HP 50G

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Page K-5

These functions are available through the CONVERT/REWRITE menu (start with

„Ú). The functions are presented in Chapter 5, except for functions

XNUM and XQ, which are described next using the corresponding entries in

the CAS help facility (IL@HELP ):

XNUM XQ

Main Page

Default Chapter5
- Table of Contents5
Chapter 1 - Getting Started30
Basic Operations30
- Batteries30
- Turning the Calculator on and off31
- Setting Time and Date36
Selecting Calculator Modes41
- Operating Mode42
- Angle Measure52
Selecting Cas Settings55
Selecting Display Modes56
Calculator Objects61
Chapter 2 - Introducing the Calculator ,2-161
Editing Expressions on the Screen63
Using the Equation Writer (Eqw) to Create Expressions70
- Creating Arithmetic Expressions71
- Creating and Editing Summations, Derivatives, and Integrals89
Organizing Data in the Calculator93
- Functions for Manipulation of Variables94
- The Casdir Sub-Directory95
- Typing Directory and Variable Names97
- Creating Subdirectories99
- Moving Among Subdirectories103
- Deleting Subdirectories103
- Creating Variables107
- Algebraic Mode112
- Checking Variables Contents112
- Replacing the Contents of Variables115
- Copying Variables116
- Reordering Variables in a Directory119
- Moving Variables Using the Files Menu120
- Deleting Variables121
Undo and CMD Functions122
- Example of Flag Setting: General Solutions Vs. Principal Value125
- Other Flags of Interest126
- Choose Boxes Vs. Soft Menu127
Chapter 3 - Calculation with Real Numbers ,3-1131
Checking Calculators Settings131
Checking Calculator Mode132
Real Number Calculations132
- Using Parentheses134
- Squares and Square Roots135
- Powers and Roots135
- Base-10 Logarithms and Powers of135
- Natural Logarithms and Exponential Function136
- Trigonometric Functions136
- Inverse Trigonometric Functions136
- Real Number Functions in the Mth Menu137
- Differences between Functions and Operators137
- Hyperbolic Functions and Their Inverses139
Real Number Functions141
- Special Functions144
Calculator Constants146
Operations with Units147
- The Units Menu147
- Available Units149
- Converting to Base Units152
- Attaching Units to Numbers153
- Units Manipulation Tools157
Physical Constants in the Calculator159
- Function Zfactor162
Special Physical Functions162
- Function F163
- Function Sidens163
Defining and Using Functions164
- Function Tinc164
Functions Defined by more than One Expression166
- Combined Ifte Functions167
Chapter 4 - Calculations with Complex Numbers ,4-1168
Setting the Calculator to Complex Mode168
- Entering Complex Numbers169
- Polar Representation of a Complex Number170
Simple Operations with Complex Numbers171
- Changing Sign of a Complex Number172
- Entering the Unit Imaginary Number172
The Cmplx Menus172
- Cmplx Menu through the Mth Menu173
- Cmplx Menu in Keyboard174
Functions Applied to Complex Numbers175
- Functions from the Mth Menu176
Function Droite: Equation of a Straight Line176
Chapter 5 - Algebraic and Arithmetic Operations ,5-1178
Entering Algebraic Objects178
Simple Operations with Algebraic Objects178
Functions in the Alg Menu180
- Factor182
- Lncollect182
- Partfrac182
- Solve182
- Subst182
- Texpand182
- Other Forms of Substitution in Algebraic Expressions183
Operations with Transcendental Functions184
Functions in the Arithmetic Menu186
- Polynomial Menu187
Applications of the Arithmetic Menu189
- Modular Arithmetic189
- The Proot Function198
- The Ptayl Function198
- The Quot and Remainder Functions198
- The Epsx0 Function and the Cas Variable Eps199
- The Simp2 Function200
- The Fcoef Function201
- The Froots Function201
- Step-By-Step Operations with Polynomials and Fractions202
The Convert Menu and Algebraic Operations203
- 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 ,6-1207
Symbolic Solution of Algebraic Equations207
- Function Solve208
- Function Solvevx209
- Function Zeros210
Numerical Solver Menu211
- Polynomial Equations212
- Financial Calculations215
- Solving Equations with One Unknown through Num.slv219
  - Function for Pipe Flow: Darcy226
  - Function FANNING226
The Solve Soft Menu232
- The Root Sub-Menu232
- Function Root232
- Variable Eq232
- The Solvr Sub-Menu232
- The Diffe Sub-Menu235
- The Poly Sub-Menu235
- The Sys Sub-Menu236
- The Tvm Sub-Menu236
Chapter 7 - Solving Multiple Equations ,7-1238
Rational Equation Systems238
- Example 1 – Projectile Motion238
- Example 2 – Stresses in a Thick Wall Cylinder239
Solution to Simultaneous Equations with Mslv241
- Example 3 - System of Polynomial Equations241
- Example 1 - Example from the Help Facility242
- Example 2 - Entrance from a Lake into an Open Channel242
Using the Multiple Equation Solver (Mes)246
- Application 1 - Solution of Triangles246
- Application 2 - Velocity and Acceleration in Polar Coordinates254
Chapter 8 - Operations with Lists ,8-1258
Creating and Storing Lists258
Composing and Decomposing Lists259
Operations with Lists of Numbers259
- Changing Sign260
- Real Number Functions from the Keyboard261
Real Number Functions from the Mth Menu262
- Examples of Functions that Use Two Arguments263
Lists of Complex Numbers264
Lists of Algebraic Objects265
The Mth/List Menu265
Manipulating Elements of a List267
- Extracting and Inserting Elements in a List267
- Element Position in the List268
- Head and Tail Functions268
- The Seq Function268
- The Map Function269
Defining Functions that Use Lists270
Applications of Lists272
- Harmonic Mean of a List272
- Geometric Mean of a List273
- Weighted Average274
- Statistics of Grouped Data275
Chapter 9 - Vectors ,9-1279
Entering Vectors279
- Storing Vectors into Variables280
- Using the Matrix Writer (Mtrw) to Enter Vectors280
Identifying, Extracting, and Inserting Vector Elements284
Simple Operations with Vectors286
- Addition, Subtraction286
- Multiplication by a Scalar, and Division by a Scalar286
The Mth/Vector Menu287
- Dot Product288
- Cross Product288
- Decomposing a Vector288
- Changing Coordinate System289
- Building a Two-Dimensional Vector289
- Building a Three-Dimensional Vector289
Application of Vector Operations292
- Angle between Vectors292
- Resultant of Forces292
- Moment of a Force293
Row Vectors, Column Vectors, and Lists295
- Function Obj296
- Function Drop297
- Transforming a Column Vector into a Row Vector298
- Transforming a List into a Vector300
- Transforming a Vector (or Matrix) into a List301
Chapter 10 !- Creating and Manipulating Matrices ,10-1303
Entering Matrices in the Stack303
- Using the Matrix Writer303
Creating Matrices with Calculator Functions304
- Functions Get and Put307
- Functions Geti and Puti307
- Function Size308
- Function Trn308
- Function con309
- Function Idn310
- Function Rdm310
- Function Ranm312
- Function Sub312
- Function Vandermonde314
A Program to Build a Matrix out of a Number of Lists315
- Function Hilbert315
- Lists Represent Columns of the Matrix316
Manipulating Matrices by Columns318
- Function Col319
- Function Cswp321
Manipulating Matrices by Rows322
- Function Row323
- Function Rswp325
- Function Rci326
- Function Rcij326
Chapter 11 - Matrix Operations and Linear Algebra ,11-1328
Operations with Matrices328
- Addition and Subtraction329
Characterizing a Matrix (the Matrix Norm Menu)334
- Function Snrm335
- Functions Rnrm and Cnrm336
- Function Srad337
- Function Cond337
- Function Rank338
- Function Det339
- Function Trace341
- Function Tran342
Additional Matrix Operations (the Matrix Oper Menu)342
- Function Axl343
- Function Axm343
- Function Lcxm343
Solution of Linear Systems344
- Using the Numerical Solver for Linear Systems345
- Least-Square Solution (Function Lsq)351
- Solution with the Inverse Matrix354
- Solution by "Division" of Matrices354
- Solving Multiple Set of Equations with the same Coefficient Matrix355
- Gaussian and Gauss-Jordan Elimination356
- Step-By-Step Calculator Procedure for Solving Linear Systems365
- Residual Errors in Linear System Solutions (Function Rsd)371
Eigenvalues and Eigenvectors372
- Function PCAR372
- Function Egvl373
- Function Jordan374
- Function Mad375
Matrix Factorization376
- Function Lu377
- Orthogonal Matrices and Singular Value Decomposition377
- Function Svd377
- Function Schur378
Matrix Quadratic Forms379
- Function Qr379
- The Quadf Menu379
- Function Axq380
- Function Qxa380
- Function Gauss381
Linear Applications381
- Function Image382
- Function Isom382
- Function Mkisom383
Chapter 12 - Graphics ,12-1384
Graphs Options in the Calculator384
Plotting an Expression of the Form y = F(X)385
- Some Useful Plot Operations for Function Plots388
Saving a Graph for Future Use390
Graphics of Transcendental Functions391
- Graph of Ln(X)391
- Graph of the Exponential Function393
The Ppar Variable394
Inverse Functions and Their Graphs394
Summary of Function Plot Operation396
Plots of Trigonometric and Hyperbolic Functions399
- The Tpar Variable400
Plots in Polar Coordinates401
Plotting Conic Curves403
Parametric Plots405
Generating a Table for Parametric Equations408
Plotting the Solution to Simple Differential Equations409
Truth Plots411
Plotting Histograms, Bar Plots, and Scatter Plots412
- Bar Plots412
- Scatter Plots414
Slope Fields416
Fast 3D Plots417
Wireframe Plots419
Ps-Contour Plots421
Y-Slice Plots422
Gridmap Plots423
Pr-Surface Plots424
- The Vpar Variable425
Interactive Drawing426
- Dot+ and Dot427
Zooming in and out in the Graphics Display430
- Zfact, Zin, Zout, and Zlast430
- Zdflt, Zauto431
- Hzin, Hzout, Vzin and Vzout431
The Symbolic Menu and Graphs432
- The Symb/Graph Menu433
Function Draw3Dmatrix435
Chapter 13 - Calculus Applications ,13-1436
The Calc (Calculus) Menu436
- Function Lim437
- Functions Deriv and Dervx438
- The Deriv&Integ Menu439
- Calculating Derivatives with439
- The Chain Rule441
- Derivatives of Equations442
- Implicit Derivatives442
Limits and Derivatives436
Application of Derivatives442
- Analyzing Graphics of Functions443
- Function Domain444
- Function Tabval444
- Function Tabvar445
- Using Derivatives to Calculate Extreme Points447
- Higher Order Derivatives448
Anti-Derivatives and Integrals449
- Functions Int, Intvx, Risch, Sigma and Sigmavx449
- Definite Integrals450
Step-By-Step Evaluation of Derivatives and Integrals451
Integrating an Equation452
Techniques of Integration453
- Substitution or Change of Variables453
- Integration by Parts and Differentials454
- Integration by Partial Fractions455
- Improper Integrals455
Integration with Units456
Infinite Series457
- Taylor and Maclaurin's Series458
- Taylor Polynomial and Reminder458
Chapter 14 - Multi-Variate Calculus Applications ,14-1461
Multi-Variate Functions461
- Higher-Order Derivatives463
- The Chain Rule for Partial Derivatives464
- Total Differential of a Function Z = Z(X,Y)465
- Determining Extrema in Functions of Two Variables465
- Using Function Hess to Analyze Extrema466
Partial Derivatives461
Multiple Integrals468
- Jacobian of Coordinate Transformation469
- Double Integral in Polar Coordinates469
Chapter 15 - Vector Analysis Applications ,15-1471
Gradient and Directional Derivative471
- A Program to Calculate the Gradient472
- Using Function Hess to Obtain the Gradient472
Potential of a Gradient473
- Irrotational Fields and Potential Function475
Vector Potential476
Chapter 16 - Differential Equations ,16-1478
Basic Operations with Differential Equations478
- Checking Solutions in the Calculator479
- Slope Field Visualization of Solutions480
The Calc/Diff Menu480
Solution to Linear and Non-Linear Equations481
- Function Ldec481
- Function Desolve484
- The Variable Odetype485
Laplace Transforms487
- Laplace Transform and Inverses in the Calculator488
- Laplace Transform Theorems489
- Dirac's Delta Function and Heaviside's Step Function492
- Applications of Laplace Transform in the Solution of Linear Odes494
Fourier Series503
- Function Fourier505
- Fourier Series for a Quadratic Function505
- Fourier Series for a Triangular Wave511
- Fourier Series for a Square Wave515
- Fourier Series Applications in Differential Equations517
Fourier Transforms519
- Definition of Fourier Transforms522
- Properties of the Fourier Transform524
Fast Fourier Transform (Fft)524
- Examples of Fft Applications525
Solution to Specific Second-Order Differential Equations528
- The Cauchy or Euler Equation528
- Legendre's Equation528
- Chebyshev or Tchebycheff Polynomials532
- Laguerre's Equation533
Numerical and Graphical Solutions to Odes534
- Weber's Equation and Hermite Polynomials534
- Numerical Solution of First-Order Ode534
- Graphical Solution of First-Order Ode536
- Numerical Solution of Second-Order Ode538
- Graphical Solution for a Second-Order Ode540
- Numerical Solution for Stiff First-Order Ode542
Numerical Solution to Odes with the Solve/Diff Menu544
- Function Rkf544
- Function Rrk545
- Function Rkfstep546
- Function Rrkstep547
- Function Rkferr548
- Function Rsberr548
Chapter 17 - Probability Applications ,17-1550
The Mth/Probability.. Sub-Menu - Part550
- Factorials, Combinations, and Permutations550
- Random Numbers551
Discrete Probability Distributions552
- Binomial Distribution553
- Poisson Distribution554
Continuous Probability Distributions555
- The Gamma Distribution555
- The Exponential Distribution555
- The Beta Distribution556
- The Weibull Distribution556
- Functions for Continuous Distributions556
Continuous Distributions for Statistical Inference558
- Normal Distribution Pdf558
- Normal Distribution Cdf559
- The Student-T Distribution559
- The Chi-Square Distribution560
- The F Distribution561
Inverse Cumulative Distribution Functions562
Pre-Programmed Statistical Features568
- Entering Data568
- Calculating Single-Variable Statistics569
- Obtaining Frequency Distributions572
- Fitting Data to a Function y = F(X)577
- Obtaining Additional Summary Statistics580
- Calculation of Percentiles581
Chapter 18 - Statistical Applications ,18-1568
The Stat Soft Menu582
- The Data Sub-Menu583
- The Par Sub-Menu583
- The 1Var Sub Menu584
- The Plot Sub-Menu584
- The Fit Sub-Menu585
- The Sums Sub-Menu585
- Example of Stat Menu Operations586
- Confidence Intervals589
- Estimation of Confidence Intervals590
- Confidence Interval for a Proportion592
- Sampling Distribution of Differences and Sums of Statistics592
- Confidence Intervals for Sums and Differences of Mean Values593
Determining Confidence Intervals594
- Confidence Intervals for the Variance600
- Hypothesis Testing602
- Procedure for Testing Hypotheses602
- Errors in Hypothesis Testing603
- Inferences Concerning One Mean604
- Inferences Concerning Two Means606
- Paired Sample Tests608
- Inferences Concerning One Proportion608
- Testing the Difference between Two Proportions609
- Hypothesis Testing Using Pre-Programmed Features610
- Inferences Concerning One Variance614
- Inferences Concerning Two Variances615
Additional Notes on Linear Regression617
- Prediction Error619
- Confidence Intervals and Hypothesis Testing in Linear Regression619
Multiple Linear Fitting624
Polynomial Fitting626
- Selecting the Best Fitting629
Chapter 19 - Numbers in Different Bases ,19-1633
The Base Menu633
- Functions Hex, Dec, Oct, and bin634
- Conversion between Number Systems635
- Operations with Binary Integers636
The Logic Menu637
The Bit Menu638
The Byte Menu639
Hexadecimal Numbers for Pixel References639
Chapter 20 - Customizing Menus and Keyboard ,20-1640
Customizing Menus640
- The Prg/Modes/Menu Menu640
- Menu Numbers (Rclmenu and Menu Functions)641
- Custom Menus (Menu and Tmenu Functions)641
- Menu Specification and Cst Variable643
Customizing the Keyboard644
- The Prg/Modes/Keys Sub-Menu644
- Recall Current User-Defined Key List645
- Assign an Object to a User-Defined Key645
- Operating User-Defined Keys646
- Un-Assigning a User-Defined Key646
- Assigning Multiple User-Defined Keys646
Chapter 21 - Programming in User RPL Language ,21-1648
An Example of Programming648
- Global and Local Variables and Subprograms649
- Global Variable Scope651
The Prg Menu652
- Local Variable Scope652
- Navigating through Rpn Sub-Menus653
- Functions Listed by Sub-Menu654
- Keystroke Sequence for Commonly Used Commands657
Programs for Generating Lists of Numbers660
Examples of Sequential Programming662
- Programs Generated by Defining a Function662
- Programs that Simulate a Sequence of Stack Operations664
Interactive Input in Programs666
- Prompt with an Input String668
- A Function with an Input String669
- Input String for Two or Three Input Values671
- Input through Input Forms674
- Creating a Choose Box678
Identifying Output in Programs680
- Tagging a Numerical Result680
- Decomposing a Tagged Numerical Result into a Number and a Tag680
- De-Tagging" a Tagged Quantity680
- Examples of Tagged Output681
- Using a Message Box684
Relational and Logical Operators690
- Relational Operators690
- Logical Operators692
Program Branching693
- Branching with if694
- The If...then...end Construct694
- The Case Construct698
Program Loops700
- The for Construct706
- The Do Construct708
- The While Construct710
Errors and Error Trapping711
- Sub-Menu Iferr712
User Rpl Programming in Algebraic Mode714
Chapter 22 - Programs for Graphics Manipulation ,22-1716
The Plot Menu716
- User-Defined Key for the Plot Menu716
- Description of the Plot Menu717
Generating Plots with Programs729
- Two-Dimensional Graphics729
- The Variable Eq730
- Three-Dimensional Graphics730
- Examples of Interactive Plots Using the Plot Menu730
- Examples of Program-Generated Plots732
Drawing Commands for Use in Programming734
- Pix?, Pixon, and Pixoff736
- Programming Examples Using Drawing Functions737
Animating Graphics741
- Animating a Collection of Graphics742
- More Information on the Animate Function744
Graphic Objects (Grobs)744
- The Grob Menu746
A Program with Plotting and Drawing Functions748
- Modular Programming750
- Running the Program751
- A Program to Calculate Principal Stresses753
- Ordering the Variables in the Sub-Directory753
- A Second Example of Mohr's Circle Calculations754
An Input Form for the Mohr's Circle Program755
- Character Strings757
Chapter 23 - Charactor Strings ,23-1757
String-Related Functions in the Type Sub-Menu757
String Concatenation758
The Chars Menu758
The Characters List759
Chapter 24 - Calculator Objects and Flags ,24-1761
Description of Calculator Objects761
Function Type762
Function Vtype762
Calculator Flags763
- System Flags763
- Functions for Setting and Changing Flags763
- User Flags764
Chapter 25 - Date and Time Functions ,25-1765
The Time Menu765
- Setting an Alarm765
- Time Tools766
- Browsing Alarms766
Calculations with Dates767
Calculating with Times768
Alarm Functions768
Chapter 26 - Managing Memory ,26-1769
Memory Structure769
- The Home Directory770
- Port Memory770
Checking Objects in Memory771
Backup Objects772
Backing up Objects in Port Memory772
- Backing up and Restoring Home773
- Storing, Deleting, and Restoring Backup Objects774
Using Data in Backup Objects775
Using Sd Cards775
- Inserting and Removing an Sd Card775
- Formatting an Sd Card776
- Accessing Objects on an Sd Card777
- Storing Objects on an Sd Card777
- Purging an Object from the Sd Card779
- Purging All Objects on the Sd Card (by Reformatting)779
- Specifying a Directory on an Sd Card779
Using Libraries780
- Installing and Attaching a Library780
- Library Numbers781
- Deleting a Library781
- Creating Libraries781
Backup Battery781
Chapter 27 - the Equation Library ,27-1783
Solving a Problem with the Equation Library783
- Troubleshooting Equation Library783
- Using the Solver784
- Using the Menu Keys785
Browsing in the Equation Library786
- Viewing Equations786
- Viewing Variables and Selecting Units787
- Viewing the Picture787
Using the Multiple-Equation Solver788
- Defining a Set of Equations790
- Interpreting Results from the Multiple-Equation Solver792
- Checking Solutions793

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