Problems Based Course in Advanced Calculus [Kõva köide]

This textbook is meant for advanced calculus courses taken by majors in math and physical sciences who have completed a standard introductory calculus sequence. It focuses on conceptual development and proofs through exercises or problems, covering intervals; topology of the real line; continuous functions from R to R; sequences of real numbers; connectedness and the intermediate value theorem; compactness and the extreme value theorem; the limits of real valued functions; differentiation of real valued functions; metric spaces; interiors, closures, and boundaries; the topology of metric spaces; sequences in metric spaces; uniform convergence; compact metric spaces; sequential characterization of compactness; connectedness; complete spaces; the contractive mapping theorem; vector spaces; linearity; continuity and linearity; norms; the Cauchy integral; differential calculus; partial derivatives and iterated integrals; computations in Rn; infinite series; the implicit function theorem; and higher order derivatives. The appendices summarize prerequisite information. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)