HP 15C Manuel d'utilisateur

HP-15C Owner’s Handbook HP Part Number: 00015-90001 Edition 2.4, Sep 2011

10 Contents Appendix A: Error Conditions ... 205 Appendix B: Stack Lift and the LAST X Register ...

100 Section 8: Program Branching and Controls Flag 9. An overflow condition (described on page 61) automatically sets flag 9. Flag 9 cause

101 Section 9 Subroutines When the same set of instructions needs to be used at more than one point in a program, memory space can be conserved by st

102 Section 9: Subroutines Subroutine Limits A subroutine can call up another subroutine, and that subroutine can call up yet another subrout

Section 9: Subroutines 103 MAIN PROGRAM |¥ ´ CLEAR M (Not programmable.) 000- 001- ´ b 9 Start main program. 002- | R Radians mode. 003- O 0

104 Section 9: Subroutines Example: Nesting.       value of the expression 2222tzyx  as p

Section 9: Subroutines 105 Further Information The Subroutine Return The pending return condition means that the n instruction occurring

106 Section 10 The Index Register and Loop Control The Index register (RI) is a powerful tool in advanced programming of the HP-15C. In addition to

Section 10: The Index Register and Loop Control 107 Indirect Program Control With the Index Register The V key is used for all forms of indirect p

108 Section 10: The Index Register and Loop Control Indirect Addressing If RI contains: % will address: t V or GV will transfer to:* 21 R21 ´ b B 22

Section 10: The Index Register and Loop Control 109 To Labels. If the RI value is positive, t V and G V will transfer execution to th

Contents 11 Appendix F: Batteries ... 259 Low-Power Indication ...

110 Section 10: The Index Register and Loop Control For example, the number 0.05002 in a storage register represents: nnnnn x x x y y 0.0 5 0 0

Section 10: The Index Register and Loop Control 111 False (nnnnn > xxx) True (nnnnn  xxx) instruction ´sV loop t. 1 Instruction exit lo

112 Section 10: The Index Register and Loop Control Keystrokes Display l % 2.6458 Indirectly recalls contents of R.2. ´ X .2 2.6458 Check: same con

Section 10: The Index Register and Loop Control 113 Here is a revision of the original radioisotope decay program. This time, we will

114 Section 10: The Index Register and Loop Control Keystrokes Display 15 “ O V ´ A -15.0000 Branch line number. 2.0000 Running program loop c

Section 10: The Index Register and Loop Control 115 To display fixed point notation for all possible decimal places on the HP-15C: Keys

116 Section 10: The Index Register and Loop Control I and e For the purpose of loop control, the integer portion (the counter value) of the stored c

Section 10: The Index Register and Loop Control 117 An exception is in the case of f where the display format number in RI may range from -6 to +9

118

Part lll HP-15C Advanced Functions

12 The HP-15C: A Problem Solver The HP-15C Advanced Programmable Scientific Calculator is a powerful problem solver, convenient to carry and

120 Section 11 Calculating With Complex Numbers The HP-15C enables you to calculate with complex numbers, that is, numbers of the form a +

Section 11: Calculating With Complex Numbers 121 Complex mode is activated 1) automatically, when executing ´ V or ´ }; or 2) by setting flag 8,

122 Section 11: Calculating With Complex Numbers Example: Add 2 + 3i and 4 + 5i. (The operations are illustrated in the stack diagrams following the

Section 11: Calculating With Complex Numbers 123 Re Im Re Im Re Im Re Im Re Im T 9 8 7 7 7 0 Z 8 7 6 6 7 0 Y 7 6 2 2

124 Section 11: Calculating With Complex Numbers Stack Lift in Complex Mode Stack lift operates on the imaginary stack as it does on the real stack

Section 11: Calculating With Complex Numbers 125 of Complex mode. Instead, you can do either of the following:  Multiply by -1.  If you don&ap

126 Section 11: Calculating With Complex Numbers Clearing the Imaginary X-Register. To clear the number in the imaginary X-register, press ´ }, then

Section 11: Calculating With Complex Numbers 127 Entering Complex Numbers with −. The clearing functions − and ` can also be used with } as an al

128 Section 11: Calculating With Complex Numbers Re Im Re Im Re Im Re Im T a b a b a b a b Z c d c d c d c d Y e f e f e f e f X 7 8

Section 11: Calculating With Complex Numbers 129 Entering a Pure Imaginary Number There is a shortcut for entering a pure imaginary number into th

The HP-15C: A Problem Solver 13 The display format used in this handbook is • 4 (the decimal point is    

130 Section 11: Calculating With Complex Numbers Storing and Recalling Complex Numbers The O and l functions act on the real X-register only; theref

Section 11: Calculating With Complex Numbers 131 One-Number Functions The following functions operate on both the real and imaginary parts of the

132 Section 11: Calculating With Complex Numbers Conditional Tests For programming, the four conditional tests below will work in the complex sense:

Section 11: Calculating With Complex Numbers 133 Complex Results from Real Numbers In the preceding examples, the entry of complex numbers had ens

134 Section 11: Calculating With Complex Numbers a + ib = r (cos θ + i sin θ) = reiθ (polar) rθ (phasor) ; and : can be used to interconvert the

Section 11: Calculating With Complex Numbers 135 Example: Find the sum 2(cos 65° + i sin 65°) + 3(cos 40° + i sin 40°) and express the result i

136 Section 11: Calculating With Complex Numbers Keystrokes Display 2 ´ } 0.0000 2i. Display shows real part. 8 “ v -8.0000 6 ´ V -8.0000 -8 + 6

Section 11: Calculating With Complex Numbers 137 For Further Information The HP-15C Advanced Functions Handbook presents more detailed and

138 Section 12 Calculating With Matrices The HP-15C enables you to perform matrix calculations, giving you the capability to handle advance

Section 12: Calculating with Matrices 139 Keystrokes Display | " 8 Deactivates Complex mode. 2 v ´ m A 2.0000 Dimensions matrix A to be 2

14 The HP-15C: A Problem Solver The time an object takes to fall to the ground (ignoring air friction) is given by the formula g2ht , where t = ti

140 Section 12: Calculating with Matrices Keystrokes Display l > B b 2 1 Enters descriptor for B, the 2×1 constant matrix. l > A A 2 2 Enters

Section 12: Calculating with Matrices 141 Matrix inversion, for example, can be performed on an 8×8 matrix with real elements (or on a 4×4 matrix

142 Section 12: Calculating with Matrices Example: Dimension matrix A to be a 2×3 matrix. Keystrokes Display 2 v 2.0000 Keys number of rows into Y

Section 12: Calculating with Matrices 143 If you redimension a matrix to a larger size, elements with the value 0 are added at the end as requir

144 Section 12: Calculating with Matrices To store or recall sequential elements of a matrix: 1. Be sure the matrix is properly dimensioned. 2. Pres

Section 12: Calculating with Matrices 145 Keystrokes Display ´ > 1 Sets beginning row and column numbers in R0 and R1 to 1. (Display shows t

146 Section 12: Calculating with Matrices Using R0 and R1. To access a particular matrix element, store its row number in R0 and its col

Section 12: Calculating with Matrices 147 Example: Recall the element in row 2, column 1 of matrix A from the previous example. Use t

148 Section 12: Calculating with Matrices operate on the matrices whose descriptors are placed in the X-register and (for some operations) the Y-reg

Section 12: Calculating with Matrices 149 While the key used for any matrix operation that stores a result in the result matrix is held down, the

The HP-15C: A Problem Solver 15 Keystrokes Display |¥ 000- Sets HP-15C to Program mode. (PRGM annunciator on.) ´ CLEAR M 000- Clears program memo

150 Section 12: Calculating with Matrices One-Matrix Operations: Sign Change, Inverse, Transpose, Norms, Determinant Keystroke(s) Result in X-regis

Section 12: Calculating with Matrices 151 Example: Calculate the transpose of matrix B. Matrix B was set in preceding examples to .954321B

152 Section 12: Calculating with Matrices Operation Elements of Result Matrix* Matrix in Y-Register Scalar in Y-Register Scalar in X-Register Matri

Section 12: Calculating with Matrices 153 Keystrokes Display 1 - b 2 3 Subtracts 1 from the elements of matrix B and stores those values in the s

154 Section 12: Calculating with Matrices Keystrokes Display - C 2 3 Calculates B - A and stores values in redimensioned result matrix C. The r

Section 12: Calculating with Matrices 155 For ÷, the matrix specified in the X-register is replaced by its LU decomposition. The ÷

156 Section 12: Calculating with Matrices Solving the Equation AX = B The ÷ function is useful for solving matrix equations of the form AX = B, wher

Section 12: Calculating with Matrices 157 Week 1 2 3 Total Weight (kg) 274 233 331 Total Value $120.32 $112.96 $151.36 Silas knows that he recei

158 Section 12: Calculating with Matrices Keystrokes Display 274 OB 274.0000 Stores b11.* 233 OB 233.0000 Stores b12. 331 OB 331.0000 Stores b13.

Section 12: Calculating with Matrices 159 Silas' deliveries were: Week 1 2 3 Cabbage (kg) 186 141 215 Broccoli (kg) 88 92 116 Calculating t

16 The HP-15C: A Problem Solver With this program loaded, you can quickly calculate the time of descent of an object from different heights. Si

160 Section 12: Calculating with Matrices Using Matrices in LU Form As noted earlier, two matrix operations (calculating a determinant and

Section 12: Calculating with Matrices 161 Instead, calculations with complex matrices are performed by using real matrices derived from t

162 Section 12: Calculating with Matrices Suppose you need to do a calculation with a complex matrix that is not written as the sum of

Section 12: Calculating with Matrices 163 Example: Store the complex matrix iiii83512734Z in the form ZC, since it is written in a form

164 Section 12: Calculating with Matrices Matrix A now represents the complex matrix Z in ZP form: PartImaginary Part Real.85233174}}

Section 12: Calculating with Matrices 165 Inverting a Complex Matrix You can calculate the inverse of a complex matrix by using the fact that (

166 Section 12: Calculating with Matrices Keystrokes Display ´ < B A 4 4 Designates B as the result matrix. ∕ b 4 4 Calculates ()-1 = (-1) a

Section 12: Calculating with Matrices 167 8. Press * to calculate XP = (YX)P. The values of these matrix elements are placed in the result matr

168 Section 12: Calculating with Matrices Writing down the elements of C,  P1101110111110100500.1100000.1108000.3100000.10000.1100000.4108500.2000

Section 12: Calculating with Matrices 169 4. Recall the descriptor of the matrix representing A into the display. 5. If the elements of A we

Part l HP-15C Fundamentals

170 Section 12: Calculating with Matrices In partitioned form, 0005 and 17020020020000010BA, where the zero elements

Section 12: Calculating with Matrices 171 Keystrokes Display ´> 2 A 4 4 Transforms AP into Ã. ´< C A 4 4 Designates matrix C as result matri

172 Section 12: Calculating with Matrices 1. Store the elements of A in memory, in the form either of AP or of AC. 2. Recall the descriptor of the m

Section 12: Calculating with Matrices 173 A problem using this procedure is given in the HP-15C Advanced Functions Handbook under Solving a Large

174 Section 12: Calculating with Matrices  Pressing ´mV dimensions the matrix specified in RI according to the dimensions in the X- and Y-register

Section 12: Calculating with Matrices 175 Several matrix functions operate on the matrix specified in the X-register only and store the res

176 Section 12: Calculating with Matrices Using Matrix Operations in a Program If the calculator is in User mode during program entry when you en

Section 12: Calculating with Matrices 177 The > 7 (row norm) and > 8 (Frobenius norm) functions also operate as conditional branching instr

178 Section 12: Calculating with Matrices Keystroke(s) Results result matrix. ´> 6 Calculates residual in result matrix. ´> 7 Calculates row n

Section 12: Calculating with Matrices 179 Keystroke(s) Results O < Designates matrix specified in X-register as result matrix. ´ U Row and col

18 Section 1 Getting Started Power On and Off The = key turns the HP-15C on and off.* To conserve power, the calculator automatically tur

180 Section 13 Finding the Roots of an Equation In many applications you need to solve equations of the form f(x)=0.* This means finding the values

Section 13: Finding the Roots of an Equation 181 The basic rules for using _ are: 1. In Program mode, key in a subroutine that evaluates

182 Section 13: Finding the Roots of an Equation Keystrokes Display ´ b 0 001–42,21, 0 Begin with b instruction. Subroutine assumes stack loaded wi

Section 13: Finding the Roots of an Equation 183 Keystrokes Display ´_ 0 5.0000 The desired root. After the routine finds and displays the

184 Section 13: Finding the Roots of an Equation You have now found the two roots of f(x) = 0. Note that this quadratic equation could have be

Section 13: Finding the Roots of an Equation 185 Keystrokes Display “ 005– 16  t / 20. ' 006– 12 “ 007– 16  e t / 20.

186 Section 13: Finding the Roots of an Equation Fahr's ridget falls to the ground 9.2843 seconds after he hurls ita remarkable toss

Section 13: Finding the Roots of an Equation 187 Because the absolute-value function is minimum near an argument of zero, specify the initial e

188 Section 13: Finding the Roots of an Equation The final case points out a potential deficiency in the subroutine rather than a limitation of the

Section 13: Finding the Roots of an Equation 189 If you have some knowledge of the behavior of the function f(x) as it varies with different value

Section 1: Getting Started 19 Notice that when you press the ´ or | prefix key, an f or g annunciator appears and remains in the displa

190 Section 13: Finding the Roots of an Equation Keystrokes Display - 003– 30 * 004– 20 (x  6) x. 8 005– 8 + 005– 40 * 007– 20 ((x  6) x + 8)

Section 13: Finding the Roots of an Equation 191 By making the height 1.5 decimeters, a 5.0×1.0×1.5-decimeter box is specified. If you ignore t

192 Section 13: Finding the Roots of an Equation  Many functions exhibit special behavior when their arguments approach zero. You can check

Section 13: Finding the Roots of an Equation 193 Restriction on the Use of _ The one restriction regarding the use of _ is that _ cannot be used

194 Section 14 Numerical Integration Many problems in mathematics, science, and engineering require calculating the definite integral of a f

Section 14: Numerical Integration 195 In Run mode: 2. Key the lower limit of integration (a) into the X-register, then press v to lift it into t

196 Section 14: Numerical Integration Keystrokes Display | ¥ Run mode. 0 v 0.0000 Key lower limit, 0, into Y-register. | $ 3.1416 

Section 14: Numerical Integration 197 Before calling the subroutine you provide to evaluate f(x), the f algorithm  just like the _ algo

198 Section 14: Numerical Integration Keystrokes Display [ 002– 23 Calculate sin θ. - 003– 30 Since a value of θ will be placed into the Y-registe

Section 14: Numerical Integration 199 Find Si(2). Key in the following subroutine to evaluate the function f(x) = (sin x) / x.* Keystrokes Display

Legal Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company ma

20 Section 1: Getting Started Keystrokes Display 6.6262 6.6262 ‛ 6.6262 00 The 00 prompts you to key in the exponent. 3 6.6262 03 (6.6262×1

200 Section 14: Numerical Integration Accuracy of f The accuracy of the integral of any function depends on the accuracy of the function itself. The

Section 14: Numerical Integration 201 Because the accuracy of any integral is limited by the accuracy of the function (as indicated in

202 Section 14: Numerical Integration If the uncertainty of an approximation is larger than what you choose to tolerate, you can decrease

Section 14: Numerical Integration 203 In the preceding example, the uncertainty indicated that the approximation might be correct to only four dec

204 Section 14: Numerical Integration Memory Requirements f requires 23 registers to operate. (Appendix C explains how they are automatically allo

205 Appendix A Error Conditions If you attempt a calculation containing an improper operation  say division by zero  the display will show E

206 Appendix A: Error Conditions  x or y is noninteger;  x < 0 or y < 0;  x > y;  x or y 10. Error 1: Improper Matrix Operatio

Appendix A: Error Conditions 207 Error 3: Improper Register Number or Matrix Element Storage register named is nonexistent or matrix eleme

208 Appendix A: Error Conditions + or -, where the dimensions are incompatible. *, where:  the dimensions are incompatible; or  the result is on

209 Appendix B Stack Lift and the LAST X Register The HP-15C calculator has been designed to operate in a natural manner. As you have seen working th

Section 1: Getting Started 21 Clearing Sequence Effect ´ CLEAR M In Run mode: Repositions program memory to line 000. In Program mode: Deletes

210 Appendix B: Stack Lift and the LAST X Register Disabling Operations Stack Lift. There are four stack-disabling operations on the calcul

Appendix B: Stack Lift and the LAST X Register 211 T y y y y Z x x x x Y 4.0000 53.1301 53.1301 53.1301 X 3 5.0000 0.0000 7 Keys: |:

212 Appendix B: Stack Lift and the LAST X Register LAST X Register The following operations save x in the LAST X register: - x H \ k + [ H ] ∆ * \

213 Appendix C Memory Allocation The Memory Space Storage registers, program lines, and advanced function execution* all draw on a common memory spac

214 Appendix C: Memory Allocation Total allocatable memory: 64 registers, numbered R2 through R65. [(dd – 1) + uu + pp + (matrix elements)

Appendix C: Memory Allocation 215 Memory Status (W) To view the current memory configuration of the calculator, press | W (memory), hold

216 Appendix C: Memory Allocation 1. Place dd, the number of the highest data storage register you want allocated, into the display. 1dd65. The n

Appendix C: Memory Allocation 217 When converting registers, note that:  You can convert registers from the common pool only if they are uncommi

218 Appendix C: Memory Allocation Your very first program instruction will commit R65 (all seven bytes) from an uncommitted register to a progr

Appendix C: Memory Allocation 219 For _ and f, allocation and deallocation of the required register space takes place automatically.* Memor

22 Section 1: Getting Started Calculations One-Number Functions A one-number function performs an operation using only the number in the display. To

220 Appendix D A Detailed Look at _ Section 13, Finding the Roots of an Equation, includes the basic information needed for the effecti

Appendix D: A Detailed Look at _ 221 As discussed in section 13, page 186, the occurrence of other situations in the iteration process indicates t

222 Appendix D: A Detailed Look at _  The function's graph is either convex everywhere or concave everywhere.  The only local mi

Appendix D: A Detailed Look at _ 223 If a calculation has a result whose magnitude is smaller than 1.000000000×10-99, the result is set

224 Appendix D: A Detailed Look at _ the root 1.0000 is found for initial estimates of 1 and 2. By recognizing situations in which roun

Appendix D: A Detailed Look at _ 225 In order to find the first time at which the height is 107 meters, use initial estimates of 0 and 1 second an

226 Appendix D: A Detailed Look at _ Execute _ again: Keystrokes Display | ¥ Run mode. 0 v 0.0000 Initial estimates. 1 1 ´ v B 4.0681 The desire

Appendix D: A Detailed Look at _ 227 Special consideration is required for a different type of situation in which _ finds a root with a nonzero

228 Appendix D: A Detailed Look at _ Solution: The equation for the shear stress for x between 0 and 10 is more efficiently programmed after rewriti

Appendix D: A Detailed Look at _ 229 Keystrokes Display | ¥ Run mode. 7 v 7.0000 Initial estimates. 14 14 ´_ 2 10.0000 Possible root. )) 1,

Section 1: Getting Started 23 Example: Calculate (9 + 17  4) ÷ 4. Keystrokes Display 9 v 9.0000 Digit entry terminated. 17 + 26.0000 (9 + 17). 4

230 Appendix D: A Detailed Look at _ If the algorithm terminates its search near a local minimum of the function's magnitude, clear the Error

Appendix D: A Detailed Look at _ 231 If Error 8 is displayed as a result of a search that         

232 Appendix D: A Detailed Look at _ Keystrokes Display ÷ 017– 10 .10/x ' 018– 12 + 019– 40 xexexe2210/. 3 020– 3 +

Appendix D: A Detailed Look at _ 233 Keystrokes Display ´ _.0 Error 8 − 1.0000 –20 Best x-value. ) 1.1250 –20 Previous value. ) 2.0000 Fu

234 Appendix D: A Detailed Look at _ add a few program lines at the end of your function subroutine. These lines should subtract the known root (to

Appendix D: A Detailed Look at _ 235 Keystrokes Display - 008– 30 * 009– 20 3 010– 3 0 011– 0 0 012– 0 3 013–

236 Appendix D: A Detailed Look at _ Return to Program mode and add instructions to your subroutine to eliminate the root just found. Keys

Appendix D: A Detailed Look at _ 237 Again, use the same initial estimates to find the next root. Keystrokes Display |¥ 0.0000 Run mode. 10 “ v

238 Appendix D: A Detailed Look at _ Using the same initial estimates each time, you have found four roots for this equation involving a fou

Appendix D: A Detailed Look at _ 239 Counting Iterations While searching for a root, _ typically samples your function at least a dozen times. Occ

24 Section 2 Numeric Functions This section discusses the numeric functions of the HP-15C (excluding statistics and advanced functions). The

240 Appendix E A Detailed Look at f Section 14, Numerical Integration, presented the basic information you need to use f This appendix discusses more

Appendix E: A Detailed Look at f 241 The uncertainty of the final approximation is a number derived from the display format, which spec

242 Appendix E: A Detailed Look at f Calculate the integral in the expression for J4 (1), 0)sin4cos( d First, switch to Program mode and ke

Appendix E: A Detailed Look at f 243 The uncertainty indicates that the displayed digits of the approximation might not include any d

244 Appendix E: A Detailed Look at f All 10 digits of the approximations in i 2 and i 3 are identical: the accuracy of the approximation in i 3 is n

Appendix E: A Detailed Look at f 245 This approximation took about twice as long as the approximation in i 3 or i 2. In this case, the alg

246 Appendix E: A Detailed Look at f )(δ)()(2xxfxF , where 2(x) is the uncertainty associated with f(x) that is caused by the approxi

Appendix E: A Detailed Look at f 247 format to i n or ^ n, where n is an integer,* implies that the 

248 Appendix E: A Detailed Look at f badxx )δ( Δ dxbaxmn ]10[0.5 )(. This integral is calculated using the samples of (x) in roughl

Appendix E: A Detailed Look at f 249 Conditions That Could Cause Incorrect Results Although the f algorithm in the HP-15C is one of the best avail

Section 2: Numeric Functions 25 Keystrokes Display 123.4567 |‘ 123.0000 |K “ |‘ -123.0000 Reversing the sign does not alter digits. |K ´q -0.45

250 Appendix E: A Detailed Look at f With this number of sample points, the algorithm will calculate the same approximation for the integral of

Appendix E: A Detailed Look at f 251 t think (naively in this case, as you'll

252 Appendix E: A Detailed Look at f The graph is a spike very close to the origin. (Actually, to illustrate f(x) the width of the spike has been co

Appendix E: A Detailed Look at f 253 Note that the rapidity of variation in the function (or its low-order derivatives) must be determi

254 Appendix E: A Detailed Look at f In many cases you will be familiar enough with the function you want to     

Appendix E: A Detailed Look at f 255 Keystrokes Display 0 v 0.000 00 Keys lower limit into Y-register. ‛ 3 1 03 Keys upper limit into

256 Appendix E: A Detailed Look at f If the interval of integration were (0, 10) so that the algorithm needed to sample the function only at va

Appendix E: A Detailed Look at f 257 Obtaining the Current Approximation to an Integral When the calculation of an integral is requiring more tim

258 Appendix E: A Detailed Look at f  If any other program line is displayed, return to Run mode and single-step (Â) through the program unt

259 Appendix F Batteries Batteries The HP-15C is shipped with two 3 Volt CR2032 Lithium batteries. Battery life depends on how the calculator is us

26 Section 2: Numeric Functions Trigonometric Operations Trigonometric Modes. The trigonometric functions operate in the trigonometric mode

260 Appendix F: Batteries To install new batteries, use the following procedure: 1. With the calculator turned off, slide the battery cover off.

Appendix F: Batteries 261 Verifying Proper Operation (Self-Tests) If it appears that the calculator will not turn on or otherwise is not operating

262 Function Summary and Index= Turns the calculator's display on and off (page 18). It is also used in resetting Continuous Memory (page 63), c

263 Function Summary and Index ‛ Enter exponent; next digits keyed in are exponents of 10 (page 19). 0 through 9 digit keys (page 22). . Decimal p

264 Function Summary and Index number in display (X-register) (enter y, then x). Causes the stack to drop (page 29). Mathematics -+-÷ Arithmetic ope

Function Summary and Index 265 matrices or of one matrix and a scalar. Stores in result matrix (page 152-155). ÷ For two matrices, multiplies inve

266 Function Summary and Index register) by truncating fractional portion (page 24). & Rounds mantissa of entire (10-digit) number in X-register

Function Summary and Index 267 ` Clears contents of display (X-register) to zero (page 21). − In Run mode: removes the last digit keyed in, or cle

268 Function Summary and Index Trigonometry D Sets decimal Degrees mode for trigonometric functionsindicated by absence of GRAD or RAD annunciator

269 Programming Summary and Index¥ Program/Run mode. Sets the calculator to Program mode (PRGM annunciator on) or Run mode (PRGM annunciator cleared)

Section 2: Numeric Functions 27 Hours.Decimal Hours Hours.Minutes Seconds Decimal Seconds (H.h) (H.MMSSs) Degrees.Decimal Hours Degrees.Minutes

270 Programming Summary and Index following the G (page 101). ‚ Back step. Moves calculator back one or more lines in program memory. (Also scrolls

271 Subject Index Page numbers in bold type indicate primary references; page numbers in regular type indicate secondary references. A ___________

272 Subject Index in matrices, 177 “, 19 Clearing blinking in display, 100 complex numbers, 125-127 display, 21 memory, 63 operations, 20-21 overflo

Subject Index 273 Continuous Memory, duration of, 62 resetting (clearing), 63 what it retains, 43, 48, 58, 61, 62 Conventions, handbook, 18 Conve

274 Subject Index s 109-111, 112, 116 E ___________________________________________ ‛, 19 Electrical circuit example, 169-171 Enabling stack lift,

Subject Index 275 G ___________________________________________ |, 18 Gamma function (!), 25 g, 26 G, 101 t, 90, 97, 98 t “, 82 H ______________

276 Subject Index uncertainty in, 202-203, 240-244, 245-249 Interchanging functions (See User mode) Interference, radio and television, 271 Intermed

Subject Index 277 dimensioning, 140, 142, 142, 174 dimensions, displaying, 142, 147 equation, complex, 168 memory, 140, 171 name (See Matrix desc

278 Subject Index Multiple roots, 234 N ___________________________________________ Negative numbers, 19 in Complex mode, 124-125 Nested calculatio

Subject Index 279 position, changing, 82, 86 running, 68-69 starting, 69 stops, 68, 78 Program execution, 69 after G, 101 after t, 97 after overf

28 Section 2: Numeric Functions Logarithmic Functions Natural Logarithm. Pressing |Z calculates the natural logarithm of the number in the display;

280 Subject Index Rice yield example, 50-56 Ridget hurling example, 184-186, 224-226 Roll down, 34 Roll up, 34 Roots, eliminating, 233, 234, 237 Roo

Subject Index 281 using as a conditional test, 192 using functions with discontinuities, 227 using functions with poles, 227 using functions with

282 Subject Index Storage arithmetic, 43 Storage registers, 42 allocation, 42, 215-217 arithmetic, 43 clearing, 43 statistics, 42, 49 Subroutine lev

Subject Index 283 X ___________________________________________ X exchange (X), 42 X exchange Y (®), 34 X-register, 32, 35, 37, 42, 60, 209-210

284 Product Regulatory & Environment Information Federal Communications Commission Notice This equipment has been tested and found to comply

Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules.

286 European Union Regulatory Notice Products bearing the CE marking comply with the following EU Directives: • Low Voltage Directive 2006

Japanese Notice Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the produc

288 Chemical Substances HP is committed to providing our customers with information about the chemical substances in our products as needed to comp

Section 2: Numeric Functions 29 Two-Number Functions The HP-15C performs two-number math functions using two values entered sequentially into the

3 Introduction Congratulations! Whether you are new to HP calculators or an experienced user, you will find the HP-15C a powerful and valuable

30 Section 2: Numeric Functions For example, to find the sales tax at 3% and total cost of a $15.76 item: Keystrokes Display 15.76 v 15.7600 Enter

Section 2: Numeric Functions 31 Rectangular Conversion. Pressing ´; (rectangular) converts a set of polar coordinates (magnitude r 

32 Section 3 The Automatic Memory Stack, LAST X, and Data Storage The Automatic Memory Stack and Stack Manipulation HP operating logic is based

Section 3: The Memory Stack, LAST X, and Data Storage 33 Any number that is keyed in or results from the execution of a numeric functio

34 Section 3: The Memory Stack, LAST X, and Data Storage shading indicates that the contents of that register will be written over when t

Section 3: The Memory Stack, LAST X, and Data Storage 35 The LAST X Register and K The LAST X register, a separate memory register, preserves the va

36 Section 3: The Memory Stack, LAST X, and Data Storage Keystrokes Display * 287.0000 Reverses the function that produced the wrong answer. 13.9

Section 3: The Memory Stack, LAST X, and Data Storage 37 lost T z z z z Z z z z z Y y y y y X 7 0 6 y6 Keys: |` 6 Y Order of

38 Section 3: The Memory Stack, LAST X, and Data Storage Nested Calculations The automatic stack lift and stack drop make it possible to

Section 3: The Memory Stack, LAST X, and Data Storage 39 T y y y y Z y x y x Y x 13 x 65 X 13 5 65 4 Keys: 5 * 4 T y y y y Z x

4 Contents The HP-15C: A Problem Solver ... 12 A Quick Look at v ...

40 Section 3: The Memory Stack, LAST X, and Data Storage Example: Two close stellar neighbors of Earth are Rigel Centaurus (4.3 light-years away) an

Section 3: The Memory Stack, LAST X, and Data Storage 41 Loading the Stack with a Constant. Because the number in the T-register is replicated when

42 Section 3: The Memory Stack, LAST X, and Data Storage Keystrokes Display * 1,150.0000 Population at the end of day 1. * 1,322.5000 Day 2. * 1,5

Section 3: The Memory Stack, LAST X, and Data Storage 43 The above are stack lift-enabling operations, so the number remaining in the X-register ca

44 Section 3: The Memory Stack, LAST X, and Data Storage The number in the register is determined as follows: For storage arithmetic, new contents

Section 3: The Memory Stack, LAST X, and Data Storage 45 Example: Keep a running count of your newly blooming crocuses for two more days. Keystrokes

46 Section 3: The Memory Stack, LAST X, and Data Storage 2. Use arithmetic with constants to calculate the remaining balance of a $1000 loan

47 Section 4 Statistics Functions A word about the statistics functions: their use is based on an understanding of memory stack operation (Section 3)

48 Section 4: Statistics Functions How many different four-card hands can be dealt from a deck of 52 cards? Keystrokes Display 52 v 4 4 Fifty-two

Section 4: Statistics Functions 49 Keystrokes Display l´# 0.2809 Recall last random number generated, which is the new seed. (The ´ may be omitte

Contents 5 The Automatic Memory Stack and Stack Manipulation ... 32 Stack Manipulation Functions ...

50 Section 4: Statistics Functions In some cases involving x or y data values that differ by a relatively small amount, the calculator cannot comput

Section 4: Statistics Functions 51 X NITROGEN APPLIED 0.00 20.00 40.00 60.00 80.00 (kg per hectare *), x Y GRAIN YIELD 4.63 4.78 6.61 7.21 7.78 (m

52 Section 4: Statistics Functions Correcting Accumulated Statistics If you discover that you have entered data incorrectly, the accumulat

Section 4: Statistics Functions 53 Mean The ’ function computes the arithmetic mean (average) of the x-and y-values using the formulas shown

54 Section 4: Statistics Functions Example: Calculate the standard deviation about the mean calculated above. Keystrokes Display |S 31.62 S

Section 4: Statistics Functions 55 Example: Find the y-intercept and slope of the linear approximation of the data and compare to the plotted data

56 Section 4: Statistics Functions Linear Estimation. With the statistics accumulated, an estimated value for y, denoted ŷ, can be calculated

Section 4: Statistics Functions 57 Keystrokes Display 70 ´j 7.56 Predicted grain yield in tons/hectare. ® 0.99 The original data closely approx

58 Section 5 The Display and Continuous Memory Display Control The HP-15C has three display formats  •, i, and ^  that use a given number (0 thro

Section 5: The Display and Continuous Memory 59 Scientific Notation Display i (scientific) format displays a number in scientific notatio

6 Contents Resetting Continuous Memory ... 63 Part II: HP-15C Programming ... 6

60 Section 5: The Display and Continuous Memory Mantissa Display Regardless of the display format, the HP-15C always internally holds each number as

Section 5: The Display and Continuous Memory 61 Digit Separators The HP-15C is set at power-up so that it separates integral and fractional porti

62 Section 5: The Display and Continuous Memory Low-Power Indication When a flashing asterisk, which indicates low battery power, appears i

Section 5: The Display and Continuous Memory 63 Resetting Continuous Memory If at any time you want to reset (entirely clear) the HP-1

Part ll HP-15C Programming

66 Section 6 Programming Basics The next five sections are dedicated to explaining aspects of programming the HP-15C. Each of these programming

Section 6: Programming Basics 67 Location in Program Memory. Program memory  and therefore the calculator's position in program mem

68 Section 6: Programming Basics Keystrokes Display 2 002- 2 * 003- 20 9 004- 9 Given h in the X-register, lines 002 to

Section 6: Programming Basics 69 Keystrokes Display |¥ Run mode; no PRGM annunciator displayed. (The display will depend on any previous result

Contents 7 Flags ... 92 Examples ...

70 Section 6: Programming Basics This is the method used above, where h was placed in the X-register before running the program. No v instruct

Section 6: Programming Basics 71 The program to calculate this information uses these formulas and data: base area = r2. volume = base area × hei

72 Section 6: Programming Basics Keystrokes Display ´bA 001-42,21,11 Assigns this program the label  O 0 002- 44 0 Stores the contents o

Section 6: Programming Basics 73 Keystrokes Display + 019– 40 SIDE AREA + BASE AREA = SURFACE AREA. O + 3 020–44,40, 3 Keeps a sum of all S

74 Section 6: Programming Basics Keystrokes Display 4 4 Enter h of third can. ¦ 254.4690 VOLUME of third can. 240.3318 SURFACE AREA of third can.

Section 6: Programming Basics 75 Keycode 25: second row, fifth key. Memory Configuration Understanding memory configuration is not essential

76 Section 6: Programming Basics Memory is reallocated by telling the calculator which data storage register shall be the highest data register; al

Section 6: Programming Basics 77 Keystrokes Display 1 ´ m % 1.0000 R1 and R0 allocated for data storage; R2 to R65 available for programming and

78 Section 6: Programming Basics corresponding label. If need be, the search will wrap around at the end of program memory and continue at line

Section 6: Programming Basics 79 For example, ´b´A becomes ´bA, ´m´% becomes ´m%, and O´# becomes O#. The removal of the ´ is not ambiguous b

8 Contents I and e ... 116 Indirect Display Control ...

80 Section 6: Programming Basics Example: Write a program for 5x4 + 2x3 as (((5x + 2)x)x)x, then evaluate for x = 7 Keystrokes Display | ¥ 000- Ass

Section 6: Programming Basics 81 Problems 1. The village of Sonance has installed a 12-o'clock whistle in the firehouse steeple.

82 Section 7 Program Editing There are many reasons to modify a program after you've already stored it: you might want to add or delete a

Section 7: Program Editing 83 The Back Step (‚) Instruction. To move one line backwards in program memory, press ‚ (back step) in Progr

84 Section 7: Program Editing Let's start at the end of the program and work backwards. In this way, deletions will not change the line numbers

Section 7: Program Editing 85 Keystrokes Display − 019- 40 Line 020 deleted. | ‚ (hold) 016- 45 4 The next line to edit is line 016 (l 4

86 Section 7: Program Editing you can check the program by executing it stepwise. This is done by pressing  in Run mode. Keystrokes Dis

Section 7: Program Editing 87 Insertions and Deletions After an insertion, the display will show the instruction you just added. After

88 Section 7: Program Editing Keystrokes Display ´ b . 1 001-42,21,.1 ´ •2 002-42, 7, 2 1 003- 1 . 004- 48 0 005- 0 Interest. 7

Section 7: Program Editing 89 Make any necessary modifications in the program to also find and display s, the length of the circular arc cut by θ

Contents 9 Copying a Matrix ... 149 One-Matrix Operations ...

90 Section 8 Program Branching and Controls Although the instructions in a program are normally executed sequentially, it is often desirable to trans

Section 8: Program Branching and Controls 91 of this loop can be controlled by a conditional branch, an ¦ instruction (written into the loop),

92 Section 8: Program Branching and Controls Following a conditional test, program execution follows the "Do if True" Rule: it proceed

Section 8: Program Branching and Controls 93 Examples Example: Branching and Looping A radiobiology lab wants to predict the diminishing rad

94 Section 8: Program Branching and Controls Keystrokes Display l * 1 010-45,20, 1 Recall multiplication with the contents of R1 (N0), yielding Nt

Section 8: Program Branching and Controls 95 Example: Flags Calculations on debts or investments can be calculated in two ways: for pay

96 Section 8: Program Branching and Controls Keystrokes Display | ¥ 000- Program mode. ´ bB 001-42,21,12 Start at "B" if payments to be

Section 8: Program Branching and Controls 97 Now run the program to find the total amount needed in an account from which you want to take $2

98 Section 8: Program Branching and Controls Looping Looping is an application of branching which uses a t instruction to repeat a portion of the

Section 8: Program Branching and Controls 99 In this way, a program can accommodate two different modes of input, such as degrees and radians,