Calculus: One-variable calculus, with an introduction to linear algebra
Now available in paperback! An introduction to the calculus, with an excellent balance between theory and technique. Integration is treated before differentiation--this 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 mean-value 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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Some Basic Concepts of the Theory of Sets
A Set of Axioms for the RealNumber System
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Absolutely convergent algebraic angle arbitrary arctan Assume axioms axis basis calculus called Cartesian equation Cauchy-Schwarz 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 x-axis zero