recurrence relation

(noun)

an equation that recursively defines a sequence; each term of the sequence is defined as a function of the preceding terms

Related Terms

Examples of recurrence relation in the following topics:

  • Series Solutions

    • In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
    • After substituting the power series form, recurrence relations for $A_k$ is obtained, which can be used to reconstruct $f$.
    • We can rearrange this to get a recurrence relation for $A_{k+2}$:
    • and all coefficients with larger indices can be similarly obtained using the recurrence relation.

  • Related Rates

    • Related rates problems involve finding a rate by relating that quantity to other quantities whose rates of change are known.
    • What is a related rate?
    • In differential calculus, related rates problems involve finding a rate at which a quantity changes by relating that quantity to other quantities whose rates of change are known.
    • Because science and engineering often relate quantities to each other, the methods of related rates have broad applications in these fields.
    • Solve problems using related rates (using a quantity whose rate is known to find the rate at which a related quantity changes)

  • Real Numbers, Functions, and Graphs

    • Functions relate a set of inputs to a set of outputs such that each input is related to exactly one output.
    • A function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.
    • An example is the function that relates each real number $x$ to its square: $f(x)= x^{2}$.

  • Stokes' Theorem

    • Stokes' theorem relates the integral of the curl of a vector field over a surface to the line integral of the field around the boundary.
    • Given a vector field, the theorem relates the integral of the curl of the vector field over some surface to the line integral of the vector field around the boundary of the surface.

  • Four Ways to Represent a Function

    • A function is a relation between a set of inputs and a set of permissible outputs, provided that each input is related to exactly one output.
    • An example is the function that relates each real number $x$ to its square $x^2$.

  • The Divergence Theorem

    • The divergence theorem relates the flow of a vector field through a surface to the behavior of the vector field inside the surface.
    • The divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface.

  • Trigonometric Functions

    • Trigonometric functions are functions of an angle, relating the angles of a triangle to the lengths of the sides of a triangle.
    • They are used to relate the angles of a triangle to the lengths of the sides of a triangle.

  • Physics and Engineering: Fluid Pressure and Force

    • It relates the vector surface element (a vector normal to the surface) with the normal force acting on it.
    • The pressure is the scalar proportionality constant that relates the two normal vectors:

  • Trigonometric Limits

    • This relation can be proven by substituting $t=\frac{1}{x}$ into the first relation we derived:

  • Solving Differential Equations

    • A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself to its derivatives of various orders.
    • As you can see, such an equation relates a function $f(x)$ to its derivative.