NUMERICAL METHODS FOR ENGINEERS 7TH EDITION
BY STEVEN CHAPRA E-BOOK
, CONTENTS
PREFACE xiv
ABOUT THE AUTHORS xvi
PART ONE
MODELING, PT1.1 Motivation 3
COMPUTERS, AND PT1.2 Mathematical Background 5
ERROR ANALYSIS3 PT1.3 Orientation 8
CHAPTER 1
Mathematical Modeling and Engineering Problem Solving 11
1.1 A Simple Mathematical Model 11
1.2 Conservation Laws and Engineering 18
Problems 21
CHAPTER 2
Programming and Software 27
2.1 Packages and Programming 27
2.2 Structured Programming 28
2.3 Modular Programming 37
2.4 Excel 39
2.5 MATLAB 43
2.6 Mathca d 47
2.7 Other Languages and Libraries 48
Problems 49
CHAPTER 3
Approximations and Round-Off Errors 55
3.1 Significant Figures 56
3.2 Accuracy and Precision 58
3.3 Error Definitions 59
3.4 Round-Off Errors 65
Problems 79
iv
, CONTENTS v
CHAPTER 4
Truncation Errors and the Taylor Series 81
4.1 The Taylor Series 81
4.2 Error Propagation 97
4.3 Total Numerical Error 101
4.4 Blunders, Formulation Errors, and Data Uncertainty 106
Problems 108
EPILOGUE: PART ONE 110
PT1.4 Trade-Offs 110
PT1.5 Important Relationships and Formulas 113
PT1.6 Advanced Methods and Additional References 113
PART TWO
ROOTS OF PT2.1 Motivation 117
EQUATIONS 117 PT2.2 Mathematical Background 119
PT2.3 Orientation 120
CHAPTER 5
Bracketing Methods 123
5.1 Graphical Methods 123
5.2 The Bisection Method 127
5.3 The False-Position Method 135
5.4 Incremental Searches and Determining Initial Guesses 141
Problems 142
CHAPTER 6
Open Methods 145
6.1 Simple Fixed-Point Iteration 146
6.2 The Newton-Raphson Method 151
6.3 The Secant Method 157
6.4 Brent’s Method 162
6.5 Multiple Roots 166
6.6 Systems of Nonlinear Equations 169
Problems 173
CHAPTER 7
Roots of Polynomials 176
7.1 Polynomi als in Engineering and Science 176
7.2 Computing with Polynomials 179
7.3 Conventional Methods 182
, vi CONTENTS
7.4 Müller’s Method 183
7.5 Bairstow’s Method 187
7.6 Other Methods 192
7.7 Root Location with Software Packages 192
Problems 202
CHAPTER 8
Case Studies: Roots of Equations 204
8.1 Ideal and Nonideal Gas Laws (Chemical/Bio Engineering) 204
8.2 Greenhouse Gases and Rainwater (Civil/Environmental Engineering) 207
8.3 Design of an Electric Circuit (Electrical Engineering) 209
8.4 Pipe Friction (Mechanical/ Aeros pace Engineering) 212
Problems 215
EPILOGUE: PART TWO 226
PT2.4 Trade-Offs 226
PT2.5 Important Relationships and Formulas 227
PT2.6 Advanced Methods and Additional References 227
PART THREE
LINEAR ALGEBRAIC PT3.1 Motivation 231
EQUATIONS 231 PT3.2 Mathematical Background 233
PT3.3 Orientation 241
CHAPTER 9
Gauss Elimination 245
9.1 Solving Small Numbers of Equations 245
9.2 Naive Gauss Elimination 252
9.3 Pitfalls of Elimination Methods 258
9.4 Techniques for Improving Solutions 264
9.5 Complex Systems 271
9.6 Nonlinear Systems of Equations 271
9.7 Gauss-Jorda n 273
9.8 Summary 275
Problems 275
CHAPTER 10
LU Decomposition and Matrix Inversion 278
10.1 LU Decomposition 278
10.2 The Matrix Inverse 287
10.3 Error Analysis and System Condition 291
Problems 297
BY STEVEN CHAPRA E-BOOK
, CONTENTS
PREFACE xiv
ABOUT THE AUTHORS xvi
PART ONE
MODELING, PT1.1 Motivation 3
COMPUTERS, AND PT1.2 Mathematical Background 5
ERROR ANALYSIS3 PT1.3 Orientation 8
CHAPTER 1
Mathematical Modeling and Engineering Problem Solving 11
1.1 A Simple Mathematical Model 11
1.2 Conservation Laws and Engineering 18
Problems 21
CHAPTER 2
Programming and Software 27
2.1 Packages and Programming 27
2.2 Structured Programming 28
2.3 Modular Programming 37
2.4 Excel 39
2.5 MATLAB 43
2.6 Mathca d 47
2.7 Other Languages and Libraries 48
Problems 49
CHAPTER 3
Approximations and Round-Off Errors 55
3.1 Significant Figures 56
3.2 Accuracy and Precision 58
3.3 Error Definitions 59
3.4 Round-Off Errors 65
Problems 79
iv
, CONTENTS v
CHAPTER 4
Truncation Errors and the Taylor Series 81
4.1 The Taylor Series 81
4.2 Error Propagation 97
4.3 Total Numerical Error 101
4.4 Blunders, Formulation Errors, and Data Uncertainty 106
Problems 108
EPILOGUE: PART ONE 110
PT1.4 Trade-Offs 110
PT1.5 Important Relationships and Formulas 113
PT1.6 Advanced Methods and Additional References 113
PART TWO
ROOTS OF PT2.1 Motivation 117
EQUATIONS 117 PT2.2 Mathematical Background 119
PT2.3 Orientation 120
CHAPTER 5
Bracketing Methods 123
5.1 Graphical Methods 123
5.2 The Bisection Method 127
5.3 The False-Position Method 135
5.4 Incremental Searches and Determining Initial Guesses 141
Problems 142
CHAPTER 6
Open Methods 145
6.1 Simple Fixed-Point Iteration 146
6.2 The Newton-Raphson Method 151
6.3 The Secant Method 157
6.4 Brent’s Method 162
6.5 Multiple Roots 166
6.6 Systems of Nonlinear Equations 169
Problems 173
CHAPTER 7
Roots of Polynomials 176
7.1 Polynomi als in Engineering and Science 176
7.2 Computing with Polynomials 179
7.3 Conventional Methods 182
, vi CONTENTS
7.4 Müller’s Method 183
7.5 Bairstow’s Method 187
7.6 Other Methods 192
7.7 Root Location with Software Packages 192
Problems 202
CHAPTER 8
Case Studies: Roots of Equations 204
8.1 Ideal and Nonideal Gas Laws (Chemical/Bio Engineering) 204
8.2 Greenhouse Gases and Rainwater (Civil/Environmental Engineering) 207
8.3 Design of an Electric Circuit (Electrical Engineering) 209
8.4 Pipe Friction (Mechanical/ Aeros pace Engineering) 212
Problems 215
EPILOGUE: PART TWO 226
PT2.4 Trade-Offs 226
PT2.5 Important Relationships and Formulas 227
PT2.6 Advanced Methods and Additional References 227
PART THREE
LINEAR ALGEBRAIC PT3.1 Motivation 231
EQUATIONS 231 PT3.2 Mathematical Background 233
PT3.3 Orientation 241
CHAPTER 9
Gauss Elimination 245
9.1 Solving Small Numbers of Equations 245
9.2 Naive Gauss Elimination 252
9.3 Pitfalls of Elimination Methods 258
9.4 Techniques for Improving Solutions 264
9.5 Complex Systems 271
9.6 Nonlinear Systems of Equations 271
9.7 Gauss-Jorda n 273
9.8 Summary 275
Problems 275
CHAPTER 10
LU Decomposition and Matrix Inversion 278
10.1 LU Decomposition 278
10.2 The Matrix Inverse 287
10.3 Error Analysis and System Condition 291
Problems 297
