Mesoamerican Masterclass in Classical Partial Differential Equations and Applications

Registration from May 5 to August 15, 2017

Date and Time

September 4-29, 2017. 09:00 to 13:00 and 16:00 to 18:00

Place

Sala de Usos Múltiples del MCTP,

Ciudad Universitaria Carretera Emiliano Zapata Km. 8, Real del Bosque (Terán).

Tuxtla Gutiérrez, Chiapas, México.

Sponsors

MCTP, CONACYT and UNAM.

Organizers

Horst R Beyer, UNAM-MCTP, horstbeyer@gmail.com

Maricela Beyer, MCTP, mghostwriter21@gmail.com

Summary

There is a rapid increase in the application of more advanced mathematics, in particular, in physics, engineering and technology. In particular, current modern applications are dominated by the mathematical field of partial differential equations.

On the other hand, courses in partial differential equations (PDE) are still relatively rare in mathematics departments. Therefore, a significant increase of courses in this area of mathematics needs to become a priority.

In this connection, it needs to be taken into account that specialist courses in PDE, usually require a considerable background of functional analysis, which cannot always be expected from students from applications, like physicists and engineers. On the other hand, a considerable part of PDE can be taught using “classical methods, ” that require little more than good mastery “calculus/analysis,” without the necessity of sacrificing mathematical rigor. In addition, such a course provides the basis as well as motivation for taking courses in PDE that rely heavily on functional analysis methods, such as courses given by one of the main organizers, Horst R Beyer, in abstract quasilinear evolution equations.

Contents

1 Conventions

2 Basic Definitions

3 Three Main Examples of PDE

4 First-Order Quasi-Linear PDE for One Real-Valued Function

4.1 The Linear Case

4.1.1 Integral Curves of Vector Fields

4.1.2 The Linear Case

4.1.3 Characteristic Surfaces

4.1.4 Time Decay of Solutions of PDE (“Energy Method”)

4.2 The Quasi-Linear Case

4.2.1 Incompressible Euler’s Equations in One Space Dimension

5 Systems of Quasi-Linear PDE

5.1 Linear Symmetric Hyperbolic Systems

5.2 Compressible Euler’s Equations in One Space Dimension

5.3 Hyperbolic Systems

5.4 The Inhomogeneous Wave Equation in One Space Dimension

6 Second-Order PDE for One Unknown Function

6.1 Classification of Quasi-Linear Second-Order PDE

6.1.1 Second-Order Equations With Constant Coefficients

6.2 Main Examples of Hyperbolic Equations

6.2.1 The Wave Equation in Three Space Dimensions

6.2.2 The Wave Equation in Two Space Dimensions

6.2.3 Inhomogeneous Wave Equations

6.3 Conservation Laws for Wave Equations

6.4 Main Examples of Elliptic Equations

6.4.1 The Method of Separation of Variables

6.4.2 Simple Transformations of the Laplace Operator

6.4.3 Strong Maximum Principles

6.5 Green’s Representation Formula

6.6 The Solution of the Dirichlet Problem for Balls in

6.7 Heat Equation

Registration

Interested persons should pre-register using the "Pre-registro" https://goo.gl/DBhHA0

After preregistration, persons from Mesoamerica in need of support can apply for support for lodging and transportation. In this case, please, send your application letter plus CV to: mghostwriter21@gmail.com. (Note that financial support is granted only to selected participants, after an evaluation.)

UNACH/MCTP, Ciudad Universitaria

Carretera Emiliano Zapata Km. 4,

Real del Bosque (Terán).

Tuxtla Gutiérrez, Chiapas, México.

C. P. 29050

Teléfono 52 (961) 617-80-00

Ext. 8200 y 1380

Carretera Emiliano Zapata Km. 4,

Real del Bosque (Terán).

Tuxtla Gutiérrez, Chiapas, México.

C. P. 29050

Teléfono 52 (961) 617-80-00

Ext. 8200 y 1380

mctp@unach.mx

© 2013 MCTP

Desarrollado por MCTP

© 2013 MCTP

Desarrollado por MCTP