Partial Differential Equations

The Mathematics of PDEs and the Wave Equation

Author: 
Michael P. Lamoureux
Date: 
Tue, Aug 1, 2006
Location: 
University of Calgary, Calgary, Canada
Conference: 
Seismic Imaging Summer School
Abstract: 

We look at the mathematical theory of partial differential equations as applied to the wave equation. In particular, we examine questions about existence and uniqueness of solutions, and various solution techniques.

Notes: 
PDF icon Lamoureux_Michael.pdf
Class: 
Applied
Subject: 
Partial Differential Equations

Mathematics of Seismic Imaging

Author: 
William W. Symes
Date: 
Fri, Jul 1, 2005
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
PIMS Distinguished Chair Lectures
Abstract: 

These lectures present a mathematical view of reflection seismic imaging, as practiced in the petroleum industry.

Notes: 
PDF icon symes.pdf
Class: 
Applied
Subject: 
Geophysics
Partial Differential Equations

The Richness of Thin Films

Author: 
Mary Pugh
Date: 
Fri, Jan 2, 2004
Location: 
University of British Columbia, Vancouver, Canada
Conference: 
IAM-PIMS Distinguished Colloquium Series
Abstract: 

I will present a survey of modelling, computational, and analytical work on thin liquid films of viscous fluids. I will particularly focus on films that are being acted on by more than one force. For example, if you've painted the ceiling, how do you model the effects of surface tension and gravity? How do you study the dynamics of the air/liquid interface? How do things change if you're considering a freshly painted wall? Or floor?

Notes: 
PDF icon MaryPugh_DCS.pdf
Class: 
Applied
Subject: 
Fluid Mechanics
Partial Differential Equations

PDE from a probability point of view

Author: 
Richard Bass
Date: 
Thu, Jan 1, 2004
Location: 
UBC, Vancouver, Canada
Abstract: 

These notes are for a course I gave while on sabbatical at UBC. The topics covered are: stochastic differential equations, solving PDEs using probability, Harnack inequalities for nondivergence form elliptic operators, martingale problems, and divergence form elliptic operators.

This course presupposes the reader is familiar with stochastic calculus; see the notes on my web page for Stochastic Calculus, for example. These notes for the most part are based on my book Diffusions and Elliptic Operators, Springer-Verlag, 1997.

Notes: 
PDF icon Bass.pdf
Class: 
Scientific
Subject: 
Partial Differential Equations
Probability

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