## Advanced Mathematical MethodsWritten in an appealing and informal style, this text is a self-contained second course on mathematical methods in linear algebra and multivariate calculus. The prerequisites are elementary courses in linear algebra and calculus, but the author has maintained a balance between a rigorous theoretical and a "cookbook" approach, so that the material will be accessible to students who have not studied mathematics in depth. Indeed, as much of the material is normally available only in technical textbooks, this book will have wide appeal to students whose interests are in application rather than theory. The book is amply supplied with examples and exercises: complete solutions to a large proportion of these are provided. |

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#### LibraryThing Review

User Review - amarcobio - LibraryThingIt is more like a compilation of methods rather than an accurate description of them. The Calculus part is particularly good, with tons of exercises to practice. I miss some detail on Fourier ... Read full review

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very good

### Contents

Linear algebra | 1 |

Geometry in Rⁿ | 15 |

Matrices | 30 |

Projections | 48 |

Spectral theory | 59 |

Reduction to upper triangular form | 80 |

Reduction to tridiagonal form | 92 |

Inverses | 101 |

Nonlinear programming | 195 |

Advanced calculus | 207 |

Manipulation of integrals | 257 |

Multiple integrals | 300 |

Differential and difference equations revision | 347 |

Laplace transforms | 380 |

Series solution of linear ordinary differential equations | 406 |

Calculus of variations | 423 |

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### Common terms and phrases

affine hull approximation argument assume basis bounded variation calculation change of variable co-ordinates coefficients compute concave consider constant constraints continuous conv convergence convex combination convex cone convex function convex hull convex set corresponding curve deduce definition denote differential equation dx dy eigenvalues eigenvectors example exists extreme point finite formula generalised inverse geometric given graph Hence Hint illustrated in Figure improper integral inequality integral integrand Jacobian Kuhn-Tucker Laplace transforms limit linear transformation linearly independent matrix maximise non-negative non-singular non-zero objective function observe obtain optimal orthogonal projection orthonormal partition plane Player polynomial positive problem proof prove quadrant question rank ratio region result Riemann-Stieltjes integral satisfies Section selected exercises Show solution set Solutions to selected solve subspace supporting hyperplane Suppose term theorem vector space write zero