Introduction to Mathematical Analysis

Introduction to Mathematical Analysis

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An Introduction to Mathematical Analysis provides detailed explanations and exhaustive proofs, and follows an axiomatic approach to presenting the material. The text assumes little background in mathematical analysis. The proofs are formal, complete, and augmented by an informal and heuristic explanation. The author presents the subject in clear and evocative language, and includes treatment of the Lebesgue integral, a topic not usually found in texts of this level. Features: * All the information introduced is proved by axioms * Extensive proofs are formal and complete * Includes a novel treatment of the Lebesgue integral * Emphasis on developing proofs helps students acquire skills essential to subsequent courses
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Product details

  • Hardback | 252 pages
  • 165.1 x 241.3 x 25.4mm | 612.35g
  • Academic Press Inc
  • San Diego, United States
  • English
  • b&w illustrations
  • 0120839407
  • 9780120839407

Table of contents

Exhortation; the field axioms; the order relation; the natural numbers; finite and infinite sets; long division and prime factorization; the completeness axiom and sequences; three heavy theorems on sequences; alternative completeness axioms; continuous functions; uniform continuity; closed sets, open sets, compact sets; derivatives; the Darboux integral; the Riemann definition; log x and e x; unordered sums and infinte series; the calculus of series; sequences and series of functions; topology in R2; calculus of two variables; complex numbers; curves in the plane; trigonometric functions; line integrals; power series; the transcendental functions; Cauchy's integral theorems; Lebesgue measure in (0,1); measurable sets; the Lebesgue integral; measurable functions; convergence theorems.
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