PDE Vocabulary Quiz (Jonathan)

Definition: A differential equation that contains unknown multivariable functions and their partial derivatives.

(a)  

Match the following

• Mixed Boundary Condition

• A statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus. Stokes' theorem says that the integral of a differential form ω over the boundary of some orientable manifold Ω is equal to the integral of its exterior derivative dω over the whole of Ω.

• Dirichlet Boundary Condition

• A mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated.

• Neumann Boundary Condition

• When imposed on an ordinary or a partial differential equation, it

  specifies the values that the derivative of a solution is to take on the boundary of the domain.

• Stoke's Theorem

• When imposed on an ordinary or a partial differential equation, it specifies the values that a solution needs to take on along the boundary of the domain.

Definition: The relation of two lines at right angles to one another (perpendicularity), and the generalization of this relation into n dimensions; and to a variety of mathematical relations thought of as describing non- overlapping, uncorrelated, or independent objects of some kinds.

(a)  

Definition: A vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R.

(a)  

Match the following

• Constant

• A mathematical relation such that each element of one set is associated with at least one element of another set

• Function

• A symbol that represents a quantity in a mathematical expression, as used in many sciences

• Coefficient

• A quantity that does not vary

• Variable

• A multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but in any case does not involve any variable of the expression.

Definition: Also known as a stationary wave – is a wave in a medium in which each point on the axis of the wave has an associated constant amplitude

(a)  

Match the following

• Ordinary Differential Equation

• A differential equation containing one or more functions of one independent variable and its derivatives.

• Delta Function

• An important second- order linear partial differential equation for the description of waves—as they occur in physics—such as sound waves, light waves and water waves. It arises in fields like acoustics, electromagnetics, and fluid dynamics.

• Diffusion Equation

• A generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line. The delta function is sometimes thought of as an infinitely high, infinitely thin spike at the origin, with total area one under the spike, and physically represents the density of an idealized point mass or point charge

• Quadratic Equation

• A partial differential equation which describes density dynamics in a material undergoing diffusion. It is also used to describe processes exhibiting diffusive-like behaviour.

• Wave Equation

• Any equation having the form where x represents an unknown, and a, b, and c represent known numbers such that a is not equal to 0. If a = 0, then the equation is linear, not

Match the following

• Parabola

• A quadric – a type of surface in three dimension

• Symmetric Matrix

• Two-dimensional, mirror-symmetrical curve, which is approximately U-shaped when oriented as shown in the diagram below, but which can be in any orientation in its plane.

• Hyperboloid

• A square matrix that is equal to its transpose