## Numerical Methods with VBA ProgrammingNumerical Methods with VBA Programming provides a unique and unified treatment of numerical methods and VBA computer programming, topics that naturally support one another within the study of engineering and science. This engaging text incorporates real-world scenarios to motivate technical material, helping students understand and retain difficult and key concepts. Such examples include comparing a two-point boundary value problem to determining when you should leave for the airport to catch a scheduled flight. Numerical examples are accompanied by closed-form solutions to demonstrate their correctness. Within the programming sections, tips are included that go beyond language basics to make programming more accessible for students. A unique section suggest ways in which the starting values for non-linear equations may be estimated. Flow charts for many of the numerical techniques discussed provide general guidance to students without revealing all of the details. Useful appendices provide summaries of Excel and VBA commands, Excel functions accessible in VBA, basics of differentiation, and more! |

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### Contents

Chapter 1 Introduction | 1 |

Arithmetic InputOutput and All That | 5 |

Chapter 3 Errors Series and Uncertainty | 43 |

Which Is Bigger? How Many Times? | 63 |

Chapter 5 Numerical Integration | 81 |

Useful Specialists | 101 |

Finding Zero | 111 |

Take One Step Forward | 137 |

Excel Basics | 253 |

Computer Representation of Numbers | 259 |

VBA Command Summary | 263 |

Glossary | 267 |

Numerical Methods with the Casio fx115MS Calculator | 269 |

Excel Functions in VBA | 273 |

Differentiation Fundamentals | 275 |

CashKarp RungeKutta VBA Program for Two Ordinary Differential Equations | 277 |

Chapter 9 Sets of Linear Equations | 173 |

Variables with a Family Name | 199 |

Chapter 11 Curve Fitting | 219 |

Chapter 12 Elliptic Partial Differential Equations | 243 |

281 | |

283 | |

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### Common terms and phrases

answer Apply your program array average calculated cell Chapter coefficients Collatz criterion column Consider the equation convergence correct value curve fit defined diagonal dialog box displays dV dt ea’s End Sub equation set Euler method evaluate example Excel flowchart formula function Gaussian elimination Gaussian–Seidel independent variable InputBox integral interval inverse label languages linear equations loop Maclaurin series magnitude matrix menu MsgBox Newton–Raphson method number of terms obtain ordinary differential equations Perform three iterations pivoting plot problem program to input program to solve quadratic equation radians rearrangement relative error require Romberg integration root Runge–Kutta method secant rule second-order significant figures Simpson’s 1/3 rule solution spline spreadsheet square starting values statements step subprogram Taylor series tion trapezoid rule true error uncertainty VBA program velocity Write a program xn+1 yields zero