HP 50G

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With these four equations, whenever you launch the numerical solver you have

the following choices:

Examples of solution of equations EQNA, EQTA, EQCA, and EQFA are shown

below:

ʳʳʳʳʳ

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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