Description

Book Synopsis


Table of Contents
  • Intervals
  • Toplogy of the real line
  • Continuous functions from $\mathbb{R}$ to $\mathbb{R}$
  • Sequences of real numbers
  • Connectedness and the intermediate value theorem;
  • Compactness and the extreme value theorem;
  • 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;
  • More on continuity and limits;
  • Compact metric spaces;
  • Sequenctial characterization of compactness;
  • Connectedness;
  • Complete spaces;
  • A fixed point theorem;
  • Vector spaces;
  • Linearity;
  • Norms;
  • Continuity and linearity;
  • The Cauchy integral;
  • Differential calculus;
  • Partial derivatives and iterated integrals;
  • Computations in $\mathbb{R}^n$;
  • Infinite series;
  • The implicit function theorem;
  • Higher order derivatives;
  • Quantifiers;
  • Sets;
  • Special subsets of $\mathbb{R}$;
  • Logical connectives;
  • Writing mathematics;
  • Set operations;
  • Arithmetic;
  • Order propertiers of $\mathbb{R}$;
  • Natural numbers and mathematical induction;
  • Least upper bounds and greatest lower bounds;
  • Products, relations, and functions;
  • Properties of functions;
  • Functions that have inverses;
  • Products;
  • Finite and infinite sets;
  • Countable and uncountable sets;
  • Bibliography;
  • Index.

A Problems Based Course in Advanced Calculus

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    A Hardback by John M. Erdman

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      Publisher: MP-AMM American Mathematical
      Publication Date: Publication Date: 8/30/2018 12:00:00 AM
      ISBN13: 9781470442460, 978-1470442460
      ISBN10: 1470442469
      Also in:
      Not Just Books Stationery

      Description

      Book Synopsis


      Table of Contents
      • Intervals
      • Toplogy of the real line
      • Continuous functions from $\mathbb{R}$ to $\mathbb{R}$
      • Sequences of real numbers
      • Connectedness and the intermediate value theorem;
      • Compactness and the extreme value theorem;
      • 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;
      • More on continuity and limits;
      • Compact metric spaces;
      • Sequenctial characterization of compactness;
      • Connectedness;
      • Complete spaces;
      • A fixed point theorem;
      • Vector spaces;
      • Linearity;
      • Norms;
      • Continuity and linearity;
      • The Cauchy integral;
      • Differential calculus;
      • Partial derivatives and iterated integrals;
      • Computations in $\mathbb{R}^n$;
      • Infinite series;
      • The implicit function theorem;
      • Higher order derivatives;
      • Quantifiers;
      • Sets;
      • Special subsets of $\mathbb{R}$;
      • Logical connectives;
      • Writing mathematics;
      • Set operations;
      • Arithmetic;
      • Order propertiers of $\mathbb{R}$;
      • Natural numbers and mathematical induction;
      • Least upper bounds and greatest lower bounds;
      • Products, relations, and functions;
      • Properties of functions;
      • Functions that have inverses;
      • Products;
      • Finite and infinite sets;
      • Countable and uncountable sets;
      • Bibliography;
      • Index.

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