## The Art of Modeling in Science and Engineering with MathematicaThoroughly revised and updated, The Art of Modeling in Science and Engineering with explores the mathematical tools and procedures used in modeling based on the laws of conservation of mass, energy, momentum, and electrical charge. The authors have culled and consolidated the best from the first edition andMathematica, Second Edition |

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### Contents

1 | |

Analytical Tools The Solution of Ordinary Differential Equations ... | 37 |

The Use of Mathematica in Modeling Physical Systems ... | 123 |

Elementary Applications of the Conservation Laws ... | 139 |

Partial Differential Equations Classification Types and Properties Some Simple Transformations ... | 237 |

Solution of Linear Systems by Superposition Methods ... | 299 |

Vector Calculus Generalized Transport Equations ... | 341 |

Analytical Solutions of Partial Differential Equations | 419 |

499 | |

503 | |

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### Common terms and phrases

algebraic applied arise Bessel functions boundary conditions calculate Chapter characteristics concentration conduction consider constant continuity equation convective cylinder derivative diameter differential equations diffusion dimensionless distance distribution energy balance evaluated example expression Fick’s first-order flow rate fluid flux Fourier Fourier series Fourier’s equation geometry given gradient Green’s functions heat transfer Illustration independent variables infinite initial conditions integral inversion Laplace transform Laplace’s equation linear liquid mass balance mass transfer Mathematica method nondimensionalized nonhomogeneous nonlinear Note obtain one-dimensional ordinary differential equations parameters particle pipe Practice Problem pressure radial reaction reactor relation result second-order ODE semi-infinite separation of variables shown in Figure Simplify solid solution solve steady stream function superposition surface Table tank temperature thermal Type unsteady vector vector calculus velocity viscous yields zero