Partial Differential Equations 0.15 alpha
© Leon van Dommelen
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1.1 Basic Concepts
1
. Introduction
Subsections
1
.
1
Basic Concepts
1
.
1
.
1
The prevalence of partial differential equations
1
.
1
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2
Definitions
1
.
1
.
3
Typical boundary conditions
1
.
2
The Standard Examples
1
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2
.
1
The Laplace equation
1
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2
.
2
The heat equation
1
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2
.
3
The wave equation
1
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3
Classification
1
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3
.
1
Introduction
1
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3
.
2
Scalar second order equations
1
.
4
Changes of Coordinates
1
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4
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1
Introduction
1
.
4
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2
The formulae for coordinate transformations
1
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4
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3
Rotation of coordinates
1
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4
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4
Explanation of the classification
1
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5
Two-Dimensional Coordinate Transforms
1
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5
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1
Characteristic Coordinates
1
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5
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2
Parabolic equations in two dimensions
1
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5
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3
Elliptic equations in two dimensions
1
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6
Properly Posedness
1
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6
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1
The conditions for properly posedness
1
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6
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2
An improperly posed parabolic problem
1
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6
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3
An improperly posed elliptic problem
1
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6
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4
Improperly posed hyperbolic problems
1
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7
Energy methods
1
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7
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1
The Poisson equation
1
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7
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2
The heat equation
1
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7
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3
The wave equation
1
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8
Variational methods [None]
Next:
1.1 Basic Concepts
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