Lecture 24: Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits

Lecture 24 of 25 in Real Analysis (MIT 18.100A) by WD Academia. 1 h 15 min. Watch on YouTube

Course: Real Analysis (MIT 18.100A) (Mathematics). Covers: sequences series limits continuity riemann integral.

All lectures in Real Analysis (MIT 18.100A)

  1. Lecture 1: Sets, Set Operations and Mathematical Induction · 1 h 14 min
  2. Lecture 2: Cantor's Theory of Cardinality (Size) · 1 h 25 min
  3. Lecture 3: Cantor's Remarkable Theorem and the Rationals' Lack of the Least Upper Bound Property · 1 h 19 min
  4. Lecture 4: The Characterization of the Real Numbers · 1 h 22 min
  5. Lecture 5: The Archimedian Property, Density of the Rationals, and Absolute Value · 1 h 18 min
  6. Lecture 6: The Uncountabality of the Real Numbers · 1 h 22 min
  7. Lecture 7: Convergent Sequences of Real Numbers · 1 h 1 min
  8. Lecture 8: The Squeeze Theorem and Operations Involving Convergent Sequences · 1 h 15 min
  9. Lecture 9: Limsup, Liminf, and the Bolzano-Weierstrass Theorem · 1 h 14 min
  10. Lecture 10: The Completeness of the Real Numbers and Basic Properties of Infinite Series · 1 h 16 min
  11. Lecture 11: Absolute Convergence and the Comparison Test for Series · 1 h 0 min
  12. Lecture 12: The Ratio, Root, and Alternating Series Tests · 1 h 0 min
  13. Lecture 13: Limits of Functions · 1 h 13 min
  14. Lecture 14: Limits of Functions in Terms of Sequences and Continuity · 1 h 1 min
  15. Lecture 15: The Continuity of Sine and Cosine and the Many Discontinuities of Dirichlet's Function · 1 h 2 min
  16. Lecture 16: The Min/Max Theorem and Bolzano's Intermediate Value Theorem · 1 h 8 min
  17. Lecture 17: Uniform Continuity and the Definition of the Derivative · 1 h 13 min
  18. Lecture 18: Weierstrass's Example of a Continuous and Nowhere Differentiable Function · 1 h 16 min
  19. Lecture 19: Differentiation Rules, Rolle's Theorem, and the Mean Value Theorem · 1 h 14 min
  20. Lecture 20: Taylor's Theorem and the Definition of Riemann Sums · 53 min
  21. Lecture 21: The Riemann Integral of a Continuous Function · 1 h 7 min
  22. Lecture 22: Fundamental Theorem of Calculus, Integration by Parts, and Change of Variable Formula · 1 h 12 min
  23. Lecture 23: Pointwise and Uniform Convergence of Sequences of Functions · 1 h 9 min
  24. Lecture 24: Uniform Convergence, the Weierstrass M-Test, and Interchanging Limits · 1 h 15 min
  25. Lecture 25: Power Series and the Weierstrass Approximation Theorem · 1 h 16 min