Analysis Solution Manual
© Leon van Dommelen
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18.1 Basic Concepts
18
. Introduction
Subsections
18
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1
Basic Concepts
18
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1
.
1
The prevalence of partial differential equations
18
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1
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2
Definitions
18
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1
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3
Typical boundary conditions
18
.
2
The Standard Examples
18
.
2
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1
The Laplace equation
18
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2
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1
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1
Solution stanexl-a
18
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2
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1
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2
Solution stanexl-b
18
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2
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1
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3
Solution stanexl-b1
18
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2
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1
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4
Solution stanexl-b2
18
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2
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1
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5
Solution stanexl-b3
18
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2
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1
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6
Solution stanexl-b5
18
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2
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1
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7
Solution stanexl-c
18
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2
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1
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8
Solution stanexl-d
18
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2
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1
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9
Solution stanexl-e
18
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2
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2
The heat equation
18
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2
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2
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1
Solution stanexh-a
18
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2
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2
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2
Solution stanexh-b
18
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2
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3
The wave equation
18
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2
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3
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1
Solution stanexw-a
18
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2
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3
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2
Solution stanexw-b
18
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2
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3
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3
Solution stanexw-c
18
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2
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3
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4
Solution stanexw-e
18
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2
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3
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5
Solution stanexw-f
18
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3
Properly Posedness
18
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3
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1
The conditions for properly posedness
18
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3
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1
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1
Solution ppc-a
18
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3
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1
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2
Solution ppc-b
18
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3
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1
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3
Solution ppc-c
18
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3
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2
An improperly posed parabolic problem
18
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3
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3
An improperly posed elliptic problem
18
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3
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3
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1
Solution ppe-a
18
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3
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3
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2
Solution ppe-b
18
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3
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3
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3
Solution ppe-c
18
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3
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3
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4
Solution ppe-d
18
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3
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3
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5
Solution ppe-e
18
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3
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3
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6
Solution ppe-f
18
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3
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4
Improperly posed hyperbolic problems
18
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3
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4
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1
Solution pph-a
18
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3
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4
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2
Solution pph-b
18
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4
Energy methods
18
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4
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1
The Poisson equation
18
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4
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1
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1
Solution emp-a
18
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4
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1
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2
Solution emp-b
18
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4
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2
The heat equation
18
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4
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3
The wave equation
18
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5
Variational methods [None]
18
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6
Classification
18
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6
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1
Introduction
18
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6
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2
Scalar second order equations
18
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6
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2
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1
Solution clasnd-a
18
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7
Changes of Coordinates
18
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7
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1
Introduction
18
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7
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2
The formulae for coordinate transformations
18
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7
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3
Rotation of coordinates
18
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7
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3
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1
Solution rotcoor-a
18
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7
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4
Explanation of the classification
18
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7
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4
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1
Solution expclass-a
18
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8
Two-Dimensional Coordinate Transforms
18
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8
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1
Characteristic Coordinates
18
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8
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2
Parabolic equations in two dimensions
18
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8
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3
Elliptic equations in two dimensions
18
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8
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3
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1
Solution 2dcanel-a
Next:
18.1 Basic Concepts
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