Calculus: Multivariable 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 differentiationthis 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 meanvalue 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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Review: Calculus, Volume 1: OneVariable Calculus with an Introduction to Linear Algebra
User Review  GoodreadsI enjoyed axiomatic approach taken by Apostle, one of the best books on calculus for beginners. Read full review
Review: Calculus, Volume 1: OneVariable Calculus with an Introduction to Linear Algebra
User Review  Franklin Colorado  GoodreadsI used this book to refresh my Calculus. It's not easy. There are some newer books that are probably easier. I felt he covered everything, which is what you want. If there were any flaws I didn't notice. Read full review
Contents
LINEAR SPACES  3 
LINEAR TRANSFORMATIONS AND MATRICES  31 
DETERMINANTS  71 
Copyright  
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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 finitedimensional 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 onedimensional onetoone 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