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Mathematically, the functions in Green’s theorem will be
- a)Continuous derivatives
- b)Discrete derivatives
- c)Continuous partial derivatives
- d)Discrete partial derivatives
Correct answer is option 'C'. Can you explain this answer?
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Mathematically, the functions in Green’s theorem will bea)Contin...
The Green's function is a mathematical function that is used in physics and engineering to solve differential equations. It is named after the British mathematician George Green, who first introduced the concept.
In mathematical terms, the Green's function is a solution to the equation (L - λ)f(x) = δ(x - a), where L is a linear differential operator, λ is a constant, f(x) is the unknown function, and δ(x - a) is the Dirac delta function. The Green's function G(x, a; λ) satisfies this equation for all values of a.
The Green's function can be used to solve a wide range of problems in physics and engineering, such as the wave equation, the heat equation, and the Poisson equation. It provides a way to express the solution to these equations as an integral involving the Green's function and the source term.
The Green's function has many important properties, such as linearity, symmetry, and causality. It can also be used to calculate other quantities of interest, such as the response of a system to an external force or the steady-state behavior of a system.
Overall, the Green's function is a powerful mathematical tool that allows for the solution of differential equations in physics and engineering. It provides a way to express the solution in terms of an integral involving the Green's function and the source term, and it has many useful properties that make it a valuable tool in mathematical analysis.
In mathematical terms, the Green's function is a solution to the equation (L - λ)f(x) = δ(x - a), where L is a linear differential operator, λ is a constant, f(x) is the unknown function, and δ(x - a) is the Dirac delta function. The Green's function G(x, a; λ) satisfies this equation for all values of a.
The Green's function can be used to solve a wide range of problems in physics and engineering, such as the wave equation, the heat equation, and the Poisson equation. It provides a way to express the solution to these equations as an integral involving the Green's function and the source term.
The Green's function has many important properties, such as linearity, symmetry, and causality. It can also be used to calculate other quantities of interest, such as the response of a system to an external force or the steady-state behavior of a system.
Overall, the Green's function is a powerful mathematical tool that allows for the solution of differential equations in physics and engineering. It provides a way to express the solution in terms of an integral involving the Green's function and the source term, and it has many useful properties that make it a valuable tool in mathematical analysis.
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Mathematically, the functions in Green’s theorem will bea)Contin...
The Green’s theorem states that if L and M are functions of (x,y) in an open region containing D and having continuous partial derivatives then,
∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.
∫ (F dx + G dy) = ∫∫(dG/dx – dF/dy)dx dy, with path taken anticlockwise.
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Mathematically, the functions in Green’s theorem will bea)Continuous derivativesb)Discrete derivativesc)Continuous partial derivativesd)Discrete partial derivativesCorrect answer is option 'C'. Can you explain this answer?
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