Applied

Download The Princeton Companion to Applied Mathematics by Nicholas J. Higham PDF

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By Nicholas J. Higham

This is the main authoritative and available single-volume reference e-book on utilized arithmetic. that includes a variety of entries by way of prime specialists and arranged thematically, it introduces readers to utilized arithmetic and its makes use of; explains key thoughts; describes vital equations, legislation, and services; appears at interesting parts of analysis; covers modeling and simulation; explores parts of program; and more.

Modeled at the well known Princeton spouse to Mathematics, this quantity is an vital source for undergraduate and graduate scholars, researchers, and practitioners in different disciplines looking a simple reference ebook on utilized mathematics.

  • Features approximately two hundred entries geared up thematically and written by way of a global group of amazing contributors
  • Presents the main rules and branches of utilized arithmetic in a transparent and available way
  • Explains vital mathematical suggestions, equipment, equations, and applications
  • Introduces the language of utilized arithmetic and the targets of utilized mathematical research
  • Gives a variety of examples of mathematical modeling
  • Covers continuum mechanics, dynamical structures, numerical research, discrete and combinatorial arithmetic, mathematical physics, and lots more and plenty more
  • Explores the connections among utilized arithmetic and different disciplines
  • Includes feedback for extra examining, cross-references, and a complete index

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Extra resources for The Princeton Companion to Applied Mathematics

Sample text

Recurrence relations have a theory analogous to that of differential equations, though it is much less frequently encountered in courses and textbooks than it was fifty years ago. The elements in a recurrence can be functions as well as numbers. Most transcendental functions that carry subscripts satisfy a recurrence. 2] Jn (x) of order n satisfies the threeterm recurrence 2n Jn (x) − Jn−1 (x). 29]. 14 Polynomials Polynomials are one of the simplest and most familiar classes of functions and they find wide use in applied mathematics.

Rational functions are more versatile than polynomials as a means of approximating other functions. As x grows larger, a polynomial of degree 1 or higher necessarily blows up to infinity. In contrast, a rational function rmm with equal-degree numerator and denominator is asymptotic to am /bm , as x → ∞, while for m < n, rmn (x) converges to zero as x → ∞. Moreover, a rational function has poles: certain finite values of x for which it is infinite (the roots of the denominator polynomial qn ). The representation of a rational function as a ratio of polynomials is just one of several possibilities.

The function f is continuous at x = a if f (a) exists and limx→a f (x) = f (a). 11 The definitions of limit and continuity apply equally well to functions of a complex variable. Here, the condition |x − a| < δ places x in a disk of radius less than δ in the complex plane instead of an open interval on the real axis. The function f is continuous on [a, b] if it is continuous at every point in that interval. A more restricted form of continuity is Lipschitz continuity. The function f is Lipschitz continuous on [a, b] if |f (x) − f (y)| L|x − y| for all x, y ∈ [a, b] for some constant L, which is called the Lipschitz constant.

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