PDE in ℝx(0,∞): Solving the Unknown

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SUMMARY

The discussion focuses on the partial differential equation (PDE) defined as uxx + uyy = 0 in the domain ℝx(0,∞). This notation represents the Cartesian product of the real numbers with the positive real numbers, specifically the set of ordered pairs (x,y) where y is greater than zero. The participants clarify that ℝx(0,∞) denotes the region in the Cartesian plane where y is positive, which is essential for solving the given PDE.

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  • Understanding of partial differential equations (PDEs)
  • Familiarity with Cartesian coordinates and their notation
  • Basic knowledge of real analysis
  • Concept of ordered pairs in mathematics
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  • Study the methods for solving Laplace's equation, which is represented by uxx + uyy = 0
  • Explore the concept of boundary conditions in PDEs
  • Learn about the implications of the Cartesian product in mathematical contexts
  • Investigate the applications of PDEs in physics and engineering
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Dubz
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The problem is a PDE
uxx+uyy= 0 in ℝx(0,∞)

what does this mean ℝx(0,∞) ?
Came across it in my math book, and I have not idea what to google to find this.
 
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Dubz said:
The problem is a PDE
uxx+uyy= 0 in ℝx(0,∞)

what does this mean ℝx(0,∞) ?
Came across it in my math book, and I have not idea what to google to find this.
It probably means the set ##\{(x,y) \in \mathbb{R}^2\,\vert \,y>0\} = \mathbb{R} \times \mathbb{R}_+\,.##
 
To answer your google question, it is called the Cartesian product. As fresh said, it is just the set of ordered tuples.
 

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