + J + Lx + K + M = ⋅ the sign of JK a1/2 15-22Mathematics Programs Polynomial 15-24Mathematics Programs ! B2= -a2 Checksum and length C7A6B0 =a04a0 a32 a12 B1 = a3a1 4a0 15-26Mathematics Programs JK. a1 + L + M 15-28Mathematics Programs Terms and Coefficients Order 15-30Mathematics Programs %/ Coordinate Transformations 15-32Mathematics Programs Old coordinate System 15-34Mathematics Programs Checksum and length 8C82 15-36Mathematics Programs Remark Ÿ @ 15-38Mathematics Programs Curve Fitting Statistics ProgramsStatistics Programs = B + MIn 16-2Statistics Programs Description 16-4Statistics Programs #$ #$ 16-6Statistics Programs 16-8Statistics Programs XS%@ 40.5 g &@ value 104.5 g %@ 38.6 g &@ %@ 37.9 g &@ / 16-10Statistics Programs/ / %@ Logarithmic Exponential Power Normal and Inverse-Normal Distributions 16-12Statistics Programs Function 16-14Statistics Programs ª º ª -+. H % ! Inverse program Variable used temporarily to pass the value S ⋅ 2 π toXS@ 16-16Statistics Programs Grouped Standard Deviation 2f − 16-18Statistics Programs Updates ƒxi 2fi in register Increments or decrements N 16-20Statistics Programs %@ @ Group/ XU/ %@ 13 g @ / %@ 16-22Statistics Programs%@ %@ Time Value of Money Miscellaneous Programs and EquationsMiscellaneous Programs and Equations ›LI …LN `QLI ›LF z 17-2Miscellaneous Programs and Equations Solve instructions šas Keys Display Description RPN mode17-4Miscellaneous Programs and Equations Retains 5750 in B calculates monthly interest rate Prime Number Generator 17-6Miscellaneous Programs and Equations LBL Y 17-8Miscellaneous Programs and Equations #$ No test is made to ensure that the input is greater than 17-10Miscellaneous Programs and Equations Appendixes and Reference Page Calculator Support Support, Batteries ServiceSupport, Batteries, and Service A-1 Answers to Common Questions Environmental Limits 2Support, Batteries, and ServiceChanging the Batteries Support, Batteries, and Service A-3 To install batteries Do not mutilate, puncture, or dispose of batteries Testing Calculator Operation4Support, Batteries, and Service Fire. The batteries can burst or explode Self-Test Support, Batteries, and Service A-5™Ÿ˜—š Warranty 6Support, Batteries, and Service Support, Batteries, and Service A-7 ServiceEurope Country Telephone numbers Asia Pacific Country Telephone numbers 8Support, Batteries, and ServiceAmerica Country Telephone numbers Regulatory Information Support, Batteries, and Service A-9Canada 10Support, Batteries, and Service Japan Managing Calculator Memory User Memory and the StackUser Memory and the Stack Resetting the Calculator 2User Memory and the Stack Clearing Memory DefaultCategory Neutral Operations Status of Stack LiftDisabling Operations 4User Memory and the Stack Vlabel nnnn EQN FDISP 6User Memory and the Stack Status of the Last X Register€ θ ,r About ALG ALG SummaryALG Summary C-1 Simple Arithmetic Power FunctionsDoing Two-number Arithmetic in ALG 2ALG Summary ‘27 Q… Percentage CalculationsALG Summary C-3 16.12 T Permutations and CombinationsQuotient and Remainder Of Division 4ALG Summary Keys Display Description ALG Summary C-5 Reviewing the Stack 6ALG Summary Coordinate Conversions ALG Summary C-7 Q3 z Integrating an Equation8ALG Summary To view the result of complex operations Operations with Complex NumbersALG Summary C-9 Complex Operations ` Q2 › 2 ›3 `10ALG Summary Ë5 ¹cº  ºy3 ÃË  ºy4 ÃË2ALG Summary C-11 Initial x, y Corrected x, y 12ALG Summary 20 ALG Summary C-13Page How Solve Finds a Root More about SolvingMore about Solving D-1 2More about Solving Function Whose Roots Can Be Found More about Solving D-3 Interpreting ResultsExample An Equation With One Root 4More about Solving Example An Equation with Two Roots / More about Solving D-5/ -%. 6More about Solving LX `’1.5 Example Discontinuous Function − 1= More about Solving D-7 When Solve Cannot Find a Root 8More about Solving More about Solving D-9 Example a Relative Minimum 10More about Solving Example An Asymptote More about Solving D-11 ⎟ x + 0.3 − 0.5 =#LX q LX ›3 ``… Example Find the root of the equation !1%ª1%-22 12More about SolvingExample a Local Flat Region Round-Off Error More about Solving D-13 Underflow 14More about Solving How the Integral Is Evaluated More about IntegrationMore about Integration Conditions That Could Cause Incorrect Results 2More about Integration ≥0∞ xe −x dx ‡ LX zLX ` 4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time 8More about Integration . More about Integration Page Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 # variable 4Messages Self-Test Messages Name Keys and Description Operation IndexOperation Index G-1 h ˜or —j 2Operation Index Operation Index G-3 Polar to rectangular coordinates P 4Operation Index M Operation Index G-5 ›Complex 6Operation IndexGComplex Change sign …Complex Subtraction Operation Index G-7 VRadians to degrees 8Operation IndexRHyperbolic DSE variable Mvariable Wlabel Operation Index G-9Natural exponential ?Fractional part label 10Operation IndexGTO label Vlabel Nnnn Input variable ‰variable ”I”Operation Index G-11 Integer part ISG variable Lvariable Natural logarithm 12Operation IndexLBL label •label Common logarithm FPause Operation Index G-13Permutations of n items WDegrees to radians 14Operation Index Operation Index G-15 16Operation Index Operation Index G-17 18Operation Index If x=0, skips the next program Line ≤0? 13-7 Operation Index G-19≠0? 13-7 11-10 Given an x-value Power Returns y raised to the xth power 20Operation Index Index Index-1 Index-2 Index-3 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Index-12 RPN Index-13 Index-14 View Index-15

HP 33s Scientific manual LP z LV LN z LR z LT , 14-4Solving and Integrating Programs

Models: 33s Scientific

Keys:

Description:

(In ALG mode)

value

value

value

value

Example: Program Using Equation.

Keys:

Description:

(In RPN mode)

LP z

LV

LN z

LR z

LT

14–4Solving and Integrating Programs

Keys:

Description:

(In ALG mode)

value

value

value

value

Example: Program Using Equation.

Keys:

Description:

(In RPN mode)

LP z

LV 

LN z

LR z

LT 

14–4Solving and Integrating Programs

LV

LT