PDE Lecture Notes
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This page contains lecture notes for Math 231 . The notes are in PDF format. Click on the link to get the desired file(s).

Compiled Analysis and PDE Notes.

The notes are split into two files. The first being mostly real analysis and the second being mostly PDE.  Furthermore you may download them in two formats. (These notes will be available for a limited time only since they are not finished and not yet ready for widespread distribution.) So please do not distribute.

Format 1 (More pages to print.)

bulletPart 1: Analysis Notes in one page format
bulletPart 2: PDE Notes in one page format

Format 2 (Fewer  pages to print.)

bulletPart 1: Analysis Notes in two page format
bulletPart 2: PDE Notes in two page format

 

Original Notes from the course follow.

Math 231A Course Notes

bulletPDE Lecture_Notes: Chapters 1- 2. (PDE Intro and Quasi-linear first order PDE)
bulletPDE Lecture_Notes: Chapter 3 (Non-linear first order PDE)
bulletPDE Lecture_Notes: Chapter 4 (Cauchy -- Kovalevskaya Theorem )
bulletPDE Lecture_Notes: Chapter 5 (A Very Short introduction to Generalized Functions)
bulletPDE Lecture_Notes: Chapter 6 (Elliptic second order ODE)

Math 231B Course Notes

bulletCompact and Fredholm Operators
bulletConvolutions, Test functions, and partitions of unity.
bulletSurface integrals and the divergence theorem
bulletThe Poisson and Dirichlet Problem
bulletFourier Transform
bulletSpectral_Theorem
bulletConstant Coefficient PDE
bulletHeat Equation
bulletAbstract wave Equation
bulletWave_Equation on R^n

Math 231C Course Notes

bulletWeak and Strong Derivatives (Basic Properties)
bulletSobolev Spaces (Basic Properties)
bulletHolder-spaces
bulletSobolev Inequalities
bulletElliptic PDE: I
bullet 

Appendices

Math 231A

bulletLecture_Notes: Basic Analysis
bulletLecture_Notes: Riemann Integral for Banach Space Valued Functions
bulletLecture_Notes: Ordinary Differential Equations
bulletLecture_Notes: Calculus on Banach Space, Inverse and Implicit Function Theorems, More ODE

Math 231B

bulletHilbert Space

Math 231C

bullet Lecture Notes: Chapter 11- Convolutions and Approximations
bulletLecture_Notes: Lax-Milgram method and unbounded operators

 

 

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Last modified on April 03, 2003 at 09:25 AM.