M2: Analysis II - Continuity and Differentiability (2024-25)

Section outline

• Select section General

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  General

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  • Select activity Announcements

    

    Announcements Forum
  • Select activity Reading List

    

    Reading List URL
  • Select activity Discussion Forum

    

    Discussion Forum
  • Select activity Prelims Mathematics Syllabus

    

    Prelims Mathematics Syllabus File
  • Select activity Mathematics and Philosophy Syllabus

    

    Mathematics and Philosophy Syllabus File
• Select section Course Materials

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  Course Materials

  • Select activity Lecture Notes

    

    Lecture Notes File

    Lecture notes for HT 2025.

  • Select activity Sheet 1

    

    Sheet 1 Assignment

    Limit points and function limits.

  • Select activity Sheet 2

    

    Sheet 2 Assignment

    Continuity, Boundedness Theorem.

  • Select activity Sheet 3

    

    Sheet 3 Assignment

    IVT, Continuous IFT, monotone functions.

  • Select activity Sheet 4

    

    Sheet 4 Assignment

    Uniform continuity, uniform convergence.

  • Select activity Sheet 5

    

    Sheet 5 Assignment

    Differentiation.

  • Select activity Sheet 6

    

    Sheet 6 Assignment

    MVT and its consequences.

  • Select activity Sheet 7

    

    Sheet 7 Assignment

    Taylor's Theorem.

  • Select activity Sheet 8

    

    Sheet 8 Assignment

    L'Hopital's rule, calculating limits.

  • Select activity The Exponential Function

    

    The Exponential Function File

    Supplementary notes on exp(x) (non-examinable). Uses material from Analysis I only.
    

  • Select activity Space Filling Curves

    

    Space Filling Curves File

    Construction of a space filling curve (non-examinable). Uses material from the course on uniform convergence.

  • Select activity The Basel Problem

    

    The Basel Problem File

    Elementary (non-examinable) proof of ∑1/n² = π²/6. Later parts use Mean Value Theorem.