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force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on. A common occurrence in physics is the time derivative of a vector, such as velocity or displacement. In dealing with such a derivative, both magnitude and orientation may depend upon time.
The second derivative of a function f can be used to determine the concavity of the graph of f. [2] A function whose second derivative is positive is said to be concave up (also referred to as convex), meaning that the tangent line near the point where it touches the function will lie below the graph of the function.
First order LTI systems are characterized by the differential equation + = where τ represents the exponential decay constant and V is a function of time t = (). The right-hand side is the forcing function f(t) describing an external driving function of time, which can be regarded as the system input, to which V(t) is the response, or system output.
Derivation of equations that describe the time course of change for a system with zero-order input and first-order elimination are presented in the articles Exponential decay and Biological half-life, and in scientific literature. [1] [7] = C t is concentration after time t
Second order approximation, an approximation that includes quadratic terms; Second-order arithmetic, an axiomatization allowing quantification of sets of numbers; Second-order differential equation, a differential equation in which the highest derivative is the second; Second-order logic, an extension of predicate logic
For a function :, this second definition merely states that for every strictly between and , the point (, ()) on the graph of is above the straight line joining the points (, ()) and (, ()). A function f {\displaystyle f} is quasiconcave if the upper contour sets of the function S ( a ) = { x : f ( x ) ≥ a } {\displaystyle S(a)=\{x:f(x)\geq a ...
Graph order, the number of nodes in a graph; First order and second order logic of graphs; Topological ordering of directed acyclic graphs; Degeneracy ordering of undirected graphs; Elimination ordering of chordal graphs; Order, the complexity of a structure within a graph: see haven (graph theory) and bramble (graph theory)
A subsystem of second-order arithmetic is a theory in the language of second-order arithmetic each axiom of which is a theorem of full second-order arithmetic (Z 2). Such subsystems are essential to reverse mathematics , a research program investigating how much of classical mathematics can be derived in certain weak subsystems of varying strength.