Lecture Notes | Differential Analysis II: Partial Differential Equations and Fourier Analysis | Mathematics | MIT OpenCourseWare

Course Info

Instructor

Prof. Lawrence D Guth

Departments

Mathematics

As Taught In

Spring 2016

Level

Graduate

Topics

Mathematics
- Differential Equations
- Mathematical Analysis

Learning Resource Types

Problem Sets

Lecture Notes

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Lecture Notes

Lecture Summary, Course Description for Real Analysis

Lecture 1-2 Harmonic Functions

Lecture 3 Korn's Inequality

Lecture 4 Korn's Inequality (cont.)

Lecture 5 Proof of Korn's Inequality

Lecture 6 Schauder Estimate and "Solving" Elliptic PDE

Lecture 7 Elliptic Dirichlet Problem

Lecture 8 Sobolev Inequality

Lecture 9 Sobolev Inequality (cont.)

Lecture 10-12 DiGeorgi-Nash-Moser Theorem

Lecture 13 Non-linear Elliptic PDE

Lecture 14 Comparison Principle for Nonlinear Equations

Lecture 15 Comparison Principle for Nonlinear Equations (cont.)

Lecture 16-17 Minimal Graphs

Lecture 20 Fourier Analysis

Lecture 21 Sierpinski Theorem

Lecture 22-24 Schr ̈odinger Equation

Lecture 25 Applications of Interpolation and Calderon-Zygmund Theorem

Lecture 26 Proof of the Calderon Zygmund Theorem

Lecture 27 Discussion of Problem Set 4 and Calderon-Zygmund Theorem

Lecture 28 Proof of the Calderon Zygmund Theorem (cont.)

Lecture 29 Strichartz Inequality and Inhomogeneous Schrodinger Equation

Lecture 30 Proof of Strichartz Theorem

Lecture 31-34 Non-Linear Schrödinger Equation

Course Info

Instructor

Prof. Lawrence D Guth

Departments

Mathematics

As Taught In

Spring 2016

Level

Graduate

Topics

Mathematics
- Differential Equations
- Mathematical Analysis

Learning Resource Types

Problem Sets

Lecture Notes

Download Course

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