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Real Analysis

Real analysis cover.png
  • Foreword
  • Introduction

The real numbers 50% developed

  • Ordered Sets \mathbb{N} and \mathbb{Z}
  • Ordered Fields \mathbb{Q}
  • Axioms of The Real Numbers \mathbb{R}
  • Properties of Real Numbers \mathbb{R}
  • Exercises
    • Hints
    • Answers
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Sequences and series 50% developed  as of May 25, 2008 (May 25, 2008)

  • Sequences
  • Series
  • Construction of the Real Numbers \mathbb{R}
  • Exercises
    • Hints
    • Answers
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Metric Spaces 0% developed

  • Metric Spaces
  • Compact Sets
  • Connected Sets
  • Complete Sets
  • Normed Linear Spaces
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Basic Topology of \mathbb{R}^n0% developed  as of March 29, 2009 (March 29, 2009)

  • Open and Closed Sets
  • Limit Points (Accumulation Points)
  • Interior, Closure, Boundary
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Limits and Continuity 50% developed

  • Limits
  • Continuity
  • Topological Continuity
  • Total Variation
  • Arc Length
  • The Exponential Function
  • Exercises
    • Hints
    • Answers
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Differentiation 75% developed

  • Differentiation
  • Applications of Derivatives
  • Multivariable Derivatives
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Integration 75% developed

  • Riemann integration
  • Fundamental Theorem of Calculus
  • Darboux Integral
  • Generalized Integration
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Sequences of Functions 0% developed

  • Pointwise Convergence
  • Uniform Convergence
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Power Series 25% developed

  • Power Series
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Multivariate analysis 25% developed

  • Differentiation in Rn
  • Inverse Function Theorem
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Appendices 100% developed

  • Dedekind's construction
  • Landau notation
  • Bibliography
  • Index
  • Symbols used in this book
    50% developed
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Last modified on 22 September 2012, at 02:50
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