HP 15c Scientific manual Logarithmic Functions, Hyperbolic Functions

Page 28

28 Section 2: Numeric Functions

Logarithmic Functions

Natural Logarithm. Pressing Z calculates the natural logarithm of the number in the display; that is, the logarithm to the base e.

Natural Antilogarithm. Pressing ' calculates the natural antilogarithm of the number in the display; that is, raises e to the power of that number.

Common Logarithm. Pressing o calculates the common logarithm of the number in the display; that is, the logarithm to the base 10.

Common Antilogarithm. Pressing @ calculates the common antilogarithm of the number in the display; that is, raises 10 to the power of that number.

Keystrokes

Display

45 Z

3.8067

3.4012

'

30.0001

12.4578 o

1.0954

3.1354

@

1,365.8405

Hyperbolic Functions

Given x in the display (X-register):

Natural log of 45. Natural antilog of 3.4012. Common log of 12.4578.

Common antilog of 3.1354.

Pressing

Calculates

 

 

´P[

hyperbolic sine of x

H[

inverse hyperbolic sine of x

´P\

hyperbolic cosine of x

H\

inverse hyperbolic cosine of x

´P]

hyperbolic tangent of x

H]

inverse hyperbolic tangent of x

 

 

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Contents HP-15C Owner’s Handbook HP Part Number 00015-90001 Edition 2.4, SepLegal Notice Introduction Contents Contents Display and Continuous MemoryProgram Editing Program Branching and ControlsSubroutines Calculating With Complex Numbers Indirect Display ControlCalculating With Matrices Numerical Integration Contents Appendix a Error Conditions Appendix C Memory AllocationAppendix D a Detailed Look at Appendix E a Detailed Look at fContents Appendix F Batteries Function Summary and IndexProgramming Summary and Index Subject IndexHP-15C Problem Solver Quick Look atManual Solutions To Compute Keystrokes DisplayProgrammed Solutions Keystrokes DisplayKeystrokesDisplay 001-42,21,11002 003 004 005 006 007 008 009 8313 300.51HP-15C a Problem Solver Part l HP-15C Fundamentals Power On and Off Getting StartedKeyboard Operation SectionPrefix Keys Changing SignsKeying in Exponents I O m ´ P I l F T s ? t H bClear Keys Digit entry not terminated Display Clearing ` and −Clears only the last digit Calculations One-Number FunctionsTwo-Number Functions 653217 + 26.0000 22.0000 500013.0000 78.0000Numeric Functions Number Alteration FunctionsOne-Number Functions General FunctionsTime and Angle Conversions Trigonometric OperationsPressing Calculates Degrees/Radians Conversions 7069Radians 40.5000Logarithmic Functions Hyperbolic FunctionsPower Function Two-Number FunctionsPercentages To Calculate Keystrokes DisplayPolar and Rectangular Coordinate Conversions Enters the base number the priceCalculates 3% of $15.76 the tax Polar Conversion. PressingKeystrokes Display Automatic Memory Stack Last X, and Data Storage Automatic Memory Stack Stack ManipulationAutomatic Memory Stack Registers Always displayedMemory Stack, Last X, and Data Storage Stack Manipulation FunctionsLost Lost Last X Register and K 287.000022.2481 12.900013.9 + Calculator Functions and the Stack20.6475 Order of Entry and the v Key +15 X15Nested Calculations 7 +65.0000 69.0000Arithmetic Calculations With Constants 5 ‛15 Keys 1000 Keystrokes Display Growth factor000 Storage Register Operations Storing and Recalling Numbers322.5000 520.8750Clearing Data Storage Registers Storage and Recall ArithmeticFor storage arithmetic For recall arithmeticProblems Overflow and Underflow24 l-0 15.0000Memory Stack, Last X, and Data Storage Probability Calculations Statistics Functions60.0000 Random Number Generator 270,725.00005764 3422Accumulating Statistics RegistersRegister Contents 20.00 40.00 60.00 80.00 Kg per hectare Metric tons per Hectare, y20 z 61v 40 z 7.21 60 z 7.78 80 z l Σy2Correcting Accumulated Statistics 20 w 20 zStandard Deviation Mean40.00 Linear Regression 31.62Standard deviation about the mean nitrogen ApplicationLinear Estimation and Correlation Coefficient Statistics Functions Other Applications 70 ´jDisplay Control Display Continuous MemoryFixed Decimal Display Scientific Notation Display Engineering Notation Display234568 234567Round-Off Error Special DisplaysMantissa Display AnnunciatorsError Display Digit Separators12,345.67 12.345.6700Continuous Memory Low-Power IndicationStatus Resetting Continuous Memory Page Part ll HP-15C Programming Programming Basics MechanicsCreating a Program Loading a ProgramProgramming Basics ´b aRunning a Program Intermediate Program Stops002 003 004 005 006 007 008 How to Enter Data 300.51 300.51 ´AProgram Memory Radius, r Height, h Base Area Volume Surface Area Totals002 004 005007-44,40 010Or G a Program Instructions Further InformationInstruction Coding Memory Configuration Keycode 25 second row, fifth keyInitial Memory Configuration 60 ´ m%Program Boundaries ´ m %19 ´ m% 19.0000Abbreviated Key Sequences Unexpected Program Stops´bA ´b3 End of memory User Mode Polynomial Expressions and Horners Method¤ @ y ∕ LOG %Nonprogrammable Functions 001-42,21,12002 003 004 005 006 007 008 009 0000 12,691.0000Problems Program Editing Moving to a Line in Program MemoryDeleting Program Lines ExamplesInserting Program Lines Or use  Single-Step Operations Line Position ÂholdRelease ResultInsertions and Deletions Initializing Calculator Status+ i n InterestPV 1 + i n 100 270 ´bA D ´4 O0 2* O1 2÷ * ´ ´ l0 l1 ´r * nProgram Branching Controls BranchingConditional Tests TestFlags  n will clear flag number nExample Branching and Looping 010-45,20 013-43,30014 016-44,40Example Flags Formula is002-43 004-42,21,15005-43, 4 006-42,21Go to 250.000048.0000 10,698.3049Looping Conditional BranchingSystem Flags Flags 8 Program Branching and Controls Subroutines Go To Subroutine and ReturnSubroutine Execution ´b.1Subroutine Limits 000 001- ´b9 002- R003- O0 004´ b.4 ´b.5Subroutine Return Nested SubroutinesV and % Keys Index Register Loop Control106 Indirect Program Control With the Index Register Program Loop ControlIndex Register Storage and Recall Index Register and Loop ControlExchanging the X-Register Index Register ArithmeticIndirect Branching With Indirect Display Format Control With Indirect Flag Control WithLoop Control With Counters I and e Nnnnn x x x y y 5 0 0 Start count at zero Count by twos Count up toExamples Register Operations IterationsStoring and Recalling Keystrokes Display 12.3456Exchanging the X-Register Example Loop Control with eStorage Register Arithmetic Loop control number in R2 −− 011- 42012-42, 5 013- 2215 O Example Display Format Control64.8420 0000 50.0000 Index Register Contents Indirect Display Control Index Register and Loop Control 118 Part lll HP-15C Advanced Functions Complex Stack and Complex Mode Calculating With Complex NumbersCreating the Complex Stack 120Complex Numbers and the Stack Deactivating Complex ModeEntering Complex Numbers ´ % hold 8.0000 release Z 8 Y 7 X Keys Stack Lift in Complex Mode Manipulating the Real and Imaginary StacksClearing a Complex Number Or other operationContinue with any operation − 4 v Continue with any operation´ %hold release Entering Complex Numbers with −. The clearing functions −0000 17.0000 144.0000 Entering a Real Number Followed by another numberEntering a Pure Imaginary Number ´ Continue with any operationOperations With Complex Numbers Storing and Recalling Complex Numbers´ O L 2 ´¤x N o ∕ @ a + * ÷ y2000 70000428 0491Polar and Rectangular Coordinate Conversions Complex Results from Real Numbers5708 ´ % hold Release1.5708Cos θ + i sin θ = re iθ Polar + ib = ∠ θ 2981 8452+ 3.1434 352.0000 872.00002361 4721For Further Information Calculating With Matrices 138Keystrokes Display Deactivates Complex Mode = A-1BMatrix Dimensions Running11.2887 2496Dimensioning a Matrix Number Rows ColumnsDisplaying Matrix Dimensions Changing Matrix Dimensions´mA Keystrokes l B DisplayStoring and Recalling Matrix Elements Storing and Recalling All Elements in Order⎡ a Checking and Changing Matrix Elements Individually Keystrokes Display Storing a Number in All Elements of a Matrix Matrix OperationsMatrix Descriptors Result Matrix Copying a Matrix One-Matrix OperationsCalculating with Matrices Scalar Operations LB bElements of Result Matrix LA aKeystrokes Display Subtracts 1 from the elements Arithmetic OperationsLB b 2 LA a 2 Matrix Multiplication = AT B Keystrokes Display l a aSolving the Equation AX = B 24 OA 240086 OA 8600274 OB 233 OB 331 OB 120.32 OB 112.96 OB 151.36 OB ´Á Calculating the Residual Week Cabbage kg 186 141 215 Broccoli kg 116Using Matrices in LU Form Calculations With Complex MatricesStoring the Elements of a Complex Matrix Then Z can be represented in the calculator byPressing Transforms Into = ⎢ LA aComplex Transformations Between ZP and Z Inverting a Complex Matrix Multiplying Complex Matrices ´ aKeystrokes lA lB Display Displays descriptor of matrix a ´U lC LC lC lC lC lC lC lC ´USolving the Complex Equation AX = B ZZ −1AX = B 200.0000 170.00000372 13110437 1543Calculating with Matrices Using Matrix Descriptors in the Index Register Using a Matrix Element With Register OperationsMiscellaneous Operations Involving Matrices Stack Operation for Matrix Calculations Conditional Tests on Matrix DescriptorsCalculating with Matrices Using Matrix Operations in a Program Keystrokes Results Summary of Matrix Functions´m a Calculates residual in result matrix For Further Information Finding the Roots An Equation Using180 Finding the Roots of an Equation Clear program memory´b0 001-42,21002 003 005 006 007Finding the Roots of an Equation Desired rootKeystrokes ¥ ´ bA000 001-42,21,11 003 0045000 1 e t Brings another t-valueInto X-register 200 tWhen No Root Is Found 000 001-42,21 002 003 004 005Error Choosing Initial Estimates Label 003 004 005 007 X + 8008 009 6 x + 8Finding the Roots of an Equation Using in a Program Restriction on the Use Memory RequirementsNumerical Integration Using f194 002 003 004 4040 1416 7652Begin subroutine with a label $ ÷ 38254401 6054 Accuracy of f ´ i ´ f 8826 7091Using f in a Program 382Memory Requirements Error Conditions Error 0 Improper Mathematics OperationAppendix a 205Error 1 Improper Matrix Operation Error 2 Improper Statistics OperationError 3 Improper Register Number or Matrix Element Error 4 Improper Line Number or Label CallError 5 Subroutine Level Too Deep Error 6 Improper Flag NumberPr Error Power Error Stack Lift Last X Register Digit Entry TerminationStack Lift Appendix BDisabling Operations Enabling OperationsStack Stack Enabled. disabled 53.1301 No stack Lift Neutral OperationsAppendix B Stack Lift and the Last X Register Keys Nnn Clear u ¥Last X Register \ k + H ∆ \ h ÷ À P* q r c ‘ / N z ∕ P\ o jMemory Allocation Memory SpaceAppendix C RegistersAppendix C Memory Allocation Memory Status W Memory ReallocationM % Function ´m% 1.0000 Whold 1 64 Restrictions on Reallocation19 ´ m Program Memory Automatic Program Memory ReallocationMemory Requirements for the Advanced Functions Two-Byte Program InstructionsIf executed TogetherAppendix C Memory Allocation Detailed Look at How WorksAppendix D 220Appendix D a Detailed Look at Accuracy of the Root X4 = 000 1718 006 007 008 009 010-43,30 011 012-43,30 013´ v B Interpreting Results0681 − 45 For 0 x Test for x range Branch for x ≥3x 45x 2 + End subroutine000.0000 Initial estimates1358 Possible rootAppendix D a Detailed Look at ´ b.0 001-42,21,.0 002 003 004 005 Bring x-value into X-register007 008 009 010 013 014 015 016017 018 10 v ´ ‛ 20Error 0000 1250 5626 Finding Several RootsFx = xx a3 = 002 003 004 005 006 0076667 Same initial estimates Second rootStores root for deflation Deflated function valueDeflation for third root Limiting the Estimation Time Counting Iterations For Advanced InformationSpecifying a Tolerance Detailed Look at f How f WorksAppendix E 240Accuracy, Uncertainty, and Calculation Time X = π1 0π cos4θ − x sinθ dθ0000 1416 ´ i ´ fKeystrokes Display Return approximation to ´ Clear u HoldKeystrokes ´ i Display ´ f ´ Clear u hold7858 7807Uncertainty and the Display Format Functions values for example Δx = 0.5×10−n ×10m = aδx dxb = ab 0.5×10−n + m x dx Conditions That Could Cause Incorrect Results ∞ xe− xdx 001-42,21 002- 1 003 004 005 Appendix E a Detailed Look at f Appendix E a Detailed Look at f Conditions That Prolong Calculation Time Keys lower limit into Keys upper limit intoApproximation to integral UncertaintyAppendix E a Detailed Look at f Obtaining the Current Approximation to an Integral For Advanced Information Low-Power Indication Installing New BatteriesBatteries BatteriesAppendix F Batteries Verifying Proper Operation Self-Tests 2.C 3.HFunction Summary and Index Complex FunctionsConversions Digit EntryDisplay Control Index Register ControlLogarithmic Exponential Functions Mantissa. PressingMatrix Functions Mathematics146 To ZP page164 Number AlterationTo XT Percentage ProbabilityStack Manipulation Clear uStatistics StorageTrigonometry Programming Summary and Index 269Programming Summary and Index Subject Index 271Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Subject Index Federal Communications Commission Notice Product Regulatory Environment InformationModifications Canadian Notice Avis CanadienEuropean Union Regulatory Notice Body number is inserted between CE
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