Excel for scientists and engineers: numerical methods
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Hoboken, NJ
Wiley
2007
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIX, 454 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| ISBN: | 0471387347 9780471387343 |
Internformat
MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV022425221 | ||
| 003 | DE-604 | ||
| 005 | 20080205 | ||
| 007 | t | ||
| 008 | 070515s2007 xxuad|| |||| 00||| eng d | ||
| 010 | |a 2006052999 | ||
| 020 | |a 0471387347 |9 0-471-38734-7 | ||
| 020 | |a 9780471387343 |9 978-0-471-38734-3 | ||
| 035 | |a (OCoLC)249400952 | ||
| 035 | |a (DE-599)BVBBV022425221 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 044 | |a xxu |c US | ||
| 049 | |a DE-1102 |a DE-861 |a DE-898 |a DE-20 |a DE-634 |a DE-11 |a DE-2070s | ||
| 050 | 0 | |a TA345 | |
| 082 | 0 | |a 620.00285/5369 | |
| 084 | |a ST 371 |0 (DE-625)143672: |2 rvk | ||
| 084 | |a ST 620 |0 (DE-625)143684: |2 rvk | ||
| 100 | 1 | |a Billo, E. Joseph |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Excel for scientists and engineers |b numerical methods |c E. Joseph Billo |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2007 | |
| 300 | |a XIX, 454 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index | ||
| 630 | 0 | 4 | |a Microsoft Excel (Computer file) |
| 650 | 4 | |a Bilim - Bilgi işlem | |
| 650 | 4 | |a Elektronik kutu çizimler | |
| 650 | 4 | |a Ingénierie - Informatique | |
| 650 | 4 | |a Muhhendislik - Bilgi işlem | |
| 650 | 4 | |a Sciences - Informatique | |
| 650 | 4 | |a Tableurs | |
| 650 | 4 | |a Datenverarbeitung | |
| 650 | 4 | |a Ingenieurwissenschaften | |
| 650 | 4 | |a Naturwissenschaft | |
| 650 | 4 | |a Engineering |x Data processing | |
| 650 | 4 | |a Science |x Data processing | |
| 650 | 4 | |a Electronic spreadsheets | |
| 650 | 0 | 7 | |a EXCEL |0 (DE-588)4138932-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a EXCEL |0 (DE-588)4138932-3 |D s |
| 689 | 0 | 1 | |a Numerisches Verfahren |0 (DE-588)4128130-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-015633486 | |
Datensatz im Suchindex
| _version_ | 1807864528189259776 |
|---|---|
| adam_text |
Summary of Contents
Detailed Table of Contents vii
Preface xv
Acknowledgments xix
About the Author xix
Chapter 1 Introducing Visual Basic for Applications 1
Chapter 2 Fundamentals of Programming with VBA 15
Chapter 3 Worksheet Functions for Working with Matrices 57
Chapter 4 Number Series 69
Chapter 5 Interpolation 77
Chapter 6 Differentiation 99
Chapter 7 Integration 127
Chapter 8 Roots of Equations 147
Chapter 9 Systems of Simultaneous Equations 189
Chapter 10 Numerical Integration of Ordinary Differential Equations
Part I: Initial Conditions 217
Chapter 11 Numerical Integration of Ordinary Differential Equations
Part II: Boundary Conditions 245
Chapter 12 Partial Differential Equations 263
Chapter 13 Linear Regression and Curve Fitting 287
Chapter 14 Nonlinear Regression Using the Solver 313
Chapter 15 Random Numbers and the Monte Carlo Method 341
APPENDICES
Appendix 1 Selected VBA Keywords 365
Appendix 2 Shortcut Keys for VBA 387
Appendix 3 Custom Functions Help File 389
Appendix 4 Some Equations for Curve Fitting 409
Appendix 5 Engineering and Other Functions 423
Appendix 6 ASCII Codes 427
Appendix 7 Bibliography 429
Appendix 8 Answers and Comments for End of Chapter Problems 431
INDEX 443
v
Contents
Preface xv
Acknowledgments xix
Aboutthe Author xix
Chapter 1 Introducing Visual Basic for Applications 1
The Visual Basic Editor 1
Visual Basic Procedures 4
There Are Two Kinds of Macros 4
The Structure of a Sub Procedure 4
The Structure ofaFunction Procedure 5
Using the Recorder to Create a Sub Procedure 5
The Personal Macro Workbook 7
Running a Sub Procedure 8
Assigning a Shortcut Key to a Sub Procedure 8
Entering VBA Code 9
Creating a Simple Custom Function 10
Using a Function Macro 10
A Shortcut to Enter a Function 12
SomeFAQs 13
Chapter 2 Fundamentals of Programming with VBA 15
Components of Visual Basic Statements 15
Operators 16
Variables 16
Objects, Properties, and Methods 17
Objects 17
Properties 17
Using Properties 19
Functions 20
Using Worksheet Functions with VBA 22
Some Useful Methods 22
Other Keywords 23
Program Control 23
Branching 23
Logical Operators 24
SelectCase 24
Looping 24
For.Next Loop 25
DoWhile.Loop 25
vii
vüi EXCEL: NUMERICAL METHODS
ForEach.NextLoop 25
NestedLoops 26
Exiting from a Loop or from a Procedure 26
VBA Data Types 27
The Variant Data Type 28
Subroutines 28
Scoping a Subroutine 29
VBA Code for Command Macros 29
Objects and Collections of Objects 29
"Objects" That Are Really Properties 30
You Can Define Your Own Objects 30
Methods 31
Some Useful Methods 31
Two Ways to Specify Arguments of Methods 32
Arguments with or without Parentheses 33
Making a Reference to a Cell or a Range 33
A Reference to the Active Cell or a Selected Range 33
A Reference to a Cell Other than the Active Cell 34
References Using the Union or Intersect Method 35
Examples of Expressions to Refer to a Cell or Range 35
Getting Values from a Worksheet 36
Sending Values to a Worksheet 37
Interacting with the User 37
MsgBox 37
MsgBox Return Values 39
InputBox 39
Visual Basic Arrays 41
Dimensioning an Array 41
Use the Name of the Array Variable to Specify the Whole Array 42
Multidimensional Arrays 42
Declaringthe Variable Type of an Array 42
Returning the Size of an Array 42
Dynamic Arrays 43
Preserving Values in Dynamic Arrays 43
Working with Arrays in Sub Procedures:
Passing Values from Worksheet to VBA Module 44
A Range Specified in a Sub Procedure Can Be Used as an Array 44
Some Worksheet Functions Used Within VBA
Create an Array Automatically 4 *
Some Worksheet Functions Used Within VBA
Create an Array Automatically 45
An Array ofObject Variables 4^
CONTENTS ix
Working with Arrays in Sub Procedures:
Passing Values from a VBA Module to a Worksheet 45
A One Dimensional Array Assigned to a Worksheet Range
Can Cause Problems 46
Custom Functions 47
Specifying the Data Type of an Argument 47
Specifying the Data Type Returned by a Function Procedure 47
Returning an Error Value from a Function Procedure 48
A Custom Function that Takes an Optional Argument 48
Arrays in Function Procedures 48
A Range Passed to a Function Procedure Can Be Used as an Array 48
Passing an Indefinite Number of Arguments:
Using the ParamArray Keyword 49
Returning an Array of Values as a Result 49
Creating Add In Function Macros 50
How to Create an Add In Macro 51
Testing and Debugging 51
Tracing Execution 52
Stepping Through Code 52
Adding a Breakpoint 52
Examiningthe Values of Variables While in BreakMode 53
Examining the Values of Variables During Execution 54
Chapter 3 Worksheet Functions for Working with Matrices 57
Arrays, Matrices and Determinants 57
SomeTypesof Matrices 57
An Introduction to Matrix Mathematics 58
Excel's Built in Matrix Functions 60
Some Additional Matrix Functions 63
Problems 66
Chapter 4 Number Series 69
Evaluating Series Formulas 70
Using Array Constants to Create Series Formulas 70
Using the ROW Worksheet Function to Create Series Formulas 71
The INDIRECT Worksheet Function 71
Using the INDIRECT Worksheet Function
with the ROW Worksheet Function to Create Series Formulas 72
The Taylor Series 72
The Taylor Series: An Example 73
Problems 75
x EXCEL: NUMERICAL METHODS
Chapter 5 Interpolation 77
Obtaining Values from a Table 77
Using Excel's Lookup Functions to Obtain Values from a Table 77
Using VLOOKUP to Obtain Values from a Table 78
Using the LOOKUP Function to Obtain Values from a Table 79
Creating a Custom Lookup Formula to Obtain Values from a Table 80
Using Excel's Lookup Functions
to Obtain Values from a Two Way Table 81
Interpolation 83
Linear Interpolation in a Table by Means of Worksheet Formulas 83
Linear Interpolation in a Table by Using the TREND Worksheet Function .85
Linear Interpolation in a Table by Means of a Custom Function 86
Cubic Interpolation 87
Cubic Interpolation in a Table by Using the TREND Worksheet Function.89
Linear Interpolation in a Two Way Table
by Means of Worksheet Formulas ™
Cubic Interpolation in a Two Way Table
by Means of Worksheet Formulas "
Cubic Interpolation in a Two Way Table
by Means of a Custom Function "¦*
Problems 96
Chapter 6 Differentiation "
First and Second Derivatives of Data in a Table
Calculating First and Second Derivatives
Using LINEST as a Fitting Function 105
Derivativesofa Worksheet Formula *
Derivatives of a Worksheet Formula Calculated by Using
a VBA Function Procedure *
First Derivative of a Worksheet Formula Calculated by Using
the Finite Difference Method 110
The Newton Quotient ll0
Derivative of a Worksheet Formula Calculated by Using
the Finite Difference Method *
First Derivative of a Worksheet Formula Calculated by Using
a VBA Sub Procedure Using the Finite Difference Method 1!
First Derivative of a Worksheet Formula Calculated by Using
a VBA Function Procedure Using the Finite Difference Method *li
Improving the VBA Function Procedure l l
Second Derivative of a Worksheet Formula
Concerningthe Choice of Ax forthe Finite Difference Method ll]
Problems 124
CONTENTS x]
Chapter 7 Integration 127
Area under a Curve 127
Calculating the Area under a Curve Defined by a Table of Data Points 129
Calculating the Area under a Curve Defined by a Table of Data Points
by Means of a VBA Function Procedure 130
Calculating the Area under a Curve Defined by a Formula 131
Areabetween Two Curves 132
Integrating a Function 133
Integrating a Function Defined by a Worksheet Formula
by Means of a VBA Function Procedure 133
Gaussian Quadrature 137
Integration with an Upper or Lower Limit of Infinity 140
Distance Traveled AlongaCurved Path 141
Problems 143
Chapter 8 Roots of Equations 147
A Graphical Method 147
The Interval Halving or Bisection Method 149
The Interval Method with Linear Interpolation
(the Regula Falsi Method) 151
The Regula Falsi Method with Correction for Slow Convergence 153
The Newton Raphson Method 154
Using Goal Seek 156
The Secant Method 160
The Newton Raphson Method Using Circular Reference and Iteration 161
A Newton Raphson Custom Function 163
Bairstow's Method to Find All Roots of a Regulär Polynomial 166
Finding Values Other than Zeroes of a Function 174
Using Goal Seek. to Find the Point of Intersection of Two Curves 174
Using the Newton Raphson Method
to Find the Point of Intersection of Two Lines 176
Using the Newton Raphson Method to Find Multiple Intersections
of a Straight Line and a Curve 178
A Goal Seek Custom Function 180
Problems 185
Chapter 9 Systems of Simultaneous Equations 189
Cramer'sRule 190
Solving Simultaneous Equations by Matrix Inversion 191
Solving Simultaneous Equations by Gaussian Elimination 191
The Gauss Jordan Method 196
Solving Linear Systems by Iteration 200
The Jacobi Method Implemented on a Worksheet 200
xji EXCEL: NUMERICAL METHODS
The Gauss Seidel Method Implemented on a Worksheet 203
The Gauss Seidel Method Implemented on a Worksheet
Using Circular References 204
A Custom Function Procedure forthe Gauss Seidel Method 205
Solving Nonlinear Systems by Iteration 207
Newton's Iteration Method 207
Problems 213
Chapter 10 Numerical Integration of Ordinary Differential Equations
Part I: Initial Conditions 217
Solving a Single First Order Differential Equation 218
Euler's Method 218
The Fourth Order Runge Kutta Method 220
Fourth Order Runge Kutta Method Implemented on a Worksheet 220
Runge Kutta Method Applied to a Differential Equation
Involving Both x andy 223
Fourth Order Runge Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Coded in the Procedure 224
Fourth Order Runge Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Passed as an Argument 225
Systems of First Order Differential Equations 228
Fourth Order Runge Kutta Custom Function
for Systems of Differential Equations 229
Predictor Corrector Methods 235
A Simple Predictor Corrector Method 235
A Simple Predictor Corrector Method
Utilizing an Intentional Circular Reference 236
Higher Order Differential Equations 238
Problems 241
Chapter 11 Numerical Integration of Ordinary Differential Equations
Part II: Boundary Conditions 245
The Shooting Method 245
An Example: Deflection of a Simply Supported Beam 246
Solving a Second Order Ordinary Differential Equation
by the Shooting Method and Euler's Method 249
Solving a Second Order Ordinary Differential Equation
by the Shooting Method and the RK Method 251
Finite Difference Methods 254
Solving a Second Order Ordinary Differential Equation
by the Finite Difference Method 254
CONTENTS xüi
Another Example 258
A Limitation on the Finite Difference Method 261
Problems 262
Chapter 12 Partial Differential Equations 263
Elliptic, Parabolic and Hyperbolic Partial Differential Equations 263
Elliptic Partial Differential Equations 264
Solving Elliptic Partial Differential Equations:
Replacing Derivatives with Finite Differences 265
An Example: Temperature Distribution in a Heated Metal Plate 267
Parabolic Partial Differential Equations 269
Solving Parabolic Partial Differential Equations: The Explicit Method 270
An Example: Heat Conduction in a Brass Rod 272
Solving Parabolic Partial Differential Equations:
The Crank Nicholson or Implicit Method 274
An Example: Vapor Diffusion in a Tube 275
Vapor Diffusion in a Tube Revisited 277
Vapor Diffusion in a Tube (Again) 279
A Crank Nicholson Custom Function 280
Vapor Diffusion in a Tube Solved by Using a Custom Function 282
Hyperbolic Partial Differential Equations 282
Solving Hyperbolic Partial Differential Equations:
Replacing Derivatives with Finite Differences 282
An Example: Vibration of a String 283
Problems 286
Chapter 13 Linear Regression and Curve Fitting 287
Linear Regression 287
Least Squares Fit to a Straight Line 288
Least Squares Fit to a Straight Line Using the Worksheet Functions
SLOPE, INTERCEPT and RSQ 289
Multiple Linear Regression 291
Least Squares Fit to a Straight Line Using LINEST 292
Multiple Linear Regression Using LINEST 293
Handling Noncontiguous Ranges ofknown_x's in LINEST 297
A LINEST Shortcut 297
LINEST's Regression Statistics 297
Linear Regression Using Trendline 298
Limitations of Trendline 301
Importing Trendline Coefficients into a Spreadsheet
by Using Worksheet Formulas 302
Using the Regression Tool in Analysis Tools 303
Limitations of the Regression Tool 305
xiv EXCEL: NUMERICAL METHODS
Importing the Trendline Equation from a Chart into a Worksheet 305
Problems 309
Chapter 14 Nonlinear Regression Using the Solver 313
Nonlinear Least Squares Curve Fitting 314
Introducing the Solver 316
How the Solver Works 316
Loading the Solver Add In 317
WhyUse the Solver for Nonlinear Regression? 317
Nonlinear Regression Using the Solver: An Example 318
Some Notes on Using the Solver 323
Some Notes on the Solver Parameters Dialog Box 323
Some Notes on the Solver Options Dialog Box 324
When to Use Manual Scaling 326
Statistics of Nonlinear Regression 327
The Solver Statistics Macro 328
Be Cautious When Using Linearized Forms of Nonlinear Equations 329
Problems 332
Chapter 15 Random Numbers and the Monte Carlo Method 341
Random Numbers in Excel 341
How Excel Generates Random Numbers 341
Using Random Numbers in Excel 3
Adding "Noise" to a Signal Generated by a Formula 344
Selecting Items Randomly from a List 3
Random Sampling by Using Analysis Tools 3 '
Simulating a Normal Random Distribution of a Variable 34V
Monte Carlo Simulation 35°
Monte Carlo Integration 3^
The Area of an Irregulär Polygon 3
Problems 362
APPENDICES 363
Appendix 1 Selected VBA Keywords 365
Appendix 2 Shortcut Keys for VBA 387
Appendix 3 Custom Functions Help File 389
Appendix 4 Some Equations for Curve Fitting 409
Appendix 5 Engineering and Other Functions
Appendix 6 ASCII Codes 42?
Appendix 7 Bibliography 429
Appendix 8 Answers and Comments for End of Chapter Problems 43
INDEX 443 |
| adam_txt |
Summary of Contents
Detailed Table of Contents vii
Preface xv
Acknowledgments xix
About the Author xix
Chapter 1 Introducing Visual Basic for Applications 1
Chapter 2 Fundamentals of Programming with VBA 15
Chapter 3 Worksheet Functions for Working with Matrices 57
Chapter 4 Number Series 69
Chapter 5 Interpolation 77
Chapter 6 Differentiation 99
Chapter 7 Integration 127
Chapter 8 Roots of Equations 147
Chapter 9 Systems of Simultaneous Equations 189
Chapter 10 Numerical Integration of Ordinary Differential Equations
Part I: Initial Conditions 217
Chapter 11 Numerical Integration of Ordinary Differential Equations
Part II: Boundary Conditions 245
Chapter 12 Partial Differential Equations 263
Chapter 13 Linear Regression and Curve Fitting 287
Chapter 14 Nonlinear Regression Using the Solver 313
Chapter 15 Random Numbers and the Monte Carlo Method 341
APPENDICES
Appendix 1 Selected VBA Keywords 365
Appendix 2 Shortcut Keys for VBA 387
Appendix 3 Custom Functions Help File 389
Appendix 4 Some Equations for Curve Fitting 409
Appendix 5 Engineering and Other Functions 423
Appendix 6 ASCII Codes 427
Appendix 7 Bibliography 429
Appendix 8 Answers and Comments for End of Chapter Problems 431
INDEX 443
v
Contents
Preface xv
Acknowledgments xix
Aboutthe Author xix
Chapter 1 Introducing Visual Basic for Applications 1
The Visual Basic Editor 1
Visual Basic Procedures 4
There Are Two Kinds of Macros 4
The Structure of a Sub Procedure 4
The Structure ofaFunction Procedure 5
Using the Recorder to Create a Sub Procedure 5
The Personal Macro Workbook 7
Running a Sub Procedure 8
Assigning a Shortcut Key to a Sub Procedure 8
Entering VBA Code 9
Creating a Simple Custom Function 10
Using a Function Macro 10
A Shortcut to Enter a Function 12
SomeFAQs 13
Chapter 2 Fundamentals of Programming with VBA 15
Components of Visual Basic Statements 15
Operators 16
Variables 16
Objects, Properties, and Methods 17
Objects 17
Properties 17
Using Properties 19
Functions 20
Using Worksheet Functions with VBA 22
Some Useful Methods 22
Other Keywords 23
Program Control 23
Branching 23
Logical Operators 24
SelectCase 24
Looping 24
For.Next Loop 25
DoWhile.Loop 25
vii
vüi EXCEL: NUMERICAL METHODS
ForEach.NextLoop 25
NestedLoops 26
Exiting from a Loop or from a Procedure 26
VBA Data Types 27
The Variant Data Type 28
Subroutines 28
Scoping a Subroutine 29
VBA Code for Command Macros 29
Objects and Collections of Objects 29
"Objects" That Are Really Properties 30
You Can Define Your Own Objects 30
Methods 31
Some Useful Methods 31
Two Ways to Specify Arguments of Methods 32
Arguments with or without Parentheses 33
Making a Reference to a Cell or a Range 33
A Reference to the Active Cell or a Selected Range 33
A Reference to a Cell Other than the Active Cell 34
References Using the Union or Intersect Method 35
Examples of Expressions to Refer to a Cell or Range 35
Getting Values from a Worksheet 36
Sending Values to a Worksheet 37
Interacting with the User 37
MsgBox 37
MsgBox Return Values 39
InputBox 39
Visual Basic Arrays 41
Dimensioning an Array 41
Use the Name of the Array Variable to Specify the Whole Array 42
Multidimensional Arrays 42
Declaringthe Variable Type of an Array 42
Returning the Size of an Array 42
Dynamic Arrays 43
Preserving Values in Dynamic Arrays 43
Working with Arrays in Sub Procedures:
Passing Values from Worksheet to VBA Module 44
A Range Specified in a Sub Procedure Can Be Used as an Array 44
Some Worksheet Functions Used Within VBA
Create an Array Automatically 4 *
Some Worksheet Functions Used Within VBA
Create an Array Automatically 45
An Array ofObject Variables 4^
CONTENTS ix
Working with Arrays in Sub Procedures:
Passing Values from a VBA Module to a Worksheet 45
A One Dimensional Array Assigned to a Worksheet Range
Can Cause Problems 46
Custom Functions 47
Specifying the Data Type of an Argument 47
Specifying the Data Type Returned by a Function Procedure 47
Returning an Error Value from a Function Procedure 48
A Custom Function that Takes an Optional Argument 48
Arrays in Function Procedures 48
A Range Passed to a Function Procedure Can Be Used as an Array 48
Passing an Indefinite Number of Arguments:
Using the ParamArray Keyword 49
Returning an Array of Values as a Result 49
Creating Add In Function Macros 50
How to Create an Add In Macro 51
Testing and Debugging 51
Tracing Execution 52
Stepping Through Code 52
Adding a Breakpoint 52
Examiningthe Values of Variables While in BreakMode 53
Examining the Values of Variables During Execution 54
Chapter 3 Worksheet Functions for Working with Matrices 57
Arrays, Matrices and Determinants 57
SomeTypesof Matrices 57
An Introduction to Matrix Mathematics 58
Excel's Built in Matrix Functions 60
Some Additional Matrix Functions 63
Problems 66
Chapter 4 Number Series 69
Evaluating Series Formulas 70
Using Array Constants to Create Series Formulas 70
Using the ROW Worksheet Function to Create Series Formulas 71
The INDIRECT Worksheet Function 71
Using the INDIRECT Worksheet Function
with the ROW Worksheet Function to Create Series Formulas 72
The Taylor Series 72
The Taylor Series: An Example 73
Problems 75
x EXCEL: NUMERICAL METHODS
Chapter 5 Interpolation 77
Obtaining Values from a Table 77
Using Excel's Lookup Functions to Obtain Values from a Table 77
Using VLOOKUP to Obtain Values from a Table 78
Using the LOOKUP Function to Obtain Values from a Table 79
Creating a Custom Lookup Formula to Obtain Values from a Table 80
Using Excel's Lookup Functions
to Obtain Values from a Two Way Table 81
Interpolation 83
Linear Interpolation in a Table by Means of Worksheet Formulas 83
Linear Interpolation in a Table by Using the TREND Worksheet Function .85
Linear Interpolation in a Table by Means of a Custom Function 86
Cubic Interpolation 87
Cubic Interpolation in a Table by Using the TREND Worksheet Function.89
Linear Interpolation in a Two Way Table
by Means of Worksheet Formulas ™
Cubic Interpolation in a Two Way Table
by Means of Worksheet Formulas "
Cubic Interpolation in a Two Way Table
by Means of a Custom Function "¦*
Problems 96
Chapter 6 Differentiation "
First and Second Derivatives of Data in a Table
Calculating First and Second Derivatives
Using LINEST as a Fitting Function 105
Derivativesofa Worksheet Formula *
Derivatives of a Worksheet Formula Calculated by Using
a VBA Function Procedure *
First Derivative of a Worksheet Formula Calculated by Using
the Finite Difference Method 110
The Newton Quotient ll0
Derivative of a Worksheet Formula Calculated by Using
the Finite Difference Method *
First Derivative of a Worksheet Formula Calculated by Using
a VBA Sub Procedure Using the Finite Difference Method 1!
First Derivative of a Worksheet Formula Calculated by Using
a VBA Function Procedure Using the Finite Difference Method *li
Improving the VBA Function Procedure l l
Second Derivative of a Worksheet Formula
Concerningthe Choice of Ax forthe Finite Difference Method ll]
Problems 124
CONTENTS x]
Chapter 7 Integration 127
Area under a Curve 127
Calculating the Area under a Curve Defined by a Table of Data Points 129
Calculating the Area under a Curve Defined by a Table of Data Points
by Means of a VBA Function Procedure 130
Calculating the Area under a Curve Defined by a Formula 131
Areabetween Two Curves 132
Integrating a Function 133
Integrating a Function Defined by a Worksheet Formula
by Means of a VBA Function Procedure 133
Gaussian Quadrature 137
Integration with an Upper or Lower Limit of Infinity 140
Distance Traveled AlongaCurved Path 141
Problems 143
Chapter 8 Roots of Equations 147
A Graphical Method 147
The Interval Halving or Bisection Method 149
The Interval Method with Linear Interpolation
(the Regula Falsi Method) 151
The Regula Falsi Method with Correction for Slow Convergence 153
The Newton Raphson Method 154
Using Goal Seek 156
The Secant Method 160
The Newton Raphson Method Using Circular Reference and Iteration 161
A Newton Raphson Custom Function 163
Bairstow's Method to Find All Roots of a Regulär Polynomial 166
Finding Values Other than Zeroes of a Function 174
Using Goal Seek. to Find the Point of Intersection of Two Curves 174
Using the Newton Raphson Method
to Find the Point of Intersection of Two Lines 176
Using the Newton Raphson Method to Find Multiple Intersections
of a Straight Line and a Curve 178
A Goal Seek Custom Function 180
Problems 185
Chapter 9 Systems of Simultaneous Equations 189
Cramer'sRule 190
Solving Simultaneous Equations by Matrix Inversion 191
Solving Simultaneous Equations by Gaussian Elimination 191
The Gauss Jordan Method 196
Solving Linear Systems by Iteration 200
The Jacobi Method Implemented on a Worksheet 200
xji EXCEL: NUMERICAL METHODS
The Gauss Seidel Method Implemented on a Worksheet 203
The Gauss Seidel Method Implemented on a Worksheet
Using Circular References 204
A Custom Function Procedure forthe Gauss Seidel Method 205
Solving Nonlinear Systems by Iteration 207
Newton's Iteration Method 207
Problems 213
Chapter 10 Numerical Integration of Ordinary Differential Equations
Part I: Initial Conditions 217
Solving a Single First Order Differential Equation 218
Euler's Method 218
The Fourth Order Runge Kutta Method 220
Fourth Order Runge Kutta Method Implemented on a Worksheet 220
Runge Kutta Method Applied to a Differential Equation
Involving Both x andy 223
Fourth Order Runge Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Coded in the Procedure 224
Fourth Order Runge Kutta Custom Function
for a Single Differential Equation with the Derivative Expression
Passed as an Argument 225
Systems of First Order Differential Equations 228
Fourth Order Runge Kutta Custom Function
for Systems of Differential Equations 229
Predictor Corrector Methods 235
A Simple Predictor Corrector Method 235
A Simple Predictor Corrector Method
Utilizing an Intentional Circular Reference 236
Higher Order Differential Equations 238
Problems 241
Chapter 11 Numerical Integration of Ordinary Differential Equations
Part II: Boundary Conditions 245
The Shooting Method 245
An Example: Deflection of a Simply Supported Beam 246
Solving a Second Order Ordinary Differential Equation
by the Shooting Method and Euler's Method 249
Solving a Second Order Ordinary Differential Equation
by the Shooting Method and the RK Method 251
Finite Difference Methods 254
Solving a Second Order Ordinary Differential Equation
by the Finite Difference Method 254
CONTENTS xüi
Another Example 258
A Limitation on the Finite Difference Method 261
Problems 262
Chapter 12 Partial Differential Equations 263
Elliptic, Parabolic and Hyperbolic Partial Differential Equations 263
Elliptic Partial Differential Equations 264
Solving Elliptic Partial Differential Equations:
Replacing Derivatives with Finite Differences 265
An Example: Temperature Distribution in a Heated Metal Plate 267
Parabolic Partial Differential Equations 269
Solving Parabolic Partial Differential Equations: The Explicit Method 270
An Example: Heat Conduction in a Brass Rod 272
Solving Parabolic Partial Differential Equations:
The Crank Nicholson or Implicit Method 274
An Example: Vapor Diffusion in a Tube 275
Vapor Diffusion in a Tube Revisited 277
Vapor Diffusion in a Tube (Again) 279
A Crank Nicholson Custom Function 280
Vapor Diffusion in a Tube Solved by Using a Custom Function 282
Hyperbolic Partial Differential Equations 282
Solving Hyperbolic Partial Differential Equations:
Replacing Derivatives with Finite Differences 282
An Example: Vibration of a String 283
Problems 286
Chapter 13 Linear Regression and Curve Fitting 287
Linear Regression 287
Least Squares Fit to a Straight Line 288
Least Squares Fit to a Straight Line Using the Worksheet Functions
SLOPE, INTERCEPT and RSQ 289
Multiple Linear Regression 291
Least Squares Fit to a Straight Line Using LINEST 292
Multiple Linear Regression Using LINEST 293
Handling Noncontiguous Ranges ofknown_x's in LINEST 297
A LINEST Shortcut 297
LINEST's Regression Statistics 297
Linear Regression Using Trendline 298
Limitations of Trendline 301
Importing Trendline Coefficients into a Spreadsheet
by Using Worksheet Formulas 302
Using the Regression Tool in Analysis Tools 303
Limitations of the Regression Tool 305
xiv EXCEL: NUMERICAL METHODS
Importing the Trendline Equation from a Chart into a Worksheet 305
Problems 309
Chapter 14 Nonlinear Regression Using the Solver 313
Nonlinear Least Squares Curve Fitting 314
Introducing the Solver 316
How the Solver Works 316
Loading the Solver Add In 317
WhyUse the Solver for Nonlinear Regression? 317
Nonlinear Regression Using the Solver: An Example 318
Some Notes on Using the Solver 323
Some Notes on the Solver Parameters Dialog Box 323
Some Notes on the Solver Options Dialog Box 324
When to Use Manual Scaling 326
Statistics of Nonlinear Regression 327
The Solver Statistics Macro 328
Be Cautious When Using Linearized Forms of Nonlinear Equations 329
Problems 332
Chapter 15 Random Numbers and the Monte Carlo Method 341
Random Numbers in Excel 341
How Excel Generates Random Numbers 341
Using Random Numbers in Excel 3
Adding "Noise" to a Signal Generated by a Formula 344
Selecting Items Randomly from a List 3
Random Sampling by Using Analysis Tools 3 '
Simulating a Normal Random Distribution of a Variable 34V
Monte Carlo Simulation 35°
Monte Carlo Integration 3^
The Area of an Irregulär Polygon 3
Problems 362
APPENDICES 363
Appendix 1 Selected VBA Keywords 365
Appendix 2 Shortcut Keys for VBA 387
Appendix 3 Custom Functions Help File 389
Appendix 4 Some Equations for Curve Fitting 409
Appendix 5 Engineering and Other Functions
Appendix 6 ASCII Codes 42?
Appendix 7 Bibliography 429
Appendix 8 Answers and Comments for End of Chapter Problems 43
INDEX 443 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Billo, E. Joseph |
| author_facet | Billo, E. Joseph |
| author_role | aut |
| author_sort | Billo, E. Joseph |
| author_variant | e j b ej ejb |
| building | Verbundindex |
| bvnumber | BV022425221 |
| callnumber-first | T - Technology |
| callnumber-label | TA345 |
| callnumber-raw | TA345 |
| callnumber-search | TA345 |
| callnumber-sort | TA 3345 |
| callnumber-subject | TA - General and Civil Engineering |
| classification_rvk | ST 371 ST 620 |
| ctrlnum | (OCoLC)249400952 (DE-599)BVBBV022425221 |
| dewey-full | 620.00285/5369 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 620 - Engineering and allied operations |
| dewey-raw | 620.00285/5369 |
| dewey-search | 620.00285/5369 |
| dewey-sort | 3620.00285 45369 |
| dewey-tens | 620 - Engineering and allied operations |
| discipline | Informatik |
| discipline_str_mv | Informatik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000zc 4500</leader><controlfield tag="001">BV022425221</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20080205</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">070515s2007 xxuad|| |||| 00||| eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="a">2006052999</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">0471387347</subfield><subfield code="9">0-471-38734-7</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9780471387343</subfield><subfield code="9">978-0-471-38734-3</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)249400952</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV022425221</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="044" ind1=" " ind2=" "><subfield code="a">xxu</subfield><subfield code="c">US</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1102</subfield><subfield code="a">DE-861</subfield><subfield code="a">DE-898</subfield><subfield code="a">DE-20</subfield><subfield code="a">DE-634</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-2070s</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">TA345</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">620.00285/5369</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 371</subfield><subfield code="0">(DE-625)143672:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 620</subfield><subfield code="0">(DE-625)143684:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Billo, E. Joseph</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Excel for scientists and engineers</subfield><subfield code="b">numerical methods</subfield><subfield code="c">E. Joseph Billo</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Hoboken, NJ</subfield><subfield code="b">Wiley</subfield><subfield code="c">2007</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIX, 454 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield><subfield code="e">1 CD-ROM (12 cm)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references and index</subfield></datafield><datafield tag="630" ind1="0" ind2="4"><subfield code="a">Microsoft Excel (Computer file)</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Bilim - Bilgi işlem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Elektronik kutu çizimler</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ingénierie - Informatique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Muhhendislik - Bilgi işlem</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Sciences - Informatique</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Tableurs</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Datenverarbeitung</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Ingenieurwissenschaften</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Naturwissenschaft</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Engineering</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Science</subfield><subfield code="x">Data processing</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Electronic spreadsheets</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">EXCEL</subfield><subfield code="0">(DE-588)4138932-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">EXCEL</subfield><subfield code="0">(DE-588)4138932-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Numerisches Verfahren</subfield><subfield code="0">(DE-588)4128130-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-015633486</subfield></datafield></record></collection> |
| id | DE-604.BV022425221 |
| illustrated | Illustrated |
| index_date | 2024-07-02T17:27:11Z |
| indexdate | 2024-08-20T00:32:48Z |
| institution | BVB |
| isbn | 0471387347 9780471387343 |
| language | English |
| lccn | 2006052999 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015633486 |
| oclc_num | 249400952 |
| open_access_boolean | |
| owner | DE-1102 DE-861 DE-898 DE-BY-UBR DE-20 DE-634 DE-11 DE-2070s |
| owner_facet | DE-1102 DE-861 DE-898 DE-BY-UBR DE-20 DE-634 DE-11 DE-2070s |
| physical | XIX, 454 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2007 |
| publishDateSearch | 2007 |
| publishDateSort | 2007 |
| publisher | Wiley |
| record_format | marc |
| spelling | Billo, E. Joseph Verfasser aut Excel for scientists and engineers numerical methods E. Joseph Billo Hoboken, NJ Wiley 2007 XIX, 454 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Microsoft Excel (Computer file) Bilim - Bilgi işlem Elektronik kutu çizimler Ingénierie - Informatique Muhhendislik - Bilgi işlem Sciences - Informatique Tableurs Datenverarbeitung Ingenieurwissenschaften Naturwissenschaft Engineering Data processing Science Data processing Electronic spreadsheets EXCEL (DE-588)4138932-3 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf EXCEL (DE-588)4138932-3 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Billo, E. Joseph Excel for scientists and engineers numerical methods Microsoft Excel (Computer file) Bilim - Bilgi işlem Elektronik kutu çizimler Ingénierie - Informatique Muhhendislik - Bilgi işlem Sciences - Informatique Tableurs Datenverarbeitung Ingenieurwissenschaften Naturwissenschaft Engineering Data processing Science Data processing Electronic spreadsheets EXCEL (DE-588)4138932-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4138932-3 (DE-588)4128130-5 |
| title | Excel for scientists and engineers numerical methods |
| title_auth | Excel for scientists and engineers numerical methods |
| title_exact_search | Excel for scientists and engineers numerical methods |
| title_exact_search_txtP | Excel for scientists and engineers numerical methods |
| title_full | Excel for scientists and engineers numerical methods E. Joseph Billo |
| title_fullStr | Excel for scientists and engineers numerical methods E. Joseph Billo |
| title_full_unstemmed | Excel for scientists and engineers numerical methods E. Joseph Billo |
| title_short | Excel for scientists and engineers |
| title_sort | excel for scientists and engineers numerical methods |
| title_sub | numerical methods |
| topic | Microsoft Excel (Computer file) Bilim - Bilgi işlem Elektronik kutu çizimler Ingénierie - Informatique Muhhendislik - Bilgi işlem Sciences - Informatique Tableurs Datenverarbeitung Ingenieurwissenschaften Naturwissenschaft Engineering Data processing Science Data processing Electronic spreadsheets EXCEL (DE-588)4138932-3 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Microsoft Excel (Computer file) Bilim - Bilgi işlem Elektronik kutu çizimler Ingénierie - Informatique Muhhendislik - Bilgi işlem Sciences - Informatique Tableurs Datenverarbeitung Ingenieurwissenschaften Naturwissenschaft Engineering Data processing Science Data processing Electronic spreadsheets EXCEL Numerisches Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015633486&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT billoejoseph excelforscientistsandengineersnumericalmethods |