WJWJ Maths
Real Analysis
  • Topology of the Real Line
  • Intervals
  • Closed Sets
  • Open Sets
  • Compact Sets
  • Cantor’s Intersection or Nested Interval theorem
  • Connected Sets
  • Practice Problems
  • Continuous functions
  • Limits of functions
  • Continuous functions
  • Properties of Continuous functions
  • Continuity and Compactness
  • Continuity and Connectedness
  • Uniform Continuity
  • Uniform Convergence
  • Sequence of functions
  • Approximation
  • Monotone and Inverse functions
  • Practice Problems
  • Functions of Bounded Variation
  • Algebraic Properties
  • Differentiable functions
  • Differentiability and Continuity
  • Rolle’s Theorem And The Mean Value Theorem (MVT)
  • Local Maximum and Local Minimum
  • Higher Order Derivatives
  • Taylor’s Theorem
  • L’H\(\hat {\text {o}}\)pital’s Rule
  • Practice Problems
  • The Riemann Integral
  • Partitions and the Riemann Sums
  • Properties of the Riemann Integral
  • Fundamental Theorem of Calculus
  • Improper Integrals
  • Riemann-Stieljes Integral
  • References
  • Practice Problems

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4 Differentiable functions

4.1 Differentiability and Continuity
4.2 Rolle’s Theorem And The Mean Value Theorem (MVT)
4.3 Local Maximum and Local Minimum
4.4 Higher Order Derivatives
4.5 Taylor’s Theorem
4.6 L’H\(\hat {\text {o}}\)pital’s Rule
4.7 Practice Problems

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