## Calculus: Multi-variable calculus and linear algebra, with applications to differential equations and probabilityNow available in paperback! An introduction to the calculus, with an excellent balance between theory & technique. Integration is treated before differentiation--this is a departure from most modern texts, but it is historically correct, & it is the best way to establish the true connection between the integral & the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems & their applications earlier in the text, incorporates a treatment of linear algebra, & contains many new & easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept. |

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### Contents

LINEAR SPACES | 3 |

LINEAR TRANSFORMATIONS AND MATRICES | 31 |

DETERMINANTS | 71 |

Copyright | |

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### Common terms and phrases

approximation Assume axioms basis Calculate called chain rule coefficients components constant continuous converges coordinates corresponding countable curve defined definition denote density described determine diagonal matrix differential equation distribution function double integral dx dy dy dz eigenvalues eigenvectors elements equal Euclidean space event example Exercises exists finite finite-dimensional fixed formula function F given gradient graph Green's theorem Hence Hermitian homogeneous implies independent inequality inner product interpolation Jacobian line integral linear combination linear space linear transformation mapping mass multiplication n x n nonsingular nonzero norm normal null space obtain one-dimensional one-to-one open interval operator orthogonal orthonormal parametric partial derivatives plane polynomial of degree properties prove quadratic random variable real numbers rectangle region sample space satisfies scalar field Section shown in Figure solution subsets subspace surface integral vector field zero