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Texas Instruments voyage 200 User Manual - Page 420

Setting the Initial Conditions, Value, For Differential Equation Graphs

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Tool ‡ Math For Differential Equation Graphs: Only 1:Value is available. • With TIME axes, the y(t) solution value (represented by yc) is displayed for a specified t value. • With CUSTOM axes, the values that correspond to x and y depend on the axes you choose. Note: During a trace, you can move the cursor to a particular point by typing a value for t and pressing ¸. You can use QuickCenter at any time during a trace, even if the cursor is still on the screen. Setting the Initial Conditions You can enter initial conditions in the Y= Editor, let the Voyage™ 200 Graphing Calculator calculate initial conditions automatically, or select them interactively from the Graph screen. Differential Equation Graphing 420

Section	Page
Voyage™ 200 Graphing Calculator Graphing Calculator	1
Getting Started	4
Initial start-up	4
Voyage™ 200 keys	10
Mode settings	20
Using the Catalog to access commands	23
Calculator Home screen	26
Working with Apps	30
Checking status information	38
Turning off the Apps desktop	40
Using the clock	41
Using menus	49
Using split screens	59
Managing Apps and operating system (OS) versions	64
Connecting your Voyage™ 200 to other devices	66
Batteries	67
Previews	70
Performing Computations	70
Symbolic Manipulation	79
Constants and Measurement Units	81
Basic Function Graphing I	85
Basic Function Graphing II	88
Basic Function Graphing III	90
Parametric Graphing	92
Polar Graphing	94
Sequence Graphing	96
3D Graphing	99
Differential Equation Graphing	103
Additional Graphing Topics	108
Tables	110
Split Screens	112
Data/Matrix Editor	115
Statistics and Data Plots	117
Programming	126
Text Operations	130
Numeric Solver	132
Number Bases	134
Memory and Variable Management	136
Operating the Calculator	144
Turning the Calculator On and Off	144
Setting the Display Contrast	146
The Voyage™ 200 Keyboard	147
Modifier Keys	149
Entering Alphabetic Characters	152
Entering Numbers	153
Entering Expressions and Instructions	155
Formats of Displayed Results	162
Editing an Expression in the Entry Line	168
Menus	172
Selecting an Application	177
Setting Modes	183
Using the Clean Up Menu to Start a New Problem	187
Using the Catalog Dialog Box	189
Storing and Recalling Variable Values	195
Status Line Indicators in the Display	199
Calculator Home Screen	203
Calculator Home Screen	203
Saving the Calculator Home Screen Entries as a Text Editor Script	208
Cutting, Copying, and Pasting Information	210
Reusing a Previous Entry or the Last Answer	214
Auto-Pasting an Entry or Answer from the History Area	218
Creating and Evaluating User-Defined Functions	220
If an Entry or Answer Is “Too Big”	226
Using the Custom Menu	228
Finding the Software Version and ID Number	230
Symbolic Manipulation	233
Using Undefined or Defined Variables	233
Using Exact, Approximate, and Auto Modes	238
Automatic Simplification	242
Delayed Simplification for Certain Built-In Functions	245
Substituting Values and Setting Constraints	247
Overview of the Algebra Menu	253
Common Algebraic Operations	256
Overview of the Calc Menu	263
Common Calculus Operations	265
User-Defined Functions and Symbolic Manipulation	267
If You Get an Out-of-Memory Error	271
Special Constants Used in Symbolic Manipulation	273
Constants and Measurement Units	277
Entering Constants or Units	277
Converting from One Unit to Another	281
Setting the Default Units for Displayed Results	285
Creating Your Own User-Defined Units	288
List of Pre-Defined Constants and Units	290
Basic Function Graphing	300
Overview of Steps in Graphing Functions	300
Setting the Graph Mode	301
Defining Functions for Graphing	303
Selecting Functions to Graph	307
Setting the Display Style for a Function	309
Defining the Viewing Window	311
Changing the Graph Format	313
Graphing the Selected Functions	315
Displaying Coordinates with the Free-Moving Cursor	317
Tracing a Function	318
Using Zooms to Explore a Graph	322
Using Math Tools to Analyze Functions	328
Polar Graphing	338
Overview of Steps in Graphing Polar Equations	338
Differences in Polar and Function Graphing	340
Parametric Graphing	345
Overview of Steps in Graphing Parametric Equations	345
Differences in Parametric and Function Graphing	347
Sequence Graphing	353
Overview of Steps in Graphing Sequences	353
Differences in Sequence and Function Graphing	355
Setting Axes for Time, Web, or Custom Plots	362
Using Web Plots	363
Using Custom Plots	369
Using a Sequence to Generate a Table	372
3D Graphing	374
Overview of Steps in Graphing 3D Equations	374
Differences in 3D and Function Graphing	376
Moving the Cursor in 3D	381
Rotating and/or Elevating the Viewing Angle	385
Animating a 3D Graph Interactively	390
Changing the Axes and Style Formats	392
Contour Plots	395
Example: Contours of a Complex Modulus Surface	401
Implicit Plots	403
Example: Implicit Plot of a More Complicated Equation	406
Differential Equation Graphing	409
Overview of Steps in Graphing Differential Equations	409
Differences in Diff Equations and Function Graphing	411
Setting the Initial Conditions	420
Defining a System for Higher-Order Equations	425
Example of a 2nd-Order Equation	427
Example of a 3rd-Order Equation	431
Setting Axes for Time or Custom Plots	434
Example of Time and Custom Axes	435
Example Comparison of RK and Euler	439
Example of the deSolve( ) Function	444
Troubleshooting with the Fields Graph Format	447
Tables	454
Overview of Steps in Generating a Table	454
Setting Up the Table Parameters	455
Displaying an Automatic Table	459
Building a Manual (Ask) Table	464
Additional Graphing Topics	469
Collecting Data Points from a Graph	469
Graphing a Function Defined on the Home Screen	471
Graphing a Piecewise Defined Function	475
Graphing a Family of Curves	479
Using the Two-Graph Mode	482
Drawing a Function or Inverse on a Graph	487
Drawing a Line, Circle, or Text Label on a Graph	490
Saving and Opening a Picture of a Graph	497
Animating a Series of Graph Pictures	500
Saving and Opening a Graph Database	503
Split Screens	506
Setting and Exiting the Split Screen Mode	506
Selecting the Active Application	512
Data/Matrix Editor	516
Overview of List, Data, and Matrix Variables	516
Starting a Data/Matrix Editor Session	520
Entering and Viewing Cell Values	523
Defining a Column Header with an Expression	528
Using Shift and CumSum Functions in a Column Header	533
Sorting Columns	535
Saving a Copy of a List, Data, or Matrix Variable	537
Statistics and Data Plots	540
Overview of Steps in Statistical Analysis	540
Performing a Statistical Calculation	541
Statistical Calculation Types	545
Statistical Variables	548
Defining a Statistical Plot	550
Statistical Plot Types	554
Using the Y= Editor with Stat Plots	558
Graphing and Tracing a Defined Stat Plot	560
Using Frequencies and Categories	563
If You Have a CBL 2™ or CBR™	568
Programming	572
Running an Existing Program	572
Starting a Program Editor Session	576
Overview of Entering a Program	579
Overview of Entering a Function	585
Calling One Program from Another	590
Using Variables in a Program	593
Using Local Variables in Functions or Programs	597
String Operations	600
Conditional Tests	603
Using If, Lbl, and Goto to Control Program Flow	606
Using Loops to Repeat a Group of Commands	610
Configuring the Voyage™ 200	616
Getting Input from the User and Displaying Output	618
Creating a Custom Menu	622
Creating a Table or Graph	627
Drawing on the Graph Screen	629
Accessing Another Voyage™ 200, a CBL 2, or a CBR	632
Debugging Programs and Handling Errors	634
Example: Using Alternative Approaches	636
Assembly-Language Programs	641
Text Editor	645
Starting a Text Editor Session	645
Entering and Editing Text	648
Entering Special Characters	655
Entering and Executing a Command Script	660
Numeric Solver	665
Displaying the Solver and Entering an Equation	665
Defining the Known Variables	669
Solving for the Unknown Variable	673
Graphing the Solution	674
Number Bases	679
Entering and Converting Number Bases	679
Performing Math Operations with Hex or Bin Numbers	681
Comparing or Manipulating Bits	683
Memory and Variable Management	688
Checking and Resetting Memory	688
Displaying the VAR-LINK Screen	690
Displaying Information about Variables on the Home Screen	693
Pasting a Variable Name to an Application	704
Archiving and Unarchiving a Variable	706
If a Garbage Collection Message Is Displayed	708
Memory Error When Accessing an Archived Variable	712
Connectivity	715
Connecting Two Units	715
Transmitting Variables, Flash Applications, and Folders	716
Transmitting Variables under Program Control	724
Upgrading the Operating System (OS)	727
Collecting and Transmitting ID Lists	732
Compatibility among the TI-89 Titanium, Voyage™ 200, TI-89, and TI-92 Plus	735
Activities	737
Analyzing the Pole-Corner Problem	737
Deriving the Quadratic Formula	739
Exploring a Matrix	742
Exploring cos(x) = sin(x)	744
Finding Minimum Surface Area of a Parallelepiped	746
Running a Tutorial Script Using the Text Editor	748
Decomposing a Rational Function	750
Studying Statistics: Filtering Data by Categories	753
CBL 2™ Program for the Voyage™ 200	757
Studying the Flight of a Hit Baseball	759
Visualizing Complex Zeros of a Cubic Polynomial	762
Solving a Standard Annuity Problem	765
Computing the Time-Value-of-Money	767
Finding Rational, Real, and Complex Factors	769
Simulation of Sampling without Replacement	771
Using Vectors to Determine Velocity	772
Appendix A: Functions and Instructions	778
Appendix B: Technical Reference	918
TI-89 Titanium / Voyage™ 200 Character Codes	936
Complex Numbers and Degree Mode	936
Accuracy Information	937
EOS (Equation Operating System) Hierarchy	939
Regression Formulas	951
setGraph( )	957
setTable( )	960
Appendix D: Service and Warranty Information	961
Texas Instruments Support and Service	961
Texas Instruments (TI) Warranty Information	962