MIT OpenCourseWare

Browse materialsMIT 18.100B · Spring 2025

Real Analysis

Subjects: Calculus · Mathematics

Art: Max Brückner (1860 – 1934), Brückner Vielflache Tafel 07 · Public domain

Instructor: Prof. Tobias Holck Colding
Term: Spring 2025
Level: Undergraduate, Graduate
What's inside: 25 videos · 10 problem sets · 1 exam · 2 lecture notes · 1 reading · 50 other files · 3 web pages
Materials open: Videos here · files on MIT OCW

Start here

Start course: Lecture 1: Introduction to Real Numbers Find a topic

Progress is saved in this browser.

Export or import progress

About this course

Source: MIT OpenCourseWare 18.100B Real Analysis, Spring 2025, Prof. Tobias Holck Colding — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: MIT's own listing order, section by section. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 23, 2026. How RedLectern is built.

Materials are grouped the way MIT organized them. A verified, course-wide order has not been established here.

Before you start

Prerequisites are not listed here. Check MIT's own syllabus for this course.

This course’s cited books, in our reading lists: Elementary Real Analysis · Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics)

How this course was organized

What's here, and what isn't

MIT's own materials here did not support a verified, course-wide order, so they are grouped by section instead.

Not included here

5 items from the source could not be safely included:

MIT's page format for this item wasn't recognized clearly enough to place it safely. (5 items)

Materials by section

Grouped by section, as MIT organized them. Not sequenced or ordered.

Lecture Notes

26 files

Problem Sets

11 files

2 video transcripts

Other materials from this course

23 video transcripts

MIT OpenCourseWare, Prof. Tobias Holck Colding, 18.100B Real Analysis, Spring 2025.

License: CC BY-NC-SA 4.0 · Edition: Spring 2025 · Open the original course on OCW ↗

Organized by RedLectern, independent of MIT and not endorsed by MIT.

Per-resource rights are recorded on each resource; All-Rights-Reserved items are link-only, never mirrored.

Real Analysis

Before you start

What's here, and what isn't

Not included here

Materials by section

Lecture Notes

Problem Sets

Other materials from this course

Lecture 1: Introduction to Real Numbers

Lecture 2: Introduction to Real Numbers (cont.)

Lecture 3: How to Write a Proof; Archimedean Property

Lecture 4: Sequences; Convergence

Lecture 5: Monotone Convergence Theorem

Lecture 6: Cauchy Convergence Theorem

Lecture 7: Bolzano–Weierstrass Theorem; Cauchy Sequences; Series

Lecture 8: Convergence Tests for Series; Power Series

Lecture 9: Limsup and Liminf; Power Series; Continuous Functions; Exponential Function

Lecture 10: Continuous Functions; Exponential Function (cont.)

Lecture 11: Extreme and Intermediate Value Theorem; Metric Spaces

Review for 18.100B Real Analysis Midterm

Lecture 12: Convergence in Metric Spaces; Operations on Sets

Lecture 13: Open and Closed Sets; Coverings; Compactness

Lecture 14: Sequential Compactness; Bolzano–Weierstrass Theorem in a Metric Space

Lecture 15: Derivatives; Laws for Differentiation

Lecture 16: Rolle’s Theorem; Mean Theorem; L’Hôpital’s Rule; Taylor Expansion

Lecture 17: Taylor Polynomials; Remainder Term; Riemann Integrals

Lecture 18: Integrable Functions

Lecture 19: Fundamental Theorem of Calculus

Lecture 20: Pointwise Convergence; Uniform Convergence

Lecture 21: Integrals and Derivatives under Uniform Convergence

Lecture 22: Differentiating and Integrating Power Series; Ordinary Differential Equations (ODEs)

Lecture 23: Existence & Uniqueness for ODEs: Picard–Lindelöf Theorem

Review for the 18.100B Real Analysis Final Exam