## Advanced Mathematics for Applied and Pure SciencesCovers applicable mathematics that should provide a text, at the third year level and beyond, appropriate for both students of engineering and the pure sciences. The book is a product of close collaboration between two mathematicians and an engineer and it is of note that the engineer has been helpful in pinpointing the problems engineering students usually encounter in books written by mathematicians. Instead of just listing techniques and a few examples, or providing a list of theorems along with their proofs, it explains why the techniques work. The emphasis is on helping the student develop an understanding of mathematics and its applications. |

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### Contents

Review of Calculus and Ordinary Differential Equations | 1 |

Series Solutions and Special Functions | 89 |

Complex Variables | 191 |

Vector and Tensor Analysis | 301 |

Partial Differential Equations I | 401 |

Partial Differential Equations II | 511 |

Numerical Methods | 569 |

Numerical Solution of Partial Differential Equations | 681 |

Calculus of Variations | 739 |

Special Topics | 809 |

References | 861 |

Appendices | 867 |

878 | |

### Other editions - View all

Advanced Mathematics for Applied and Pure Sciences CF Chan Man Fong,D De Kee No preview available - 1998 |

### Common terms and phrases

analytic Answer approximate assume boundary conditions calculate Cartesian coordinate system Chapter coefficients Combining Equations complex numbers compute consider contour convergence cosh covariant curve deduce defined denote determine domain dx dy dy dx elements evaluate Example fluid formula Fourier function f given by Equation Green's function implies independent variables initial conditions integral interval iteration Laplace transform Laplace's equation Legendre linear matrix method Newtonian fluid non-zero Note obtain origin orthogonal partial differential equation plane point x0 polar coordinate system polynomial radius radius of convergence region respectively right side satisfies Equation separation of variables shown in Figure side of Equation Similarly singular point sinh solution of Equation solving Equation Substituting Equations surface Taylor series temperature theorem unit circle velocity w-plane write written yields zero