Calendar · Lecture Notes
MIT OpenCourseWare
Introduction to Partial Differential Equations
Art: Johannes Kepler, Konjukce Saturnu a Jupiteru Originál, 1596 · Public domain
- Instructor
- Prof. Tobias Holck Colding
- Term
- Fall 2005
- Level
- Undergraduate
- What's inside
- 2 problem sets · 1 lecture note · 25 other files · 3 web pages
- Materials open
- MIT OCW
Other versions of this course
- 18.152 · Fall 2011 · Study here
- 18.152 · Fall 2005 · Study here (this version)
About this course
Source: MIT OpenCourseWare 18.152 Introduction to Partial Differential Equations, Fall 2005, 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.
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.
Materials by section
Grouped by section, as MIT organized them. Not sequenced or ordered.
Lecture Notes
23 files
- Harmonic Functions and the Harnack Inequality Download
- The Gradient Estimate Download
- The Hopf Maximum Principle Download
- The Poincare Inequalities Download
- The Cacciopolli Inequality Download
- More General Operators Download
- Consequences of Cacciopolli Download
- Maximum Principles and Gradient Estimates Download
- Hopf and Harnack for L-harmonic Functions Download
- An Improved Gradient Estimate for Harmonic Functions Download
- More on Harmonic Functions on a Ball Download
- Solving the Laplace Equation in R²: The Dirichlet Problem Download
- The Heat Equation Download
- A Gradient Estimate for the Heat Equation on a Ball Download
- Campanato’s Lemma and Morrey’s Lemma Download
- Five Inequalities for Harmonic Functions Download
- Regularity of L-harmonic Functions Part I Download
- Regularity of L-harmonic Functions Part II Download
- Regularity of L-harmonic Functions Part III Download
- Smoothness of L-harmonic Functions Download
- The Mean Value Inequality Revisited Part I Download
- The Mean Value Inequality Revisited Part II Download
- Moser’s Approach Download
Assignments
- This resource contains 5 problems on harmonic function, laplacian coordinates, Green's functions… (pset.pdf) Download
- This resource contains 4 problems on harmonic functions (pset2.pdf) Download
Other materials from this course
Course outline
Calendar · Lecture Notes
Lecture 2: The Gradient Estimate
Calendar · Lecture Notes
Lecture 3: The Hopf Maximum Principle
Calendar · Lecture Notes
Lecture 4: The Poincare Inequalities
Calendar · Lecture Notes
Lecture 5: The Cacciopolli Inequality
Calendar · Lecture Notes
Lecture 6: More General Operators
Calendar · Lecture Notes
Lecture 7: Consequences of Cacciopolli
Calendar · Lecture Notes
Lecture 8: Maximum Principles and Gradient Estimates
Calendar · Lecture Notes
Lecture 9: Hopf and Harnack for L-harmonic Functions
Calendar · Lecture Notes
Lecture 10: An Improved Gradient Estimate for Harmonic Functions
Calendar · Lecture Notes
Lecture 11: More on Harmonic Functions on a Ball
Calendar · Lecture Notes
Lecture 12: Solving the Laplace Equation in R²: The Dirichlet Problem
Calendar · Lecture Notes
Lecture 13: The Heat Equation
Calendar · Lecture Notes
Lecture 14: A Gradient Estimate for the Heat Equation on a Ball
Calendar · Lecture Notes
Lecture 15: Campanato’s Lemma and Morrey’s Lemma
Calendar · Lecture Notes
Lecture 16: Five Inequalities for Harmonic Functions
Calendar · Lecture Notes
Lecture 17: Regularity of L-harmonic Functions Part I
Calendar · Lecture Notes
Lecture 18: Regularity of L-harmonic Functions Part II
Calendar · Lecture Notes
Lecture 19: Regularity of L-harmonic Functions Part III
Calendar · Lecture Notes
Lecture 20: Smoothness of L-harmonic Functions
Calendar · Lecture Notes
Lecture 21: The Mean Value Inequality Revisited Part I
Calendar · Lecture Notes
Lecture 22: The Mean Value Inequality Revisited Part II
Calendar · Lecture Notes
Lecture 23: Moser’s Approach
MIT OpenCourseWare, Prof. Tobias Holck Colding, 18.152 Introduction to Partial Differential Equations, Fall 2005.
License: CC BY-NC-SA 4.0 · Edition: Fall 2005 · Open the original course on OCW ↗
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