MIT OpenCourseWare
Differential Analysis II: Partial Differential Equations and Fourier Analysis
- Instructor
- Prof. Lawrence D Guth
- Term
- Spring 2016
- Level
- Graduate
- What's inside
- 7 problem sets · 1 lecture note · 25 other files · 3 web pages
- Materials open
- MIT OCW
Other versions of this course
- 18.156 · Spring 2016 · Study here (this version)
- 18.156 · Spring 2004 · Study here
About this course
Source: MIT OpenCourseWare 18.156 Differential Analysis II: Partial Differential Equations and Fourier Analysis, Spring 2016, Prof. Lawrence D Guth — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Study order: none is claimed; materials are grouped by MIT's own sections. 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.
How this course was organized
What's here, and what isn't
- MIT lists a session calendar for this course, but it could not be verified well enough to build a sequence from it — materials are grouped by section instead.
Not included here
2 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. (2 items)
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Syllabus
Lecture Notes
24 files
- Lecture 1-2 Harmonic Functions Download
- Lecture 3 Korn's Inequality Download
- Lecture 4 Korn's Inequality (cont.) Download
- Lecture 5 Proof of Korn's Inequality Download
- Lecture 6 Schauder Estimate and "Solving" Elliptic PDE Download
- Lecture 7 Elliptic Dirichlet Problem Download
- Lecture 8 Sobolev Inequality Download
- Lecture 9 Sobolev Inequality (cont.) Download
- Lecture 10-12 DiGeorgi-Nash-Moser Theorem Download
- Lecture 13 Non-linear Elliptic PDE Download
- Lecture 14 Comparison Principle for Nonlinear Equations Download
- Lecture 15 Comparison Principle for Nonlinear Equations (cont.) Download
- Lecture 16-17 Minimal Graphs Download
- Lecture 20 Fourier Analysis Download
- Lecture 21 Sierpinski Theorem Download
- Lecture 22-24 Schr ̈odinger Equation Download
- Lecture 25 Applications of Interpolation and Calderon-Zygmund Theorem Download
- Lecture 26 Proof of the Calderon Zygmund Theorem Download
- Lecture 27 Discussion of Problem Set 4 and Calderon-Zygmund Theorem Download
- Lecture 28 Proof of the Calderon Zygmund Theorem (cont.) Download
- Lecture 29 Strichartz Inequality and Inhomogeneous Schrodinger Equation Download
- Lecture 30 Proof of Strichartz Theorem Download
- Lecture 31-34 Non-Linear Schrödinger Equation Download
- Lecture Summary, Course Description for Real Analysis Download
Assignments
7 files
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 1 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 2 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 3 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 4 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 5 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Problem Set 6 Download
- Differential Analysis II: Partial Differential Equations and Fourier Analysis, Optional Problems for Study and Review Download
MIT OpenCourseWare, Prof. Lawrence D Guth, 18.156 Differential Analysis II: Partial Differential Equations and Fourier Analysis, Spring 2016.
License: CC BY-NC-SA 4.0 · Edition: Spring 2016 · Open the original course on OCW ↗
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