Texas Instruments TI-85 - Section 5.2 in Text: Numerical Derivatives; nDeriv for First Derivatives

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Table of Contents5
Glossary14
Getting Started15
Menu and Menu Keys16
Selecting Menu Items16
First Steps17
Entering Expressions: Savings Account Example18
Recalling and Editing a Calculation20
Graphing on the TI-8521
Entering an Equation: Illumination Example23
Entering an Equation in the SOLVER24
Solving for a Variable25
Additional Solutions with the SOLVER26
Changing the Viewing Rectangle27
Finding a Solution from a SOLVER Graph28
Defining Functions to Graph29
Displayiing the Graph30
Tracing Along a Function31
Finding a Maximum Graphically32
Graphing the Derivative33
Zooming in on the Graph34
Finding a Root Graphically35
Other Features36
Oparating the TI-8537
Turning the TI-85 on and off38
Setting the Display Contrast39
The 2Nd and ALPHA Keys40
Alpha-Lock41
The Display42
The Home Screen42
Displaying Expressions/Results42
Returning to the Home Screen42
Display Cursors43
Busy Indicator43
The Equation Operating System44
Order of Evaluation44
Implied Multiplication45
Parentheses45
Negation45
Entering and Editing46
The Cursor Movement Keys46
The Edit Keys46
Entering a Name47
Character Entry47
Expressions and Instructions48
Entering more than One Command on a Line48
Interrupting a Calculation48
Last Answer49
Using Last Answer in an Expression49
Continuing an Expression49
Storing Results49
Last Entry50
Entries Containing more than One Command50
Reexecuting the Previous Entry50
Example: Convergence of a Series51
The TI-85 Menus52
The Menu Keys/Items52
Displaying Menus53
Displaying Additional Items in a Menu53
Selecting from Menus54
Selecting an Item from the Menu on the Eighth Line54
The Menu on the Seventh Line54
Accessing Menus from an Editor55
Selecting an Item from the Menu on the Seventh Line55
"Exiting" a Menu55
Moving Around the TI-8556
Moving to a Full-Screen Editor56
Working on a Full-Screen Editor56
Leaving an Editor56
Pull-Down Screens57
The Prompt Line57
Clearing a Prompt/Correcting an Error on the Prompt Line57
The Catalog Selection Screen58
Copying a Name to an Expression58
Leaving the Catalog58
The Custom Menu59
Entering the Name of a Function or Instruction in the Custom Menu59
Blanking a Custom Menu Entry59
Using a Custom Menu Entry in an Expression59
Setting Modes60
Checking/Changing Mode Settings60
Leaving the Mode Selection Screen60
Normal, Scientifict or Enginering Notation Display Format61
Floating or Fixed Decimal Display Setting61
Radians or Degrees Angle Setting61
Rectangular or Polar Complex Number Display Format62
Function, Polar, Parametric or Differential Equation Graphing Mode62
Decimal, Binary, Octal or Hexadecimal Number Base62
Vector Coordinate Display Format63
Differentiation Type63
Setting Modes from a Command Line63
Error Conditions64
Diagnosing/Correcting an Error64
Entering and Using Data65
Data Types66
Entering and Using Numbers67
Real Numbers67
Entering a Number in Scientific or Engineering Notation67
Complex Numbers67
Variables68
Variables Names68
System Variables68
Storing a Value to a Variable STO69
Using Variable Values70
Using a Variable in an Expression70
Displaying the Value of a Variable70
Copying/Deleting a Variable70
The VARS (Variables) Menu71
Accessing Variable Names72
Copying a Variable Name to an Expression72
Leaving the Variables Screen72
Equation Variables73
Equations73
Storing an Expresson to an Equation Variable73
Errors73
Recalling Variable Contents74
Clearing Recall74
Recalling a Program74
Variable Examples75
Constants, Programs, Graphs, and Pictures76
Storing to Named Items76
Math, Calculus, and Test Operations77
Keyboard Math Functions78
The MATH Menu79
The NUM (Number) Menu80
The MATH NUM Menu80
The Round Function80
The Ipart/Fpart/Int Function80
The Abs/Sign/Min/Max/Mod Function81
The PROB (Probability) Menu82
The MATH PROB Menu82
The Factorial/Npr/Ncr/Rand Function82
The ANGLE Menu83
The MATH ANGLE Menu83
The HYP (Hyperbolic) Menu84
The MATH HYP Menu84
The Sinh, Cosh and Tanh Functions84
The MISC (Miscellaneous) Menu85
The MATH MISC Menu85
The Sum/Prod/Seq/ICM Functions85
Sums and Products of Numeric Sequences85
The Gcd/%/Peval/Root/Eval Functions86
The > Frac Instruction86
The INTER (Interpolation) Feature87
The MATH INTER Editor87
Interpolating a Value87
Using the Interpolation Function from a Command Line87
The CALC (Calculus) Menu88
The Evalf Function88
The Nder Function89
The Der1 and Der2 Functions90
The Fnint Function91
The Fmin and Fmax Functions92
The Arc Function92
The TOLER (Tolerance) Settings93
The Δ/Tol Variables93
Setting Δ or Tol from the Home Screen of a Program93
The TEST (Relational) Menu94
The Relational Functions94
Using Tests in Expressions and Instructions94
Function Graphing95
Defining a Graph96
Graph Databases/Pictures96
Graphing Modes97
Checking and Changing the Graphing MODE97
Setting the Graphing MODE from a Program97
The GRAPH Menu and Display98
The "Smart Graph" Feature99
The GRAPH Screen99
Setting the Graph Format100
Checking/Changing FORMT Settings100
Leaving the FORMT Selection Screen100
Rectangular or Polar Graphing Coordinate Display/Cursor Coordinate on or off101
Drawline or Drawdot Graph Display/Sequential or Simultaneous Graphing101
Grid off or Grid On/Axes on or Axes off Display101
Axis Label off or Axis Label on101
Defining Functions in the y(X) List102
Entering an Expression to Define a New Function103
Editing an Existing Function in the y(X) List104
Recalling an Equation Variable into a Function104
Leaving the y(X) Editor104
Entering a y(X) Function from the Home Screen or a Program104
Selecting Functions105
Turning a Function/All Functions on or off105
Selecting Functions from the Home Screen or a Program105
Defining the Viewing Rectangle106
The Range Variables106
Checking the Viewing Rectangle106
Leaving the Range Editor106
Editing the Range Variables107
Setting a Range Variable from the Home Screen or a Program107
ΔX and Δy107
Displaying a Graph108
Graphing from the Home Screen and Programs108
Displaying more of a Graph109
Graphing a Family of Curves109
Exploring a Graph with the Free-Moving Cursor110
Graphing Accuracy110
Exploring a Graph with the TRACE Feature111
Moving Along a Function/Panning Left or Right111
Tracing a Function above or below the Display/Quickzoom/Moving from Function to Function111
Tracing a Family of Curves/Cursor Coordinate Display/Leaving TRACE111
Exploring a Graph with the ZOOM Features112
The GRAPH ZOOM Menu112
Using ZOOM Box113
Defining the ZOOM Box113
Zooming in or out114
Zooming in on a Graph114
Using ZOUT114
ZOOMX and ZOOMY114
Setting ZOOM Factors115
Checking/Editing Xfact and Yfact115
Setting ZOOM Factors from the Home Screen or a Program115
Other ZOOM Features116
Previous/Standard/Fit/Square/Trig/Decimal/Integer116
The User-Defined ZOOM117
Setting User-Defined ZOOM RANGE Variables117
Recalling the User-Defined Viewing Rectangle117
The GRAPH MATH Menu118
Setting an Interval for MATH Operations119
Lower and Upper119
Setting an Interval from a Graph119
Setting an Interval from the Home Screen or a Program119
Using the MATH Operations120
The Root Operation120
The Dy/DX Operation120
The ∫F(X)/Ycpt Operation120
The FMIN and FMAX Operations121
The ISECT Operation121
The INFLC Operation121
The DIST/ARC/TANL Operations122
Using EVAL to Analyze a Graph123
Using the Eval Function from the Home Screen or a Program123
The DRAW Menu124
The GRAPH DRAW Menu124
Drawing on a Graph125
The DRAW Operations125
Before Drawing on a Graph125
Clearing a Drawing from a Graph/From the Home Screen or a Program125
Shading Areas on a Graph126
The Shading Parameters126
Drawing a Shaded Area on a Graph127
Drawing a Line from a Graph128
Drawing a Line from the Home Screen or a Program128
Drawing Vertical Lines and Tangent Lines129
Drawing Circles130
Drawing Functions and Inverses131
Using PEN to Draw on a Graph132
Drawing Points133
The PTOFF and PTCHG Instructions133
Storing and Recalling Graph Databases134
Deleting a Graph Database134
Storing and Recalling Graph Pictures135
GRAPH Menu Items in the Program Editor136
The Vars/Range/Menus136
The Zoom/Trace Instructions136
The Dispg/Draw Instruction137
FORMT Settings/Eval Functions137
Graph Databases and Pictures137
GRAPH Menu Chart138
Example: Using Lists in Graphing140
Polar Graphing141
Steps in Defining a Polar Graph142
Setting the Graphing Mode/The Pol GRAPH Menu142
Setting the Graph Format/Displaying Polar Equations142
Defining/Selecting a Polar Equation143
Displaying the Graph143
Exploring and Analyzing a Polar Graph144
The Free-Moving Cursor144
The TRACE Feature144
The ZOOM Features145
Drawing on a Polar Graph145
Evaluating Equations for a Given Θ145
The MATH Features145
Example: Graphing a Limaçon146
Parametric Graphing147
Steps in Defining a Parametric Graph148
Setting the Graphing Mode/Graph Format148
The Param GRAPH Menu148
Displaying the Components of Parametric Equations/Deleting Paramentric Equations148
Defining Components of Parametric Equations149
Selecting Parametric Equations149
Exploring and Analyzing a Parametric Graph150
Evaluating Equations for a Given T151
Example: Simulating Motion152
Differential Equation Graphing153
Defining a Difeq Graph154
The Difeq GRAPH Menu154
Displaying the Equations154
Defining a Differential Equation155
Selecting Equations155
Setting the Initial Conditions155
Displaying and Selecting the Axes156
Displaying and Exploring a Difeq Graph157
Drawing on a Difeq Graph158
Example: Transforming a Differential Equation159
Example: Solving a Differential Equation160
Example: Linear Harmonic Oscillator161
Constants and Conversions163
The CONS (Constants) Menu164
Π and E164
Built-In Constants164
Entering and Editing Constants165
Using a Constant in an Expression165
Creating and Editing User-Defined Constants166
Defining a New User-Defined Constant166
Displaying/Editing/Deleting an Existing User-Defined Constant167
The CONV (Conversions) Menu168
Using Conversions170
Strings and Characters171
Entering and Using Strings172
String Variables173
Storing a String173
Displaying a String Variable173
The STRNG (String) Menu174
Finding a Subset/Length of a String174
Concatenating Strings174
Converting an Equation to a String175
Converting a String to an Equation175
The CHAR (Character) Menu176
Using Miscellaneous Characters177
Using Greek Characters177
Using International Characters in an Expression178
Number Bases179
Using Number Bases180
Number Base Ranges180
One's and Two's Complements180
The BASE (Number Base) Menu181
Designating the Base of a Number182
Example of Number Base Entry182
Accessing Hex Digits183
Entering Hexadecimal Digits183
Displaying Results in Another Number Base184
The BASE CONV Menu184
Using Boolean Operators185
The BASE BOOL185
The Boolean Operators And, Or, and Xor185
The Boolean Operator Not185
Manipulating Number Base Digits186
The BASE BIT186
The Rotate Functions186
The Shift Functions186
Entering and Using Complex Numbers188
Complex Number Variables188
Complex Results188
Using a Complex Number in an Expression188
The CPLX (Complex Number) Menu189
The Conj/Real/Imag Functions189
The Abs/Angle Functions190
The >Rec/>Pol Instruction190
Lists191
Entering and Using Lists192
Using a List in an Expression192
Storing a List/Displaying a List Variable193
Results of List Calculations193
Lists as Arguments193
List Elements/Accessing List Elements193
The LIST Menu194
Names of Lists194
Selecting a List195
Editing a List with the LIST Editor196
Moving Around the LIST Editor196
Using Math Functions with Lists197
List Functions198
The LIST OPS Menu198
The Sort/Min and Max/Sum Functions198
The Prod/Seq/Li>VC Functions199
The Fill Instruction199
Defining and Recalling List Dimensions200
Matrices and Vectors201
Using a Matrix in an Expression202
Entering a Matrix202
Storing a Matrix203
Displaying a Matrix Variable203
Results of Matrix Calculations203
Example: Calculating 2 Times the Matrix204
Matrix Elements204
The MATRX (Matrix) Menu205
Names of Matrixes205
Defining and Editing Matrixes with the Editor206
Selecting a Matrix206
Accepting or Changing Matrix Dimensions206
Displaying Matrix Contents in the Editor207
Editing a Matrix with the Matrix Editor208
Moving Around the Matrix Editor209
Using Math Functions with Matrixes210
The Addition and Subtraction Functions210
The Multiplication/Negation/Inverse/Square/Power Functions210
The Round/Relational/Exponential, sin an Cos/Ipart, Fpart, and Int Functions211
The MATRIX MATH Menu212
The Det/Transpose/Norm/Eigvl/Eigvc Functions212
The Rnorm/Cnorm/Lu/Cond Functions213
The MATRX OPS (Operations) Menu214
The Fill Instruction/The Ident/Aug/Randm/Functions214
Defining and Recalling Matrix Dimensions215
The DIM Function215
The Row Function216
The Ref/Rref/Rswap/Radd/Multr/Mradd Functions216
Row Functions Examples217
The MATRX CPLX (Complex) Menu218
The Conj/Real/Imag/Abs/Angle Functions218
Creating a Complex Matrix218
Storing and Using Portions of a Matrix219
Accessing a Matrix Element/Matrix Row/Submatrix219
Changing a Matrix219
Entering and Using Vectors220
Entering/Storing a Vector221
Displaying a Vector Variable221
Example of Entering a Vector222
Vector Elements222
Using a Vector Element in an Expression222
The VECTR (Vector) Menu223
Defining and Editing Vectors with the Editor224
Moving Around the Vector Editor225
Using Math Functions with Vectors226
The Addition, Subtraction, Multiplication, Division Functions226
The Negation Functions226
The Ipart, Fpart, Int/Round/Relational Functions226
The VECTR MATH Menu227
The Cross/Unitv/Norm/Dot Functions227
The VECTR OPS (Operations) Menu228
The DIM Function/The Fill Instruction228
Conversions229
Display Conversion229
The >Pol/>Cyl/>Sph>/>Rec Instruction229
The Li>VC/VC>Li Function229
The VECTR CPLX (Complex) Menu230
Equation Solving231
Entering the Equation232
Defining/Displaying the Variables233
Entering Variable Values233
Solving the Equation234
Initial Guess234
Selecting the Variable and Solving the Equation234
Equations with Multiple Roots235
Further Solutions235
Editing the Values of Variables235
The Solver Instruction on a Command Line235
Exploring the Solution Graphically236
Controlling the Solution237
Using the SOLVER237
Bounding the Solution/Setting the Lower and Upper Bounds from a SOLVER Graph237
Initial Guess/Selecting a New Guess from a SOLVER Graph237
Entering the POLY (Polynomial) Equation238
Solving the Polynomial239
Editing the Coefficients239
The Poly Functon in an Expression239
Entering SIMULT (Simultaneous) Equations240
Solving Simultaneous Equations241
Storing the Coefficients or Results/Storing a Single Value241
Editing the Equation/The Simult Function in an Expression241
Example: Simultaneous Equations242
Statistical Calculation243
Statistical Analysis244
One-Variable/Two-Variable Statistics244
Statistical Data244
The STAT (Statistical) Menu245
Selecting and Loading Lists246
Loading Lists in the Editor247
Entering and Editing Data248
Editing Data Points with the STAT Editor248
Moving Around the STAT Editor249
Sorting/Clearing Lists249
Calculating Statistical Results250
The STAT CALC Menu250
Statistical Results Display251
Calculating the Results251
One-Variable Analysis251
Polynomial Regression251
The Statistical Results252
Using a Statistical Result Variable in an Expression253
Displaying the Value of a Statistical Result Variable253
The Regression Equation/Polynomial Regressions253
The STAT DRAW Menu254
Histogram254
Scatter Plot/Line Drawng/Clearing Drawing254
The Drawf Function254
Drawing Statistical Data255
Plotting Statistical Data and Regression Equations255
Storing and Recalling a Stat Drawing255
Forecasting a Statistical Data Value256
The Forecasting Screen256
Entering the X or y Value256
Storing X and y256
Using STAT Operations on a Command Line257
Using STAT Operations on the Home Screen or from a Program257
Specifying the Lists257
The STAT CALC Instructions258
The STAT CALC Menu in the Program Editor258
The STAT VARS Menu in the Program Editor258
The STAT Forecast Functions258
The STAT DRAW Instructions259
The STAT DRAW Menu in the Program Editor259
The STAT Sort Instructions259
Example: Analyzing Two-Variable Statistics260
Programming261
Using Programs262
Menus in the Program Editor262
Memory Management262
Executing/"Breaking"/Erasing a Program263
Sample Program264
The PRGM (Program) Menu265
Entering and Editing a Program266
Selecting a Program266
Entering Program Commands267
Changing/Inserting/Deleting/Undeleting a Program Command268
The I/O (Input/Output) Menu269
The Input/Output Instructions270
The Input Instruction with Graphing/With Variables/With CBL or CBR270
The Prompt Instruction270
The Disp Instruction271
Displaying the Home Screen271
Displaying Messages and Values271
The Dispg Instruction272
The Outpt Instruction for Display272
The Outpt Instruction with CBL or CBR272
The Inpst Instrucion272
The Getky Function273
The CILCD, Ptrscrn Instructions273
The CTL (Control) Menu274
The Control Instructions275
The If/If-Then/If-Then-Else/The End Instructions275
The For/While/Repeat Instructions276
The Menu/The Lbl and Goto Instructions277
The Is>/Ds</Pause/Return/Stop Instructions278
Calling Other Programs279
Calling a Program from Another Program279
Using Application Operations in Programs280
Accessing Operations in the Program Editor280
Setting Modes and Formats from Programs280
Applications281
Characteristic Polynomial and Eigenvalues282
The Fundamental Theorem of Calculus284
Symmetry of the Roots of a Complex Number286
Fractions and Matrices287
Funding the Area between Curves288
Minimizing the Solid of Revolution289
Electrical Circuits290
Unusual Equation292
Program: Taylor Series294
Convergence of the Power Series296
Linear Circuits298
Reservoir Problem300
Predator-Prey Model302
Program: Sierpinski Triangle304
Memory Management - How to Manage Memory305
The MEM (Memory) Menu306
Checking Available Memory307
Checking Memory Used by Specific Variables307
Deleting Items from Memory308
Deleting Individual Named Items308
Resetting the TI-85309
Leaving a Memory Management Screen310
Communications Link311
The TI-85 LINK312
Linking to Another TI-85/To a PC or Macintosh312
Connecting the Cable312
The LINK Menu/Leaving a LINK Screen or Menu312
Selecting Items to Send313
The SEND Menu313
Selecting Items Within a Type313
The RANGE Items314
Transmitting Items315
Receiving Items316
The Receiving Unit316
Duplicate Name316
Insufficient Memory in Receiving Unit316
Backing up Memory317
Backing up Memory - Example318
Tables319
Table of Functions and Instructions320
Table of System Variables340
Reference Information341
Battery Information342
When to Replace the Batteries342
Effects of Replacing the Batteries342
Replacing the Batteries342
Computational Accuracy343
Error Conditions Information344
In Case of Difficulty349
Product Support350
Product Service350
Warranty Information351
Index352

Texas Instruments TI-85 - Section 5.2 in Text: Numerical Derivatives; nDeriv for First Derivatives

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