Section |
Page |
Title Page |
1 |
Introduction |
7 |
The hp 39gs vs. the hp 40gs |
7 |
Getting Started |
9 |
Some Keyboard Examples |
10 |
Keys & Notation Conventions |
11 |
The SHIFT and ALPHA keys |
11 |
The ALPHA key |
11 |
The Screen keys |
12 |
Pop-up menus & short-cuts |
12 |
Everything revolves around Aplets! |
14 |
The Finance aplet (see page 155) |
14 |
The Function aplet (see page 46) |
14 |
The Inference aplet (see page 141) |
14 |
The Linear Solver aplet (see page 150 ) |
14 |
The Parametric aplet (see page 92) |
14 |
The Polar aplet (see page 98) |
14 |
The Quadratic Explorer aplet (see page 159) |
14 |
The Sequence aplet (see page 99) |
15 |
The Solve aplet (see page 105) |
15 |
The Statistics aplet (see page 114 & 123) |
15 |
The Triangle Solve aplet (see page 152 ) |
15 |
The Trig Explorer aplet (see page 162) |
15 |
Some typical aplet views |
15 |
The HOME view |
18 |
What is the HOME view? |
18 |
Exploring the keyboard |
19 |
The screen keys |
19 |
Aplet related keys |
19 |
The arrow keys |
19 |
The SYMB, PLOT and NUM keys |
20 |
Intro to the VIEWS menu |
21 |
The VARS key |
22 |
The SETUP views |
23 |
The MODES view |
24 |
Numeric formats |
24 |
The ANS key |
26 |
The negative key |
26 |
The CHARS key |
26 |
The DEL and CLEAR keys |
27 |
Angle and Numeric settings |
28 |
Memory Management |
30 |
The MEMORY MANAGER view |
30 |
Downloaded aplets & memory |
31 |
The GRAPHICS MANAGER |
32 |
The LIBRARY MANAGER |
32 |
Fractions on the hp 39gs and hp 40gs |
33 |
Pitfalls in Fraction mode |
35 |
The HOME History |
37 |
COPYing calculations |
37 |
Clearing the History |
37 |
SHOWing results |
38 |
Storing and Retrieving Memories |
39 |
Referring to other aplets from the HOME view. |
40 |
A brief introduction to the MATH Menu |
41 |
Resetting the calculator |
42 |
Summary |
45 |
The Function Aplet |
46 |
Choose the aplet |
46 |
The SYMB view |
47 |
The XT button |
47 |
ing your function |
47 |
The NUM view |
48 |
The PLOT view |
48 |
Auto Scale |
49 |
The PLOT SETUP view |
50 |
Detail vs. Faster |
50 |
Simultaneous |
51 |
Connect |
51 |
Axes |
51 |
Labels |
51 |
Grid |
51 |
The default axis settings |
52 |
The Bar |
52 |
The MENU toggle |
52 |
The Menu Bar functions |
53 |
Trace |
53 |
Defn |
53 |
Goto |
54 |
The Zoom Sub-menu |
55 |
Center |
55 |
In/Out |
55 |
Box… |
55 |
X-Zoom In/Out x4 and Y-Zoom In/Out x4 |
56 |
Square |
56 |
Auto Scale, Decimal, Integer and Trig |
56 |
The FCN menu |
57 |
Root |
57 |
Intersection |
58 |
Slope |
58 |
Signed area… |
59 |
Definite integrals |
59 |
Tracing the integral in PLOT |
60 |
Areas between and under curves |
61 |
Extremum |
61 |
The Expert: Working with Functions Effectively |
62 |
Finding a suitable set of axes |
62 |
Composite functions |
64 |
Using functions in the HOME view |
65 |
Differentiating |
66 |
Circular functions |
67 |
Trig functions |
69 |
Retaining calculated values |
70 |
The NUM view revisited |
70 |
NumStart & NumStep |
70 |
Automatic vs. Build Your Own |
71 |
ZOOM |
71 |
Integration: The definite integral using the function |
72 |
Integration: The algebraic indefinite integral |
73 |
A caveat when integrating symbolically… |
74 |
Integration: The definite integral using PLOT variables |
75 |
Piecewise defined functions |
77 |
‘Nice’ scales |
78 |
Nice scales in the PLOT-TABLE view |
79 |
Use of brackets in functions |
79 |
Problems when evaluating limits |
80 |
Gradient at a point as the limit of the slope of a chord |
83 |
Finding and accessing polynomial roots |
84 |
The VIEWS menu |
85 |
Plot-Detail |
86 |
Plot-Table |
87 |
Nice table values |
88 |
Overlay Plot |
88 |
Auto Scale |
89 |
Decimal, Integer & Trig |
89 |
Downloaded Aplets from the Internet |
91 |
Curve Areas |
91 |
Linear Programming |
91 |
Sine Define |
91 |
Periodic Table |
91 |
The Parametric Aplet |
92 |
Choose XRng, YRng & TRng |
92 |
The effect of TRng |
93 |
TStep controls smoothness |
93 |
The Expert: Vector Functions |
95 |
Fun and games |
95 |
Example 1 |
95 |
Example 2 |
95 |
Example 2 |
95 |
Vectors |
96 |
Example 1 |
96 |
Example 2 |
97 |
The Polar Aplet |
98 |
Choose XRng, YRng & Rng |
98 |
Step and smoothness |
98 |
Changing the default for Step |
98 |
Circular circles |
98 |
The Sequence Aplet |
99 |
Recursive or non-recursive |
99 |
First, second & general terms |
99 |
Convenient screen keys provided |
100 |
The Expert: Sequences & Series |
102 |
Defining a generalized GP and the sum to n terms for it. |
102 |
Solving sequence problems |
102 |
Modeling loans |
104 |
The Solve Aplet |
105 |
Equations vs. expressions |
105 |
Entering the equation |
105 |
Solving for a missing value |
106 |
The INFO report |
106 |
Multiple solutions and the initial guess |
107 |
Example 1 |
107 |
Example 2 |
107 |
Graphing in Solve |
107 |
Transferring approximate solutions |
108 |
Referring to functions from other aplets |
108 |
Example 3 |
108 |
Example 4 |
109 |
A detailed explanation of PLOT in Solve |
110 |
The meaning of messages |
112 |
The Expert: Examples for Solve |
113 |
Easy problems |
113 |
Harder problems |
113 |
The Statistics Aplet - Univariate Data |
114 |
Uni-variate vs. Bi-variate data |
114 |
Clearing data |
114 |
Sorting data |
115 |
The STATS key |
115 |
Functions of columns |
115 |
Registering columns as ‘in use’ |
116 |
Working with frequency tables |
116 |
Auto scale |
116 |
Plot Setup options |
117 |
Box and whisker graphs |
117 |
The effect of HRng |
118 |
Grouped data & HWidth |
118 |
Centering columns in the histogram |
119 |
The Expert: Simulations & random numbers |
120 |
New columns as functions of old |
120 |
Simulating Dice |
120 |
Simulation of a normal die |
121 |
Simulating Random Variables |
121 |
The Statistics Aplet - Bivariate Data |
123 |
Uni vs. Bi-variate data |
123 |
Clearing data |
123 |
Sorting paired columns |
124 |
Entering data as ordered pairs |
124 |
Adjusting the symbols used to plot points |
124 |
The cursor |
125 |
Specifying the fit model |
125 |
Multiple data sets |
125 |
Choosing from available fit models |
126 |
The User Defined model |
127 |
Connected data |
127 |
Two Variable Statistics |
128 |
Showing the line of best fit |
129 |
A caveat for bivariate data |
130 |
Predicting using PREDY |
130 |
Predicting using the PLOT view |
131 |
RelErr as a measure of non-linear fit |
131 |
The Expert: Manipulating columns & eqns |
133 |
New columns as functions of old |
133 |
Using values from in calculations |
133 |
Obtaining coefficients from the fit model |
135 |
Finding Fit Coefficients |
135 |
Correct interpretation of the PREDX function |
136 |
Assigning rank orders to sets of data |
137 |
Using Stats to find equations from point data |
138 |
The Inference Aplet |
141 |
Hypothesis test: T-Test 1- |
141 |
Confidence interval: T-Int 1- |
143 |
Hypothesis test: T-Test - |
144 |
Hypothesis test: Z-Test 1- |
145 |
The Expert: Chi2 tests & Frequency tables |
147 |
Using the Chi2 test on a frequency table |
147 |
Importing from a frequency table |
148 |
The Linear Solver Aplet |
150 |
Example 1 |
150 |
Example 2 |
150 |
Example 3 |
151 |
The Triangle Solve Aplet |
152 |
Example 1 |
152 |
Example 2 |
153 |
Example 3 |
154 |
The Finance Aplet |
155 |
Parameters |
155 |
Ordinary compound interest |
156 |
Annuities |
157 |
Loan calculations |
157 |
Amortization |
158 |
The Quad Explorer Teaching Aplet |
159 |
Objectives |
159 |
Choosing the level |
159 |
GRAPH mode |
159 |
SYMB mode |
160 |
Test mode |
160 |
The Trig Explorer Teaching Aplet |
162 |
Objectives |
162 |
SIN vs. COS |
162 |
SYMB vs. GRPH mode |
162 |
The PLOT mode |
163 |
The SYMB mode |
163 |
The MATH menus |
165 |
Accessing the MATH menu commands |
166 |
The PHYS menu commands |
168 |
Chemistry |
168 |
Physics |
168 |
Quantum Physics |
168 |
The MATH menu commands |
169 |
The ‘Real’ group of functions |
170 |
CEILING(<num>) |
170 |
DEGRAD(<deg>) |
170 |
FLOOR(<num>) |
170 |
FNROOT(<expression>,<variable>,<guess>) |
171 |
FRAC(<num>) |
171 |
HMS (<dd.mmss>) |
172 |
HMS(<num>) |
172 |
INT(<num>) |
173 |
MANT(<num>) |
173 |
MAX(num1,num2) |
173 |
MIN(num1,num2) |
174 |
<num> MOD <divisor> |
174 |
% function(<num1>,<num2>) |
174 |
%CHANGE(<num1>,<num2>) |
175 |
%TOTAL(<num1>,<num2>) |
175 |
RADDEG(<radian_measure>) |
175 |
ROUND(<num>,<dec.pts>) |
176 |
SIGN(<num>) |
176 |
TRUNCATE(<num>) |
177 |
XPON(<num>) |
177 |
The ‘Stat-Two’ group of functions |
178 |
PREDY(<x-value>) |
178 |
PREDX(<y-value>) |
178 |
The ‘Symbolic’ group of functions |
179 |
The = ‘function’ |
179 |
ISOLATE(<expression>,<var-name>) |
179 |
LINEAR?(<expression>,<var.name>) |
180 |
QUAD(<expression>,<var.name>) |
180 |
QUOTE(<var_name>) |
181 |
The | function written as: <expression> | (var1=valu |
181 |
The ‘Tests’ group of functions |
182 |
The ‘Trigonometric’ & ‘Hyperbolic’ groups of functions |
182 |
COT, SEC etc |
182 |
EXP(<num>) |
183 |
ALOG(<num>) |
183 |
EXPM1(<num>) |
183 |
LNP1(<num>) |
184 |
The ‘Calculus’ group of functions |
184 |
(<num>,<num>,<expression>,<var_name>) |
184 |
<var_name>(<expression>) |
184 |
TAYLOR(<expression>,<var_name>,<num>) |
185 |
The ‘Complex’ group of functions |
186 |
ABS(<real>) or ABS(<complex>) |
187 |
SIGN(<real>) or SIGN(<complex>) |
187 |
ARG(<complex>) or ARG(<vector>) |
187 |
CONJ(<complex>) |
188 |
IM(<complex>) |
188 |
and RE(complex) |
188 |
The ‘Constant’ group of functions |
189 |
The ‘Convert’ group of functions |
189 |
The ‘List’ group of functions |
190 |
CONCAT(<list1>, <list2>) |
190 |
LIST(<list>) |
190 |
MAKELIST(<expression>,<var_name>,<num>,<num>,<num>) |
190 |
LIST(<list>) |
191 |
POS(<list>,<num>) |
191 |
SIZE(<list>) or SIZE(<matrix>) |
192 |
LIST(<list>) |
192 |
REVERSE(<list>) |
192 |
SORT({list}) |
192 |
The ‘Loop’ group of functions |
193 |
ITERATE(<expression>,<var_name>,<num>,<num>) |
193 |
RECURSE |
194 |
(<var_name>,<num>,<num>,<expression>) |
194 |
The ‘Matrix’ group of functions |
195 |
COLNORM(<matrix>) |
195 |
COND(<matrix>) |
195 |
CROSS([vector],[vector]) |
195 |
DET(<matrix>) |
196 |
DOT([vector],[vector]) |
196 |
EIGENVAL(<matrix>) |
196 |
EIGENVV(<matrix>) |
196 |
IDENTMAT(<size>) |
196 |
INVERSE(<matrix>) |
197 |
LQ(<matrix>) |
197 |
LSQ(<matrix1>,<matrix2>) |
198 |
LU(<matrix>) |
198 |
MAKEMAT(<expression>,<rows>,<columns>) |
198 |
QR(<matrix>) |
198 |
RANK(<matrix>) |
198 |
ROWNORM(<matrix>) |
199 |
RREF(<matrix>) |
199 |
SCHUR(<matrix>) |
200 |
SIZE(<list>) or SIZE(<matrix>) |
200 |
SPECNORM(<matrix>) |
200 |
SPECRAD(<matrix>) |
200 |
SVD(<matrix>) |
201 |
SVL(<matrix>) |
201 |
TRACE(<matrix>) |
201 |
TRN(matrix) |
201 |
The ‘Polynomial’ group of functions |
202 |
POLYCOEF([root1,root2,…]) |
202 |
POLYEVAL([coeff1,coeff2,…],value) |
202 |
POLYFORM(<expression>,<var_name>) |
203 |
POLYROOT([coeff1,coeff2,…]) |
204 |
The ‘Probability’ group of functions |
205 |
COMB(<n>,<r>) |
205 |
The ! function |
205 |
PERM(<n>,<r>) |
206 |
RANDOM |
206 |
RANDSEED(<number>) |
206 |
UTPN(<mean>,<variance>,<value>) |
207 |
UTPC(<degrees>,<value>) |
208 |
UTPF(<numerator>,<denominator>,<value>) |
208 |
UTPT(<degrees>,<value>) |
208 |
Working with Matrices |
209 |
The MATRIX Catalog |
209 |
Matrix calculations in the HOME view |
210 |
Solving a system of equations |
211 |
Finding an inverse matrix |
213 |
The dot product |
214 |
Working with Lists |
215 |
The list variables |
215 |
Operations on lists |
215 |
Statistical columns as lists |
215 |
List functions |
216 |
Editing a list |
216 |
Operations on elements |
216 |
Working with Notes & the Notepad |
217 |
Aplet notes vs. independent notes |
217 |
Independent Notes and the Notepad Catalog |
219 |
Transferring notes using IR |
219 |
Editing software |
219 |
Creating a Note |
220 |
Locking ALPHA mode |
220 |
The CHARS view |
221 |
Corrupting notes |
221 |
Working with Sketches |
222 |
Adding text to a sketch |
222 |
The DRAW menu |
223 |
DOT+ |
223 |
LINE |
223 |
BOX |
223 |
CIRCLE |
224 |
Cut and paste images |
224 |
Storing to a GROB |
224 |
Using the VAR key to paste |
224 |
Simple Animations |
225 |
Capturing the PLOT screen |
225 |
Copying & Creating aplets on the calculator |
226 |
Different models use different methods to communicate |
227 |
Sending/Receiving via the infra-red link or cable. |
228 |
Creating a copy of a Standard aplet. |
230 |
Copying and adding to the Function aplet |
230 |
Copying and adding to the Stats aplet |
231 |
Some examples of saved aplets |
232 |
The Triangles aplet |
232 |
The Prob. Distributions aplet |
232 |
The Transformer aplet |
234 |
Storing aplets & notes to the PC |
237 |
Overview |
237 |
Software is required to link to a PC |
238 |
For the hp 38g, hp 39g & hp 40g |
238 |
For the hp 39g+, hp 39gs and hp 40gs |
238 |
Both models use the same cable |
239 |
Sending from calculator to PC |
239 |
Time out |
242 |
Attached programs |
243 |
Receiving from PC to calculator |
244 |
Aplets from the Internet |
245 |
Finding aplets |
245 |
The HP39DIR files |
246 |
Organizing your collection |
247 |
Using downloaded aplets |
249 |
Deleting downloaded aplets from the calculator |
250 |
Capturing screens using the Connectivity Kit |
251 |
Capturing into the Sketch view |
251 |
Editing Notes using the Connectivity Software |
252 |
Programming the hp 39gs & hp 40gs |
255 |
The design process |
255 |
An overview |
255 |
Choosing the parent aplet |
256 |
Working with Software vs Working on the Calculator |
256 |
Naming conventions |
256 |
Planning the VIEWS menu |
257 |
The SETVIEWS command |
259 |
Special entries in the SETVIEWS command |
260 |
The ‘Start’ entry |
261 |
Example aplet #1 – Displaying info |
262 |
Example aplet #2 – The Transformer Aplet |
268 |
Designing aplets on a PC |
270 |
Example program “Log X (base b)” |
270 |
Example aplet #3 – Transformer revisited |
272 |
Example aplet #4 – The Linear Explorer aplet |
274 |
Analysing the aplet |
276 |
Alternatives to HP Basic Programming |
281 |
The sRPL programming language |
281 |
The HPG-CC Programming language |
282 |
Flash ROM |
284 |
Programming Commands |
286 |
The Aplet commands |
286 |
CHECK n, UNCHECK n |
286 |
SELECT <name> |
286 |
SETVIEWS <prompt>;<program>;<view number> |
286 |
The Branch commands |
287 |
IF <test> THEN <true clause> [ELSE <false clause>] END |
287 |
CASE <if clauses> …END: |
287 |
IFFERR <statements> THEN <statements> [ELSE <statements>] EN |
287 |
RUN <program name> |
288 |
STOP |
288 |
The Drawing commands |
289 |
ARC <x-center>;<y-center>;<radius>;<start angle>;<end angle> |
289 |
BOX <x1>;<y1>;<x2>;<y2> |
289 |
ERASE |
289 |
FREEZE |
289 |
LINE <x1>;<y1>;<x2>;<y2> |
289 |
PIXON <x>;<y> and PIXOFF <x>;<y> |
289 |
TLINE <x1>;<y1>;<x2>;<y2> |
290 |
The Graphics commands |
291 |
The Loop commands |
291 |
FOR <variable> = <start value> TO <end value> [STEP <incr |
291 |
DO <statements> UNTIL <test clause> END |
291 |
WHILE <test clause> REPEAT <statements> END |
291 |
BREAK |
292 |
The Matrix commands |
292 |
EDITMAT <matrix var> |
292 |
REDIM <matrix var>;<size> |
292 |
The Print commands |
293 |
PRDISPLAY |
293 |
PRHISTORY |
293 |
PRVAR <variable> |
293 |
The Prompt commands |
294 |
BEEP <frequency>;<duration> |
294 |
CHOOSE <variable>;<title>;<menu option1>;…. |
294 |
DISP <line number>;<expression> |
295 |
DISPXY <xpos>;<ypos>;<font>;<expression> |
295 |
DISPTIME |
296 |
GETKEY <variable> |
296 |
INPUT <variable>;<title>;<prompt>;<message>;<default value> |
296 |
MSGBOX <expression> |
296 |
PROMPT <variable> |
296 |
WAIT <duration> |
297 |
Appendix A: Some Worked Examples |
298 |
Finding the intercepts of a quadratic |
298 |
Method 1 - Using the QUAD function in HOME. |
298 |
Method 2 - Using the Function aplet. |
298 |
Method 3 - Using the POLYROOT function |
299 |
Finding complex solutions to a complex equation |
299 |
Method 1 - Using the QUAD function |
299 |
Method 2 - Using POLYROOT |
299 |
Method 3 - Using the CAS on the hp 40gs |
299 |
Finding critical points and graphing a polynomial |
300 |
Solving simultaneous equations. |
302 |
Method 1 - Graphing the lines |
302 |
Method 2 - Using a matrix |
302 |
Method 3 - Using the Linear Solver aplet |
303 |
Expanding polynomials |
304 |
Exponential growth |
305 |
Solution of matrix equations |
307 |
Finding complex roots |
308 |
Complex Roots on the hp 40gs |
309 |
Analyzing vector motion and collisions |
310 |
Circular Motion and the Dot Product |
311 |
Inference testing using the Chi2 test |
312 |
Appendix B: Teaching or Learning Calculus |
314 |
Investigating the graphs of y=xn for n an integer |
314 |
Domains and Composite Functions |
315 |
Gradient at a Point |
317 |
Gradient Function |
318 |
The Chain Rule |
319 |
Optimization |
319 |
Area Under Curves |
320 |
Fields of Slopes and Curve Families |
320 |
Inequalities |
321 |
Rectilinear Motion |
321 |
Limits |
321 |
Piecewise Defined Functions |
322 |
Sequences and Series |
322 |
Transformations of Graphs |
323 |
Appendix C: The CAS on the hp 40gs |
324 |
Introduction |
324 |
What is a CAS? |
324 |
What is the difference between the hp 39g, hp 40g, hp 39g+ a |
326 |
Using the CAS |
327 |
The current variable |
327 |
Defining new variables |
328 |
Entering and editing an expression |
328 |
Special characters |
333 |
Special editing commands – Undo, multi-select & swap |
334 |
In-line editing mode |
335 |
Cursor mode |
335 |
Changing Font |
336 |
Erasing, copying, cutting and pasting |
336 |
The CAS HOME History |
337 |
Viewing results |
337 |
The PUSH and POP commands |
338 |
Pasting to an aplet |
338 |
Evaluating algebraic expressions |
339 |
Examples using the CAS |
341 |
Example 1: Simplifying a fraction with working |
341 |
Example 2: Simplifying surds |
342 |
Example 3: Using lim |
343 |
Example 4: Factorizing expressions |
345 |
Example 5: Solving equations |
346 |
Example 6: Solving simultaneous equations |
346 |
Example 7: Solving a simultaneous integration |
348 |
Example 8: Defining a user function |
350 |
Example 9: Investigation of a complex function |
352 |
Example 10: First order linear differential equation |
357 |
The CAS menus |
358 |
The Screen menus |
358 |
The MATH menu |
359 |
The CMDS menu |
360 |
On-line help |
361 |
Configuring the CAS |
362 |
Approximate vs. Exact mode |
363 |
Num. Factor mode |
364 |
Complex vs. Real mode |
364 |
Verbose vs. nonverbose mode |
364 |
Step-by-step mode |
364 |
Increasing-powers mode |
365 |
Rigorous setting |
365 |
Simplify non-rational setting |
365 |