## What is the condition that an equation to be elliptic?

If the coefficients a, b, and c are not constant but depend on x and y, then the equation is called elliptic in a given region if b2 − 4ac < 0 at all points in the region.

### What is linear elliptic equations?

In the theory of linear elliptic partial differential equations an important place is taken by fundamental solutions. For an operator (1) with sufficiently smooth coefficients a fundamental solution is defined as a function J(x,y)=Jy(x) that satisfies the condition. ∫L∗ϕ(x)J(x,y)dx=ϕ(y) for all ϕ∈C∞0.

**Which of these statements is true for elliptic equations?**

Which of these statements is true for elliptic equations? Explanation: Any change at any point in the domain of elliptic equation influences all other points. So, the solution process should be carried out simultaneously and it cannot be marched.

**Why is Laplace’s equation important?**

Laplace’s equation, second-order partial differential equation widely useful in physics because its solutions R (known as harmonic functions) occur in problems of electrical, magnetic, and gravitational potentials, of steady-state temperatures, and of hydrodynamics.

## Which of the following partial differential equation is called Laplace equation?

The Laplace equation is a basic PDE that arises in the heat and diffusion equations. The Laplace equation is defined as: ∇ 2 u = 0 ⇒ ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 + ∂ 2 u ∂ z 2 = 0 .

### What is the order of elliptic curve?

The order of a point on an elliptic curve is the order of that point as an element of the group defined on the curve. = O, and m P = O for all integers 1 ≤ m < m. If such m exists, P is said to have finite order, otherwise it has infinite order.

**Which of the following is an example of elliptic differential equation?**

Answer. Answer: The equation is said to be elliptic if b2 − 4ac < 0, parabolic if b2 − 4ac = 0 and hyperbolic if b2 − 4ac > 0. For example, given an elliptic differential operator L, the operator form of a parabolic equation is: ∂u ∂t + Lu = f ; and a second-order hyperbolic equation is then: ∂2u ∂t2 + Lu = f .

**What does Laplace’s equation tell us?**

The equation was discovered by the French mathematician and astronomer Pierre-Simon Laplace (1749–1827). Laplace’s equation states that the sum of the second-order partial derivatives of R, the unknown function, with respect to the Cartesian coordinates, equals zero: A-B-C, 1-2-3…

## Where is Laplace’s equation valid?

The Laplace equation can be used in three-dimensional problems in electrostatics and fluid flow just as in two dimensions.

### Which of the following potential does not satisfy Laplace equation?

Exercise :: Electromagnetic Field Theory – Section 1

37. | Which one of the following potential does not satisfy Laplace’s equations? |
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A. v = 10 xy B. v = p cos φ C. D. v = f cos φ + 10 Answer: Option B Explanation: . Workspace Report errors Name : Email: View Answer Discuss |

**Which of the following is the condition for a partial differential equation to be hyperbolic?**

Which of the following is the condition for a second order partial differential equation to be hyperbolic? Explanation: For a second order partial differential equation to be hyperbolic, the equation should satisfy the condition, b2-ac>0.

**What is special about elliptic curves?**

The addition of points on elliptic curves has a different definition that is much more natural, can be defined for any curve, and makes it more obvious why it is interesting for elliptic curves specifically.

## How does an elliptic curve work?

An elliptic curve for current ECC purposes is a plane curve over a finite field which is made up of the points satisfying the equation: y²=x³ + ax + b. In this elliptic curve cryptography example, any point on the curve can be mirrored over the x-axis and the curve will stay the same.

### Which of the following potentials does not satisfy Laplace’s equation?

Discussion :: Electromagnetic Field Theory – Section 1 (Q. No. 37)

37. | Which one of the following potential does not satisfy Laplace’s equations? |
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[A]. v = 10 xy [B]. v = p cos φ [C]. [D]. v = f cos φ + 10 Answer: Option B Explanation: . Workspace Report errors Name : Email: Workspace Report |