## Math Refresher for Scientists and EngineersExpanded coverage of essential math, including integral equations, calculus of variations, tensor analysis, and special integrals Math Refresher for Scientists and Engineers, Third Edition is specifically designed as a self-study guide to help busy professionals and students in science and engineering quickly refresh and improve the math skills needed to perform their jobs and advance their careers. The book focuses on practical applications and exercises that readers are likely to face in their professional environments. All the basic math skills needed to manage contemporary technology problems are addressed and presented in a clear, lucid style that readers familiar with previous editions have come to appreciate and value. The book begins with basic concepts in college algebra and trigonometry, and then moves on to explore more advanced concepts in calculus, linear algebra (including matrices), differential equations, probability, and statistics. This Third Edition has been greatly expanded to reflect the needs of today's professionals. New material includes: * A chapter on integral equations * A chapter on calculus of variations * A chapter on tensor analysis * A section on time series * A section on partial fractions * Many new exercises and solutions Collectively, the chapters teach most of the basic math skills needed by scientists and engineers. The wide range of topics covered in one title is unique. All chapters provide a review of important principles and methods. Examples, exercises, and applications are used liberally throughout to engage the readers and assist them in applying their new math skills to actual problems. Solutions to exercises are provided in an appendix. Whether to brush up on professional skills or prepare for exams, readers will find this self-study guide enables them to quickly master the math they need. It can additionally be used as a textbook for advanced-level undergraduates in physics and engineering. |

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### Contents

1 | |

2 GEOMETRY TRIGONOMETRY AND HYPERBOLIC FUNCTIONS | 21 |

3 ANALYTIC GEOMETRY | 41 |

4 LINEAR ALGEBRA I | 51 |

5 LINEAR ALGEBRA II | 65 |

6 DIFFERENTIAL CALCULUS | 79 |

7 PARTIAL DERIVATIVES | 93 |

8 INTEGRAL CALCULUS | 107 |

12 PARTIAL DIFFERENTIAL EQUATIONS | 167 |

13 INTEGRAL EQUATIONS | 181 |

14 CALCULUS OF VARIATIONS | 191 |

15 TENSOR ANALYSIS | 203 |

16 PROBABILITY | 219 |

17 PROBABILITY DISTRIBUTIONS | 229 |

18 STATISTICS | 245 |

19 SOLUTIONS TO EXERCISES | 257 |

9 SPECIAL INTEGRALS | 117 |

10 ORDINARY DIFFERENTIAL EQUATIONS | 133 |

11 ODE SOLUTION TECHNIQUES | 151 |

339 | |

343 | |

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### Common terms and phrases

2006 John Wiley algebraic analytical angle Application axis boundary conditions Calculate calculus of variations Chapter complex numbers components constant continuous random variable contravariant vector coordinate system cosh deﬁned deﬁnite integral denotes dependent variables determinant differential equation discrete random variable eigenvalues elements Euler’s equation Evaluate Example EXERCISE expansion coefﬁcients Fanchi Copyright Figure ﬁnd ﬁrst ﬁrst-order ﬁt ﬁxed ﬂoat Fourier transform frequency function f given gives grouped data initial conditions integral equation interval inverse John Wiley 81 joint probability Laplace transform LC circuit lets us write line integral linear Math Refresher method metric tensor Multiplying obtained parameter path of integration Pauli matrices points polynomial power series probability density probability distribution real number Rearranging Refresher for Scientists regression sample space satisﬁed scalar second-order sinh solution square matrix straight line Substituting Eq Suppose Taylor series transformation equation vector ﬁeld written Z transform

### Popular passages

Page 2 - B (AUB) is the set of all elements that belong to A or to B or to both.

Page 6 - Given real numbers a, and b, exactly one of the following is true: a < b, a = b, or a > b.

Page 2 - The intersection of two sets A and B is the set of all elements that belong to both A and B; that is, all elements common to A and B.