Real analysis

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<<Cover & Inter-wiki

[edit] The real numbers

[edit] Sequences and series

[edit] Limits and Continuity

[edit] Differentiation

[edit] Integration

[edit] Power Series

[edit] Sequences of Functions

[edit] Multivariate analysis


[edit] Appendices

[edit] Other suggested topics for inclusion

Since the goal here is to put calculus on a solid footing, I am going to add background, so that we develop the concept of a number first, and work to functions more slowly and methodically, to include Heine-Borel, Weierstrass, etc.

Things that seem to fit in this context:

  • (Basic) functional analysis:
    • Uniform Convergence, function spaces
    • Arzela-Ascoli Theorem
    • Stone-Weierstrass Theorem
    • Riemann-Stieltjes integrals and bounded variation
  • Measure theory:
    • Measure theory/Lebesgue integrals
  • Generalized function (distributions) theory
  • Some basic harmonic analysis (Fourier series and transforms).

However, both functional analysis and measure theory could do with their own Wikibooks

Things that might better be in Set Theory:

  • Infinite sets and cardinality

Things that might better be in Topology:

  • Introduction to different concepts of space: topological, metric, normed, inner product
  • Basic topology: accumulation points, closure, interior, boundary, convergence of sequences, in each case with discussion of the type of space the concept is appropriate to.
  • Completeness
  • Compactness
  • Connectedness
  • Continuous maps
  • Metric spaces
  • Contraction Mapping Principle
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