Applied Mathematics for Engineers and Physicists (3rd Edition) (Dover Books on Mathematics)
Lawrence R. Harvill, Louis A. Pipes
Language: English
Pages: 918
ISBN: 0486779513
Format: PDF / Kindle (mobi) / ePub
One of the most widely used reference books on applied mathematics for a generation, distributed in multiple languages throughout the world, this text is geared toward use with a one-year advanced course in applied mathematics for engineering students. The treatment assumes a solid background in the theory of complex variables and a familiarity with complex numbers, but it includes a brief review. Chapters are as self-contained as possible, offering instructors flexibility in designing their own courses.
The first eight chapters explore the analysis of lumped parameter systems. Succeeding topics include distributed parameter systems and important areas of applied mathematics. Each chapter features extensive references for further study as well as challenging problem sets. Answers and hints to select problem sets are included in an Appendix. This edition includes a new Preface by Dr. Lawrence R. Harvill
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be satisfied only when all the data points fall exactly on the desired curve. However, satisfied or not, let us consider the set of Eqs. (3.2) and rewrite them in matrix notation. If we define the following matrices Eq. (3.2) may be written in terms of the single matrix equation At first glance one might jump at the conclusion that (3.4) could be solved directly by premultiplying through by the inverse of the matrix [C]’. This operation is not possible since [C]’ is not a square matrix. Only in
approximations of the motion are obtained. If Eq. (6.4) is solved for d2x/dt2 and if the first approximation (6.5) is substituted in the right-hand member for x, we obtain Making use of (6.8), this reduces to Integration gives This second approximation may then be substituted into (6.4) to obtain the third approximation. In this manner any number of terms of the Fourier-series solution may be obtained. The investigation of the convergence of the process shows that the series obtained converges
acts in the opposite direction from x, since x is measured from the position of equilibrium. We may also write Eq. (4.3) in the more fundamental form If we differentiate the kinetic energy T of (4.1) with respect to v = , we obtain If we differentiate the potential energy V of (4.2) with respect to x, we have Hence, in terms of the energy functions, the equation of motion may be written in the form This form of the equation of motion is called Lagrange’s equation of motion and is simply a
systems are characterized completely by their kinetic-and potential-energy functions and are of great practical importance. In many problems that arise in practice the frictional forces are relatively small and may be disregarded and the system treated as a conservative one. The mathematical analyses of vibrating systems that contain frictional forces of a general nature usually lead to a formulation involving nonlinear differential equations (see Chap. 15). However, in a great many practical
Reading, Mass. 1966. Raven, F. H.: “Mathematics of Engineering Systems,” McGraw-Hill Book Company, New York. 1966. Sokolnikoff, I. S., and R. M. Redheffer: “Mathematics of Physics and Modern Engineering,” 2d ed., McGraw-Hill Book Company, New York. 1966. Wylie, C. R., Jr.: “Advanced Engineering Mathematics,” 3d ed., McGraw-Hill Book Company, New York. † H. A. Schwarz, Journal für Mathematik, vol. 70, p. 5.105, 1869. † Cf. Glauert, 1943 (see References). ‡ Cf. Milne-Thomson, 1955 (see
