A Concrete Introduction to Real Analysis.1584886544 A concrete introduction to real analysis. Carlson, Robert. Chapman & Hall/CRC 2006 296 pages $89.95 Hardcover QA300 Carlson (mathematics, U. of Colorado at Colorado Springs Colorado Springs, city (1990 pop. 281,140), seat of El Paso co., central Colo., on Monument and Fountain creeks, at the foot of Pikes Peak; inc. 1886. It is a year-round resort and a booming military, technological, and commercial city. ) takes readers from a focus on calculations to a proof-centered approach. He begins by picking up discrete calculus, including proof by induction, and moves to selected area computation (pi, anyone?), limit's and Taylor's theorem In calculus, Taylor's theorem, named after the mathematician Brook Taylor, who stated it in 1712, gives the approximation of a differentiable function near a point by a polynomial whose coefficients depend only on the derivatives of the function at that point. , including series representations and Taylor polynomials, infinite series infinite series In mathematics, the sum of infinitely many numbers, whose relationship can typically be expressed as a formula or a function. An infinite series that results in a finite sum is said to converge (see convergence). One that does not, diverges. , including both the positive and the general, beginning logic, including propositional logic (logic) propositional logic - (or "propositional calculus") A system of symbolic logic using symbols to stand for whole propositions and logical connectives. Propositional logic only considers whether a proposition is true or false. , predicates and quantifiers, and proofs, real numbers, functions such as derivatives and a substantial pair of chapters on integrals. Carlson provides exercises with each chapter. ([c]20062005 Book News, Inc., Portland, OR) |
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