## Math Refresher for Scientists and EngineersExpanded coverage of essential math, including integral equations,calculus of variations, tensor analysis, and specialintegrals Math Refresher for Scientists and Engineers, Third Edition isspecifically designed as a self-study guide to help busyprofessionals and students in science and engineering quicklyrefresh and improve the math skills needed to perform their jobsand advance their careers. The book focuses on practicalapplications and exercises that readers are likely to face in theirprofessional environments. All the basic math skills needed tomanage contemporary technology problems are addressed and presentedin a clear, lucid style that readers familiar with previouseditions have come to appreciate and value. The book begins with basic concepts in college algebra andtrigonometry, and then moves on to explore more advanced conceptsin calculus, linear algebra (including matrices), differentialequations, probability, and statistics. This Third Edition has beengreatly expanded to reflect the needs of today's professionals. Newmaterial 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 skillsneeded by scientists and engineers. The wide range of topicscovered in one title is unique. All chapters provide a review ofimportant principles and methods. Examples, exercises, andapplications are used liberally throughout to engage the readersand assist them in applying their new math skills to actualproblems. 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 quicklymaster the math they need. It can additionally be used as atextbook for advanced-level undergraduates in physics andengineering. |

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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.