Dictionary of Applied Math for Engineers and Scientists by Emma Previato

By Emma Previato

Regardless of the probably shut connections among arithmetic and different medical and engineering fields, functional causes intelligible to those that should not basically mathematicians are much more tough to discover. The Dictionary of utilized arithmetic for Engineers and Scientists fills that void. It includes authoritative but available definitions of mathematical phrases frequently encountered in different disciplines.

There will be greater dictionaries, extra entire dictionaries, and dictionaries that supply extra unique definitions, theorems, and proofs. yet there isn't any different dictionary in particular designed and written for scientists and engineers whose knowing and skill to unravel real-world difficulties paintings can depend on the appliance of arithmetic.

Concise, understandable, and handy, the Dictionary of utilized arithmetic for Engineers and Scientists is a realistic lexicon that is helping scholars and pros alike use mathematical terminology competently and completely comprehend the mathematical literature encountered of their fields

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An expansion is the reverse operation. contraction mapping theorem Let T : (M, ρ) → (M, ρ) be a contraction mapping of a complete metric space (M, ρ) into itself. , there exists a unique x0 ∈ M such that T x0 = x0 . contravariant/covariant tensor A tensor T on a vector space E, contravariant of order r and covariant of order s is a multilinear map T : E∗ × · · · × E∗ × E × · · · × E → R (r copies of E ∗ and s copies of E). convergent sequence A sequence {xn } having a limit L. That is, for every neighborhood U of L, we have xn ∈ U for all except finitely many n.

K−1 ). , it includes products and exterior differentials of generators). µk−1 ν ∧ dx ν . ¯ ∗c (J k B) is the ideal of all forms vanishing on all holonomic sections, including all (m + h)forms with h > 0. continuity equation The law of conservation of mass of a fluid with density ρ(x, t) and velocity v is called continuity equation ∂ρ + div (ρv) = 0. ∂t continuous function A function between topological spaces such that the inverse image of every open set is open. continuous spectrum The continuous spectrum σc (T ) of a linear operator T on a Hilbert space H consists of all λ ∈ C such that T − λI is a one-to-one mapping of H onto a dense proper subspace of H.

Pontrjagin classes p1 , . . , pj are defined for a real vector bundle of dimension k (or equivalently for a GL(k, R) principal bundle) pi ∈ H 4i (M). Stiefel-Whitney classes w1 , . . , wk are defined for a real vector bundle of dimension k (or equivalently for a GL(k, R) principal bundle). They are Z2 characteristic classes wi ∈ H i (M; Z2 ). characteristic cone The principal symα bol Pm (x, ξ ) = of a (lin|α|=m cα (x)ξ ear partial) differential operator P (x, D) = α |α|≤m cα (x)D is homogeneous of degree m in ξ .

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