Introduction to Classical Partial Differential Equations and Applications

Lecture: Prof. Horst R. Beyer.
Language: English-Spanish

Date and Time

December 04 to 08, 2017.
Monday to Friday from 10:00 to 13.00 hrs.


Sala de Usos Múltiples de la Facultad del MCTP,
Real del Bosque (Terán).
Tuxtla Gutiérrez, Chiapas, México.



Level of the course

Basic to Medium, participants might need basic knowledge in Calculus and Ordinary Differential Equations. Atentamente,


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


Dra. Karen Salomé Caballero Mora.
Dr. Sendic Estrada Jimenez.

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
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Desarrollado por MCTP