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HP 50G User Manual
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HP
g gr
aphing calc
ulator
user
’s guide
H
Ed
i
ti
on
1
HP part number F2
2
2
9AA-9
0006
2
Table of Contents
Default Chapter
5
Table of Contents
5
Chapter 1 - Getting Started
30
Basic Operations
30
Batteries
30
Turning the Calculator on and off
31
Setting Time and Date
36
Selecting Calculator Modes
41
Operating Mode
42
Angle Measure
52
Selecting Cas Settings
55
Selecting Display Modes
56
Calculator Objects
61
Chapter 2 - Introducing the Calculator ,2-1
61
Editing Expressions on the Screen
63
Using the Equation Writer (Eqw) to Create Expressions
70
Creating Arithmetic Expressions
71
Creating and Editing Summations, Derivatives, and Integrals
89
Organizing Data in the Calculator
93
Functions for Manipulation of Variables
94
The Casdir Sub-Directory
95
Typing Directory and Variable Names
97
Creating Subdirectories
99
Moving Among Subdirectories
103
Deleting Subdirectories
103
Creating Variables
107
Algebraic Mode
112
Checking Variables Contents
112
Replacing the Contents of Variables
115
Copying Variables
116
Reordering Variables in a Directory
119
Moving Variables Using the Files Menu
120
Deleting Variables
121
Undo and CMD Functions
122
Example of Flag Setting: General Solutions Vs. Principal Value
125
Other Flags of Interest
126
Choose Boxes Vs. Soft Menu
127
Chapter 3 - Calculation with Real Numbers ,3-1
131
Checking Calculators Settings
131
Checking Calculator Mode
132
Real Number Calculations
132
Using Parentheses
134
Squares and Square Roots
135
Powers and Roots
135
Base-10 Logarithms and Powers of
135
Natural Logarithms and Exponential Function
136
Trigonometric Functions
136
Inverse Trigonometric Functions
136
Real Number Functions in the Mth Menu
137
Differences between Functions and Operators
137
Hyperbolic Functions and Their Inverses
139
Real Number Functions
141
Special Functions
144
Calculator Constants
146
Operations with Units
147
The Units Menu
147
Available Units
149
Converting to Base Units
152
Attaching Units to Numbers
153
Units Manipulation Tools
157
Physical Constants in the Calculator
159
Function Zfactor
162
Special Physical Functions
162
Function F
163
Function Sidens
163
Defining and Using Functions
164
Function Tinc
164
Functions Defined by more than One Expression
166
Combined Ifte Functions
167
Chapter 4 - Calculations with Complex Numbers ,4-1
168
Setting the Calculator to Complex Mode
168
Entering Complex Numbers
169
Polar Representation of a Complex Number
170
Simple Operations with Complex Numbers
171
Changing Sign of a Complex Number
172
Entering the Unit Imaginary Number
172
The Cmplx Menus
172
Cmplx Menu through the Mth Menu
173
Cmplx Menu in Keyboard
174
Functions Applied to Complex Numbers
175
Functions from the Mth Menu
176
Function Droite: Equation of a Straight Line
176
Chapter 5 - Algebraic and Arithmetic Operations ,5-1
178
Entering Algebraic Objects
178
Simple Operations with Algebraic Objects
178
Functions in the Alg Menu
180
Factor
182
Lncollect
182
Partfrac
182
Solve
182
Subst
182
Texpand
182
Other Forms of Substitution in Algebraic Expressions
183
Operations with Transcendental Functions
184
Functions in the Arithmetic Menu
186
Polynomial Menu
187
Applications of the Arithmetic Menu
189
Modular Arithmetic
189
The Proot Function
198
The Ptayl Function
198
The Quot and Remainder Functions
198
The Epsx0 Function and the Cas Variable Eps
199
The Simp2 Function
200
The Fcoef Function
201
The Froots Function
201
Step-By-Step Operations with Polynomials and Fractions
202
The Convert Menu and Algebraic Operations
203
Units Convert Menu (Option)
203
Base Convert Menu (Option)
204
Trigonometric Convert Menu (Option)
204
Matrices Convert Menu (Option)
204
Rewrite Convert Menu (Option)
204
Chapter 6 - Solution to Single Equations ,6-1
207
Symbolic Solution of Algebraic Equations
207
Function Solve
208
Function Solvevx
209
Function Zeros
210
Numerical Solver Menu
211
Polynomial Equations
212
Financial Calculations
215
Solving Equations with One Unknown through Num.slv
219
Function for Pipe Flow: Darcy
226
Function FANNING
226
The Solve Soft Menu
232
The Root Sub-Menu
232
Function Root
232
Variable Eq
232
The Solvr Sub-Menu
232
The Diffe Sub-Menu
235
The Poly Sub-Menu
235
The Sys Sub-Menu
236
The Tvm Sub-Menu
236
Chapter 7 - Solving Multiple Equations ,7-1
238
Rational Equation Systems
238
Example 1 – Projectile Motion
238
Example 2 – Stresses in a Thick Wall Cylinder
239
Solution to Simultaneous Equations with Mslv
241
Example 3 - System of Polynomial Equations
241
Example 1 - Example from the Help Facility
242
Example 2 - Entrance from a Lake into an Open Channel
242
Using the Multiple Equation Solver (Mes)
246
Application 1 - Solution of Triangles
246
Application 2 - Velocity and Acceleration in Polar Coordinates
254
Chapter 8 - Operations with Lists ,8-1
258
Creating and Storing Lists
258
Composing and Decomposing Lists
259
Operations with Lists of Numbers
259
Changing Sign
260
Real Number Functions from the Keyboard
261
Real Number Functions from the Mth Menu
262
Examples of Functions that Use Two Arguments
263
Lists of Complex Numbers
264
Lists of Algebraic Objects
265
The Mth/List Menu
265
Manipulating Elements of a List
267
Extracting and Inserting Elements in a List
267
Element Position in the List
268
Head and Tail Functions
268
The Seq Function
268
The Map Function
269
Defining Functions that Use Lists
270
Applications of Lists
272
Harmonic Mean of a List
272
Geometric Mean of a List
273
Weighted Average
274
Statistics of Grouped Data
275
Chapter 9 - Vectors ,9-1
279
Entering Vectors
279
Storing Vectors into Variables
280
Using the Matrix Writer (Mtrw) to Enter Vectors
280
Identifying, Extracting, and Inserting Vector Elements
284
Simple Operations with Vectors
286
Addition, Subtraction
286
Multiplication by a Scalar, and Division by a Scalar
286
The Mth/Vector Menu
287
Dot Product
288
Cross Product
288
Decomposing a Vector
288
Changing Coordinate System
289
Building a Two-Dimensional Vector
289
Building a Three-Dimensional Vector
289
Application of Vector Operations
292
Angle between Vectors
292
Resultant of Forces
292
Moment of a Force
293
Row Vectors, Column Vectors, and Lists
295
Function Obj
296
Function Drop
297
Transforming a Column Vector into a Row Vector
298
Transforming a List into a Vector
300
Transforming a Vector (or Matrix) into a List
301
Chapter 10 !- Creating and Manipulating Matrices ,10-1
303
Entering Matrices in the Stack
303
Using the Matrix Writer
303
Creating Matrices with Calculator Functions
304
Functions Get and Put
307
Functions Geti and Puti
307
Function Size
308
Function Trn
308
Function con
309
Function Idn
310
Function Rdm
310
Function Ranm
312
Function Sub
312
Function Vandermonde
314
A Program to Build a Matrix out of a Number of Lists
315
Function Hilbert
315
Lists Represent Columns of the Matrix
316
Manipulating Matrices by Columns
318
Function Col
319
Function Cswp
321
Manipulating Matrices by Rows
322
Function Row
323
Function Rswp
325
Function Rci
326
Function Rcij
326
Chapter 11 - Matrix Operations and Linear Algebra ,11-1
328
Operations with Matrices
328
Addition and Subtraction
329
Characterizing a Matrix (the Matrix Norm Menu)
334
Function Snrm
335
Functions Rnrm and Cnrm
336
Function Srad
337
Function Cond
337
Function Rank
338
Function Det
339
Function Trace
341
Function Tran
342
Additional Matrix Operations (the Matrix Oper Menu)
342
Function Axl
343
Function Axm
343
Function Lcxm
343
Solution of Linear Systems
344
Using the Numerical Solver for Linear Systems
345
Least-Square Solution (Function Lsq)
351
Solution with the Inverse Matrix
354
Solution by "Division" of Matrices
354
Solving Multiple Set of Equations with the same Coefficient Matrix
355
Gaussian and Gauss-Jordan Elimination
356
Step-By-Step Calculator Procedure for Solving Linear Systems
365
Residual Errors in Linear System Solutions (Function Rsd)
371
Eigenvalues and Eigenvectors
372
Function PCAR
372
Function Egvl
373
Function Jordan
374
Function Mad
375
Matrix Factorization
376
Function Lu
377
Orthogonal Matrices and Singular Value Decomposition
377
Function Svd
377
Function Schur
378
Matrix Quadratic Forms
379
Function Qr
379
The Quadf Menu
379
Function Axq
380
Function Qxa
380
Function Gauss
381
Linear Applications
381
Function Image
382
Function Isom
382
Function Mkisom
383
Chapter 12 - Graphics ,12-1
384
Graphs Options in the Calculator
384
Plotting an Expression of the Form y = F(X)
385
Some Useful Plot Operations for Function Plots
388
Saving a Graph for Future Use
390
Graphics of Transcendental Functions
391
Graph of Ln(X)
391
Graph of the Exponential Function
393
The Ppar Variable
394
Inverse Functions and Their Graphs
394
Summary of Function Plot Operation
396
Plots of Trigonometric and Hyperbolic Functions
399
The Tpar Variable
400
Plots in Polar Coordinates
401
Plotting Conic Curves
403
Parametric Plots
405
Generating a Table for Parametric Equations
408
Plotting the Solution to Simple Differential Equations
409
Truth Plots
411
Plotting Histograms, Bar Plots, and Scatter Plots
412
Bar Plots
412
Scatter Plots
414
Slope Fields
416
Fast 3D Plots
417
Wireframe Plots
419
Ps-Contour Plots
421
Y-Slice Plots
422
Gridmap Plots
423
Pr-Surface Plots
424
The Vpar Variable
425
Interactive Drawing
426
Dot+ and Dot
427
Zooming in and out in the Graphics Display
430
Zfact, Zin, Zout, and Zlast
430
Zdflt, Zauto
431
Hzin, Hzout, Vzin and Vzout
431
The Symbolic Menu and Graphs
432
The Symb/Graph Menu
433
Function Draw3Dmatrix
435
Chapter 13 - Calculus Applications ,13-1
436
The Calc (Calculus) Menu
436
Function Lim
437
Functions Deriv and Dervx
438
The Deriv&Integ Menu
439
Calculating Derivatives with
439
The Chain Rule
441
Derivatives of Equations
442
Implicit Derivatives
442
Limits and Derivatives
436
Application of Derivatives
442
Analyzing Graphics of Functions
443
Function Domain
444
Function Tabval
444
Function Tabvar
445
Using Derivatives to Calculate Extreme Points
447
Higher Order Derivatives
448
Anti-Derivatives and Integrals
449
Functions Int, Intvx, Risch, Sigma and Sigmavx
449
Definite Integrals
450
Step-By-Step Evaluation of Derivatives and Integrals
451
Integrating an Equation
452
Techniques of Integration
453
Substitution or Change of Variables
453
Integration by Parts and Differentials
454
Integration by Partial Fractions
455
Improper Integrals
455
Integration with Units
456
Infinite Series
457
Taylor and Maclaurin's Series
458
Taylor Polynomial and Reminder
458
Chapter 14 - Multi-Variate Calculus Applications ,14-1
461
Multi-Variate Functions
461
Higher-Order Derivatives
463
The Chain Rule for Partial Derivatives
464
Total Differential of a Function Z = Z(X,Y)
465
Determining Extrema in Functions of Two Variables
465
Using Function Hess to Analyze Extrema
466
Partial Derivatives
461
Multiple Integrals
468
Jacobian of Coordinate Transformation
469
Double Integral in Polar Coordinates
469
Chapter 15 - Vector Analysis Applications ,15-1
471
Gradient and Directional Derivative
471
A Program to Calculate the Gradient
472
Using Function Hess to Obtain the Gradient
472
Potential of a Gradient
473
Irrotational Fields and Potential Function
475
Vector Potential
476
Chapter 16 - Differential Equations ,16-1
478
Basic Operations with Differential Equations
478
Checking Solutions in the Calculator
479
Slope Field Visualization of Solutions
480
The Calc/Diff Menu
480
Solution to Linear and Non-Linear Equations
481
Function Ldec
481
Function Desolve
484
The Variable Odetype
485
Laplace Transforms
487
Laplace Transform and Inverses in the Calculator
488
Laplace Transform Theorems
489
Dirac's Delta Function and Heaviside's Step Function
492
Applications of Laplace Transform in the Solution of Linear Odes
494
Fourier Series
503
Function Fourier
505
Fourier Series for a Quadratic Function
505
Fourier Series for a Triangular Wave
511
Fourier Series for a Square Wave
515
Fourier Series Applications in Differential Equations
517
Fourier Transforms
519
Definition of Fourier Transforms
522
Properties of the Fourier Transform
524
Fast Fourier Transform (Fft)
524
Examples of Fft Applications
525
Solution to Specific Second-Order Differential Equations
528
The Cauchy or Euler Equation
528
Legendre's Equation
528
Chebyshev or Tchebycheff Polynomials
532
Laguerre's Equation
533
Numerical and Graphical Solutions to Odes
534
Weber's Equation and Hermite Polynomials
534
Numerical Solution of First-Order Ode
534
Graphical Solution of First-Order Ode
536
Numerical Solution of Second-Order Ode
538
Graphical Solution for a Second-Order Ode
540
Numerical Solution for Stiff First-Order Ode
542
Numerical Solution to Odes with the Solve/Diff Menu
544
Function Rkf
544
Function Rrk
545
Function Rkfstep
546
Function Rrkstep
547
Function Rkferr
548
Function Rsberr
548
Chapter 17 - Probability Applications ,17-1
550
The Mth/Probability.. Sub-Menu - Part
550
Factorials, Combinations, and Permutations
550
Random Numbers
551
Discrete Probability Distributions
552
Binomial Distribution
553
Poisson Distribution
554
Continuous Probability Distributions
555
The Gamma Distribution
555
The Exponential Distribution
555
The Beta Distribution
556
The Weibull Distribution
556
Functions for Continuous Distributions
556
Continuous Distributions for Statistical Inference
558
Normal Distribution Pdf
558
Normal Distribution Cdf
559
The Student-T Distribution
559
The Chi-Square Distribution
560
The F Distribution
561
Inverse Cumulative Distribution Functions
562
Pre-Programmed Statistical Features
568
Entering Data
568
Calculating Single-Variable Statistics
569
Obtaining Frequency Distributions
572
Fitting Data to a Function y = F(X)
577
Obtaining Additional Summary Statistics
580
Calculation of Percentiles
581
Chapter 18 - Statistical Applications ,18-1
568
The Stat Soft Menu
582
The Data Sub-Menu
583
The Par Sub-Menu
583
The 1Var Sub Menu
584
The Plot Sub-Menu
584
The Fit Sub-Menu
585
The Sums Sub-Menu
585
Example of Stat Menu Operations
586
Confidence Intervals
589
Estimation of Confidence Intervals
590
Confidence Interval for a Proportion
592
Sampling Distribution of Differences and Sums of Statistics
592
Confidence Intervals for Sums and Differences of Mean Values
593
Determining Confidence Intervals
594
Confidence Intervals for the Variance
600
Hypothesis Testing
602
Procedure for Testing Hypotheses
602
Errors in Hypothesis Testing
603
Inferences Concerning One Mean
604
Inferences Concerning Two Means
606
Paired Sample Tests
608
Inferences Concerning One Proportion
608
Testing the Difference between Two Proportions
609
Hypothesis Testing Using Pre-Programmed Features
610
Inferences Concerning One Variance
614
Inferences Concerning Two Variances
615
Additional Notes on Linear Regression
617
Prediction Error
619
Confidence Intervals and Hypothesis Testing in Linear Regression
619
Multiple Linear Fitting
624
Polynomial Fitting
626
Selecting the Best Fitting
629
Chapter 19 - Numbers in Different Bases ,19-1
633
The Base Menu
633
Functions Hex, Dec, Oct, and bin
634
Conversion between Number Systems
635
Operations with Binary Integers
636
The Logic Menu
637
The Bit Menu
638
The Byte Menu
639
Hexadecimal Numbers for Pixel References
639
Chapter 20 - Customizing Menus and Keyboard ,20-1
640
Customizing Menus
640
The Prg/Modes/Menu Menu
640
Menu Numbers (Rclmenu and Menu Functions)
641
Custom Menus (Menu and Tmenu Functions)
641
Menu Specification and Cst Variable
643
Customizing the Keyboard
644
The Prg/Modes/Keys Sub-Menu
644
Recall Current User-Defined Key List
645
Assign an Object to a User-Defined Key
645
Operating User-Defined Keys
646
Un-Assigning a User-Defined Key
646
Assigning Multiple User-Defined Keys
646
Chapter 21 - Programming in User RPL Language ,21-1
648
An Example of Programming
648
Global and Local Variables and Subprograms
649
Global Variable Scope
651
The Prg Menu
652
Local Variable Scope
652
Navigating through Rpn Sub-Menus
653
Functions Listed by Sub-Menu
654
Keystroke Sequence for Commonly Used Commands
657
Programs for Generating Lists of Numbers
660
Examples of Sequential Programming
662
Programs Generated by Defining a Function
662
Programs that Simulate a Sequence of Stack Operations
664
Interactive Input in Programs
666
Prompt with an Input String
668
A Function with an Input String
669
Input String for Two or Three Input Values
671
Input through Input Forms
674
Creating a Choose Box
678
Identifying Output in Programs
680
Tagging a Numerical Result
680
Decomposing a Tagged Numerical Result into a Number and a Tag
680
De-Tagging" a Tagged Quantity
680
Examples of Tagged Output
681
Using a Message Box
684
Relational and Logical Operators
690
Relational Operators
690
Logical Operators
692
Program Branching
693
Branching with if
694
The If...then...end Construct
694
The Case Construct
698
Program Loops
700
The for Construct
706
The Do Construct
708
The While Construct
710
Errors and Error Trapping
711
Sub-Menu Iferr
712
User Rpl Programming in Algebraic Mode
714
Chapter 22 - Programs for Graphics Manipulation ,22-1
716
The Plot Menu
716
User-Defined Key for the Plot Menu
716
Description of the Plot Menu
717
Generating Plots with Programs
729
Two-Dimensional Graphics
729
The Variable Eq
730
Three-Dimensional Graphics
730
Examples of Interactive Plots Using the Plot Menu
730
Examples of Program-Generated Plots
732
Drawing Commands for Use in Programming
734
Pix?, Pixon, and Pixoff
736
Programming Examples Using Drawing Functions
737
Animating Graphics
741
Animating a Collection of Graphics
742
More Information on the Animate Function
744
Graphic Objects (Grobs)
744
The Grob Menu
746
A Program with Plotting and Drawing Functions
748
Modular Programming
750
Running the Program
751
A Program to Calculate Principal Stresses
753
Ordering the Variables in the Sub-Directory
753
A Second Example of Mohr's Circle Calculations
754
An Input Form for the Mohr's Circle Program
755
Character Strings
757
Chapter 23 - Charactor Strings ,23-1
757
String-Related Functions in the Type Sub-Menu
757
String Concatenation
758
The Chars Menu
758
The Characters List
759
Chapter 24 - Calculator Objects and Flags ,24-1
761
Description of Calculator Objects
761
Function Type
762
Function Vtype
762
Calculator Flags
763
System Flags
763
Functions for Setting and Changing Flags
763
User Flags
764
Chapter 25 - Date and Time Functions ,25-1
765
The Time Menu
765
Setting an Alarm
765
Time Tools
766
Browsing Alarms
766
Calculations with Dates
767
Calculating with Times
768
Alarm Functions
768
Chapter 26 - Managing Memory ,26-1
769
Memory Structure
769
The Home Directory
770
Port Memory
770
Checking Objects in Memory
771
Backup Objects
772
Backing up Objects in Port Memory
772
Backing up and Restoring Home
773
Storing, Deleting, and Restoring Backup Objects
774
Using Data in Backup Objects
775
Using Sd Cards
775
Inserting and Removing an Sd Card
775
Formatting an Sd Card
776
Accessing Objects on an Sd Card
777
Storing Objects on an Sd Card
777
Purging an Object from the Sd Card
779
Purging All Objects on the Sd Card (by Reformatting)
779
Specifying a Directory on an Sd Card
779
Using Libraries
780
Installing and Attaching a Library
780
Library Numbers
781
Deleting a Library
781
Creating Libraries
781
Backup Battery
781
Chapter 27 - the Equation Library ,27-1
783
Solving a Problem with the Equation Library
783
Troubleshooting Equation Library
783
Using the Solver
784
Using the Menu Keys
785
Browsing in the Equation Library
786
Viewing Equations
786
Viewing Variables and Selecting Units
787
Viewing the Picture
787
Using the Multiple-Equation Solver
788
Defining a Set of Equations
790
Interpreting Results from the Multiple-Equation Solver
792
Checking Solutions
793
Cas Settings
812
Numeric Solver
835
Math Menu
837
Cas Menu
838
The Main Menu
849
Limited Warranty
882
Regulatory Information
885
Federal Communications Commission Notice
885
Other manuals for HP 50G
Quick Start Guide
47 pages
Advanced User's Reference Manual
693 pages
Datasheet
3 pages
User Manual
184 pages
Specifications
2 pages
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HP 50G Specifications
General
Digits
33 digits
Battery type
CR2032
Type
Scientific
Form factor
Pocket
Weight and Dimensions
Weight
220 g
Dimensions (WxDxH)
87 x 184 x 23.5 mm
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