HP 15c Manual
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HP-15C Owner’s Handbook HP Part Number: 00015-90001 Edition 2.4, Sep 2011
Legal Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability non- infringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual. Hewlett-Packard Company shall not be liable for any errors or incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2011 Hewlett-Packard Development Company, LP. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company Palo Alto, CA 94304 USA
3 Introduction Congratulations! Whether you are new to HP calculators or an experienced user, you will find the HP-15C a powerful and valuable calculating tool. The HP-15C provides: 448 bytes of program memory (one or two bytes per instruction) and sophisticated programming capability, including conditional and unconditional branching, subroutines, flags, and editing. Four advanced mathematics capabilities: complex number calculations, matrix calculations, solving for roots, and numerical integration. Direct and indirect storage in up to 67 registers. This handbook is written for you, regardless of your level of expertise. The beginning part covers all the basic functions of the HP-15C and how to use them. The second part covers programming and is broken down into three subsections – The Mechanics, Examples, and Further Information – in order to make it easy for users with varying backgrounds to find the information they need. The last part describes the four advanced mathematics capabilities. Before starting these sections, you may want to gain some operating and programming experience on the HP-15C by working through the introductory material, The HP-15C: A Problem Solver, on page 12. The various appendices describe additional details of calculator operation, as well as warranty and service information. The Function Summary and Index and the Programming Summary and Index at the back of this manual can be used for quick reference to each function key and as a handy page reference to more comprehensive information inside the manual. Also available from Hewlett-Packard is the HP-15C Advanced Functions Handbook, which provides applications and technical descriptions for the root-solving, integration, complex number, and matrix functions. Note: You certainly do not need to read every part of the manual before delving into the HP-15C Advanced Functions if you are already familiar with HP calculators. The use of _ and f requires a knowledge of HP-15C programming.
4 Contents The HP-15C: A Problem Solver .................................... 12 A Quick Look at v ................................................. 12 Manual Solutions ............................................................ 13 Programmed Solutions ..................................................... 14 Part I: HP-15C Fundamentals ................................ 17 Section 1: Getting Started .......................................... 18 Power On and Off .......................................................... 18 Keyboard Operation ....................................................... 18 Primary and Alternate Functions ..................................... 18 Prefix Keys .................................................................. 19 Changing Signs ........................................................... 19 Keying in Exponents ..................................................... 19 The CLEAR Keys ........................................................ 20 Display Clearing: ` and − ................................... 21 Calculations ................................................................... 22 One-Number Functions ................................................. 22 Two-Number Functions and v ............................... 22 Section 2: Numeric Functions ..................................... 24 Pi .................................................................................. 24 Number Alteration Functions ............................................ 24 One-Number Functions .................................................... 25 General Functions ........................................................ 25 Trigonometric Operations .............................................. 26 Time and Angle Conversions ......................................... 26 Degrees/Radians Conversions ....................................... 27 Logarithmic Functions ................................................... 28 Hyperbolic Functions .................................................... 28 Two-Number Functions .................................................... 29 The Power Function ...................................................... 29 Percentages ................................................................. 29 Polar and Rectangular Coordinate Conversions ............... 30 Section 3: The Automatic Memory Stack, LAST X, and Data Storage ........................................................ 32
Contents 5 The Automatic Memory Stack and Stack Manipulation ........ 32 Stack Manipulation Functions ........................................ 33 The LAST X Register and K ....................................... 35 Calculator Functions and the Stack ................................. 36 Order of Entry and the v Key ............................... 37 Nested Calculations ..................................................... 38 Arithmetic Calculations With Constants ........................... 39 Storage Register Operations ............................................ 42 Storing and Recalling Numbers ..................................... 42 Clearing Data Storage Registers .................................... 43 Storage and Recall Arithmetic ........................................ 43 Overflow and Underflow .............................................. 45 Problems ........................................................................ 45 Section 4: Statistics Functions ..................................... 47 Probability Calculations ................................................... 47 Random Number Generator ............................................. 48 Accumulating Statistics ..................................................... 49 Correcting Accumulated Statistics ................................... 52 Mean .......................................................................... 53 Standard Deviation ....................................................... 53 Linear Regression ......................................................... 54 Linear Estimation and Correlation Coefficient ................... 55 Other Applications ....................................................... 57 Section 5: The Display and Continuous Memory ........... 58 Display Control .............................................................. 58 Fixed Decimal Display .................................................. 58 Scientific Notation Display ............................................ 59 Engineering Notation Display ........................................ 59 Mantissa Display ......................................................... 60 Round-Off Error ............................................................ 60 Special Displays ............................................................. 60 Annunciators ............................................................... 60 Digit Separators ........................................................... 61 Error Display ............................................................... 61 Overflow and Underflow .............................................. 61 Low-Power Indication .................................................... 62 Continuous Memory ........................................................ 62 Status ......................................................................... 62
6 Contents Resetting Continuous Memory ........................................ 63 Part II: HP-15C Programming ............................... 65 Section 6: Programming Basics .................................. 66 The Mechanics ............................................................... 66 Creating a Program ..................................................... 66 Loading a Program ...................................................... 66 Intermediate Program Stops ........................................... 68 Running a Program ....................................................... 68 How to Enter Data ........................................................ 69 Program Memory ......................................................... 70 Further Information .......................................................... 74 Program Instructions ..................................................... 74 Instruction Coding ........................................................ 74 Memory Configuration .................................................. 75 Program Boundaries ..................................................... 77 Unexpected Program Stops ........................................... 78 Abbreviated Key Sequences .......................................... 78 User Mode .................................................................. 79 Polynomial Expressions and Horners Method .................. 79 Nonprogrammable Functions ......................................... 80 Problems ........................................................................ 81 Section 7: Program Editing ........................................ 82 The Mechanics ............................................................... 82 Moving to a Line in Program Memory ............................. 82 Deleting Program Lines ................................................. 83 Inserting Program Lines ................................................. 83 Examples ....................................................................... 83 Further Information .......................................................... 85 Single-Step Operations ................................................. 85 Line Position ................................................................ 86 Insertions and Deletions ................................................ 87 Initializing Calculator Status .......................................... 87 Problems ........................................................................ 87 Section 8: Program Branching and Controls ................. 90 The Mechanics ............................................................... 90 Branching ................................................................... 90 Conditional Tests .......................................................... 91
Contents 7 Flags .......................................................................... 92 Examples ....................................................................... 93 Example: Branching and Looping ................................... 93 Example: Flags ............................................................ 95 Further Information .......................................................... 97 GoTo .......................................................................... 97 Looping ...................................................................... 98 Conditional Branching .................................................. 98 Flags .......................................................................... 98 The System Flags: Flags 8 and 9 .................................... 99 Section 9: Subroutines ............................................... 101 The Mechanics ............................................................... 101 GoTo Subroutine and Return .......................................... 101 Subroutine Limits .......................................................... 102 Examples ....................................................................... 102 Further Information .......................................................... 105 The Subroutine Return ................................................... 105 Nested Subroutines ...................................................... 105 Section 10: The Index Register and Loop Control ........... 106 The V and % Keys .................................................... 106 Direct Versus Indirect Data Storage With The Index Register ..................................................... 106 Indirect Program Control With the Index Register ............. 107 Program Loop Control ................................................... 107 The Mechanics ............................................................... 107 Index Register Storage and Recall .................................. 107 Index Register Arithmetic ............................................... 108 Exchanging the X-Register ............................................. 108 Indirect Branching With V ......................................... 108 Indirect Flag Control With V ...................................... 109 Indirect Display Format Control With V ....................... 109 Loop Control with Counters: I and e .................. 109 Examples ....................................................................... 111 Examples: Register Operations ....................................... 111 Example: Loop Control With s ................................. 112 Example: Display Format Control .................................... 114 Further Information .......................................................... 115 Index Register Contents ................................................. 115
8 Contents I and e .......................................................... 116 Indirect Display Control ........................................... 116 Part III: HP-15C Advanced Functions .................... 119 Section 11: Calculating With Complex Numbers .......... 120 The Complex Stack and Complex Mode ............................ 120 Creating the Complex Stack .......................................... 120 Deactivating Complex Mode ......................................... 121 Complex Numbers and the Stack ...................................... 121 Entering Complex Numbers ........................................... 121 Stack Lift in Complex Mode ........................................... 124 Manipulating the Real and Imaginary Stacks .................. 124 Changing Signs .......................................................... 124 Clearing a Complex Number ....................................... 125 Entering a Real Number ............................................... 128 Entering a Pure Imaginary Number ............................... 129 Storing and Recalling Complex Numbers ....................... 130 Operations With Complex Numbers ................................ 130 One-Number Functions ................................................ 131 Two-Number Functions ................................................. 131 Stack Manipulation Functions ....................................... 131 Conditional Tests ......................................................... 132 Complex Results from Real Numbers .............................. 133 Polar and Rectangular Coordinate Conversions ................. 133 Problems ....................................................................... 135 For Further Information ................................................... 137 Section 12: Calculating With Matrices ........................ 138 Matrix Dimensions ......................................................... 140 Dimensioning a Matrix ................................................. 141 Displaying Matrix Dimensions ....................................... 142 Changing Matrix Dimensions ........................................ 142 Storing and Recalling Matrix Elements .............................. 143 Storing and Recalling All Elements in Order ................... 143 Checking and Changing Matrix Elements Individually ..... 145 Storing a Number in All Elements of a Matrix ................. 147 Matrix Operations ......................................................... 147 Matrix Descriptors ....................................................... 147 The Result Matrix ......................................................... 148
Contents 9 Copying a Matrix ....................................................... 149 One-Matrix Operations ................................................ 149 Scalar Operations ....................................................... 151 Arithmetic Operations .................................................. 153 Matrix Multiplication ................................................... 154 Solving the Equation AX = B .......................................... 156 Calculating the Residual ............................................... 159 Using Matrices in LU Form ............................................ 160 Calculations With Complex Matrices ............................... 160 Storing the Elements of a Complex Matrix ...................... 161 The Complex Transformations Between ZP and Z ............. 164 Inverting a Complex Matrix .......................................... 165 Multiplying Complex Matrices ...................................... 166 Solving the Complex Equation AX = B ............................ 168 Miscellaneous Operations Involving Matrices ..................... 173 Using a Matrix Element With Register Operations ............ 173 Using Matrix Descriptors in the Index Register ................. 173 Conditional Tests on Matrix Descriptors .......................... 174 Stack Operation for Matrix Calculations ............................ 174 Using Matrix Operations in a Program .............................. 176 Summary of Matrix Functions ........................................... 177 For Further Information .................................................... 179 Section 13: Finding the Roots of an Equation ................ 180 Using _ ................................................................. 180 When No Root Is Found .................................................. 186 Choosing Initial Estimates ................................................ 188 Using _ in a Program .............................................. 192 Restriction on the Use of _ ....................................... 193 Memory Requirements ..................................................... 193 For Further Information .................................................... 193 Section 14: Numerical Integration .............................. 194 Using f ....................................................................... 194 Accuracy of f ............................................................. 200 Using f in a Program .................................................. 203 Memory Requirements ..................................................... 204 For Further Information .................................................... 204
10 Contents Appendix A: Error Conditions .................................... 205 Appendix B: Stack Lift and the LAST X Register ............... 209 Digit Entry Termination .................................................... 209 Stack Lift ........................................................................ 209 Disabling Operations ................................................... 210 Enabling Operations .................................................... 210 Neutral Operations ...................................................... 211 LAST X Register ............................................................... 212 Appendix C: Memory Allocation ................................ 213 The Memory Space ......................................................... 213 Registers ..................................................................... 213 Memory Status (W) .................................................. 215 Memory Reallocation ...................................................... 215 The m % Function ................................................ 215 Restrictions on Reallocation ........................................... 216 Program Memory ............................................................ 217 Automatic Program Memory Reallocation ........................ 217 Two-Byte Program Instructions ....................................... 218 Memory Requirements for the Advanced Functions ............. 218 Appendix D: A Detailed Look at _ ...................... 220 How _ Works ....................................................... 220 Accuracy of the Root ....................................................... 222 Interpreting Results .......................................................... 226 Finding Several Roots ...................................................... 233 Limiting the Estimation Time .............................................. 238 Counting Iterations ....................................................... 239 Specifying a Tolerance ................................................. 239 For Advanced Information ................................................ 239 Appendix E: A Detailed Look at f ........................... 240 How f Works ............................................................. 240 Accuracy, Uncertainty, and Calculation Time ..................... 241 Uncertainty and the Display Format ................................... 245 Conditions That Could Cause Incorrect Results .................... 249 Conditions That Prolong Calculation Time .......................... 254 Obtaining the Current Approximation to an Integral ........... 257 For Advanced Information ................................................ 258