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The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) is
- a)1
- b)0
- c)2
- d)3
Correct answer is option 'D'. Can you explain this answer?
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The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = ...
The Laplace equation is a second-order partial differential equation that is satisfied by a function f(x, y) if its second partial derivatives with respect to x and y are equal to zero. Mathematically, the Laplace equation is given by:
∂²f/∂x² + ∂²f/∂y² = 0
This equation represents a type of differential equation known as an elliptic partial differential equation. It is a fundamental equation in many areas of mathematics and physics, including potential theory and electrostatics.
Solutions to the Laplace equation are known as harmonic functions. These functions have the property that the average value of the function over any closed curve or surface is equal to the value of the function at any point inside the curve or surface. This property is known as the mean value property and is a consequence of the fact that the Laplace equation is a second-order linear partial differential equation.
In two dimensions, the Laplace equation can be written as:
∂²f/∂x² + ∂²f/∂y² = 0
This equation can be solved using various methods, including separation of variables, Fourier series, and complex analysis techniques. The solutions to the Laplace equation are often used to model physical phenomena such as heat conduction, fluid flow, and electrostatic potential.
∂²f/∂x² + ∂²f/∂y² = 0
This equation represents a type of differential equation known as an elliptic partial differential equation. It is a fundamental equation in many areas of mathematics and physics, including potential theory and electrostatics.
Solutions to the Laplace equation are known as harmonic functions. These functions have the property that the average value of the function over any closed curve or surface is equal to the value of the function at any point inside the curve or surface. This property is known as the mean value property and is a consequence of the fact that the Laplace equation is a second-order linear partial differential equation.
In two dimensions, the Laplace equation can be written as:
∂²f/∂x² + ∂²f/∂y² = 0
This equation can be solved using various methods, including separation of variables, Fourier series, and complex analysis techniques. The solutions to the Laplace equation are often used to model physical phenomena such as heat conduction, fluid flow, and electrostatic potential.
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The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = ...
According to given condition given function /(x, y) is nothing but constant function i.e. f(x, y) = 3 because this is the only function whose value is 3 at any point on the boundary of unit circle and it is also satisfying Laplace equation, so f(0, 0) = 3
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The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer?
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The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer?.
The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The function f{x, y) satisfies the Laplace equation Δ2f[x, y) = 0 on a circular domain of radius r = 1 with its center at point P with coordinates x = 0, y = 0. The value of this function on the circular boundary of this domain is equal to 3. The numerical value of f/(0, 0) isa)1b)0c)2d)3Correct answer is option 'D'. Can you explain this answer?.
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