Calculus: Onevariable calculus, with an introduction to linear algebraNow available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiationthis is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the meanvalue theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and 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
Historical Introduction  1 
Some Basic Concepts of the Theory of Sets  11 
A Set of Axioms for the RealNumber System  17 
Copyright  
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Absolutely convergent algebraic angle arbitrary arctan Assume axioms axis basis calculus called Cartesian equation CauchySchwarz inequality chain rule coefficients complex numbers compute constant continuous converges coordinate vectors coordinates cosine deduce defined definition denote derivative determine difference quotient differential equation directrix diverges dot product elements ellipse equal example Exercises finite formula geometric given graph hence indefinite integral induction inequality integer integral curves inverse length limit linear combination linear space linear transformation linearly independent logarithm mathematical matrix multiplication negative nonnegative nonzero notation obtain open interval ordinate set orthogonal parabola partial sums plane positive integer positive number Proof properties prove radius real numbers satisfies scalars Section sequence shown in Figure shows solution span step function subintervals subspace symbol tangent line Taylor polynomial theorem upper bound vector velocity write xaxis zero