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Guide

18.100B Real Analysis

  • - L1 Introduction to Real Numbers

  • - L2 Introduction to Real Numbers (cont.)

  • - L3 How to Write a Proof; Archimedean Property

  • - L4 Sequences; Convergence

  • - P1 Problem set 1 due

  • - L5 Monotone Convergence Theorem

  • - L6 Cauchy Convergence Theorem

  • - P2 Problem set 2 due

  • - L7 Bolzano–Weierstrass Theorem; Cauchy Sequences; Series

  • - L8 Convergence Tests for Series; Power Series

  • - P3 Problem set 3 due

  • - L9 Limsup and Liminf; Power Series; Continuous Functions; Exponential Function

  • - L10 Continuous Functions; Exponential Function (cont.)

  • - P4 Problem set 4 due

  • - L11 Extreme and Intermediate Value Theorem; Metric Spaces

  • - Mid-Term Review for Midterm

  • - P5 Problem set 5 due

  • - Mid-Term Midterm exam

  • - L12 Convergence in Metric Spaces; Operations on Sets

  • - L13 Open and Closed Sets; Coverings; Compactness

  • - L14 Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space

  • - P6 Problem set 6 due

  • - L15 Derivatives; Laws for Differentiation

  • - L16 Rolle’s Theorem; Mean Theorem; L’Hôpital’s Rule; Taylor Expansion

  • - P7 Problem set 7 due

  • - L17 Taylor Polynomials; Remainder Term; Riemann Integrals

  • - L18 Integrable Functions

  • - P8 Problem set 8 due

  • - L19 Fundamental Theorem of Calculus

  • - L20 Pointwise Convergence; Uniform Convergence

  • - P9 Problem set 9 due

  • - L21 Integrals and Derivatives under Uniform Convergence

  • - L22 Differentiating and Integrating Power Series; Ordinary Differential Equations (ODEs)

  • - P10 Problem set 10 due

  • - L23 Existence and Uniqueness for ODEs: Picard–Lindelöf Theorem

  • - Final Review for Final

  • - Final Final exam