Vaidik Eduservices Maths Subject Matter Expert Interview Questions, Process, and Tips

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Q1. Tell me the Laplace equation
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The Laplace equation is a second-order partial differential equation that describes the behavior of harmonic functions.
• The Laplace equation is written as ∇^2f = 0, where ∇^2 is the Laplacian operator.

• It is used in physics to describe the behavior of electric and gravitational fields.

• Solutions to the Laplace equation are called harmonic functions.

• Examples of harmonic functions include the electric potential in a region ...read more
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Q2. Give difference between stokes theorem and divergence theorem
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Stokes theorem relates a surface integral over a closed surface to a line integral around its boundary, while divergence theorem relates a volume integral of a vector field to a surface integral of its divergence.
• Stokes theorem deals with the circulation of a vector field around a closed curve in space, while divergence theorem deals with the flow of a vector field through a closed surface in space.

• Stokes theorem is a ...read more
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Q1. Explain Laplace transform formula
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Laplace transform formula is a mathematical tool used to transform a function of time into a function of complex frequency.
• The Laplace transform of a function f(t) is defined as F(s) = L{f(t)} = ∫[0,∞] e^(-st) * f(t) dt

• It is commonly used in engineering and physics to solve differential equations

• Example: Laplace transform of f(t) = 1 is F(s) = 1/s
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Q2. Explain divergence theorem Formula of surface in space created by rotating a curve
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Divergence theorem relates a triple integral over a region to a surface integral over the boundary of the region.
• Divergence theorem, also known as Gauss's theorem, states that the flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the region enclosed by the surface.

• It is a fundamental theorem in vector calculus and has applications in physics, engineering...read more
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