Some Mathematical Methods of PhysicsCourier Corporation, 2014 M03 5 - 320 páginas This well-rounded, thorough treatment for advanced undergraduates and graduate students introduces basic concepts of mathematical physics involved in the study of linear systems. The text emphasizes eigenvalues, eigenfunctions, and Green's functions. Prerequisites include differential equations and a first course in theoretical physics. The three-part presentation begins with an exploration of systems with a finite number of degrees of freedom (described by matrices). In part two, the concepts developed for discrete systems in previous chapters are extended to continuous systems. New concepts useful in the treatment of continuous systems are also introduced. The final part examines approximation methods — including perturbation theory, variational methods, and numerical methods — relevant to addressing most of the problems of nature that confront applied physicists. Two Appendixes include background and supplementary material. 1960 edition. |
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Página 6
... It is clear that a problem in this category is specified by stating the n functions F,(t) in addition to the n2 numbers m”. The form of the equations for the steady-state problem is 6 SYSTEMS WITH A FINITE NUMBER OF DEGREE OF FREEDOM.
... It is clear that a problem in this category is specified by stating the n functions F,(t) in addition to the n2 numbers m”. The form of the equations for the steady-state problem is 6 SYSTEMS WITH A FINITE NUMBER OF DEGREE OF FREEDOM.
Página 7
... specified by n2 quantities m,,-, but require in addition the n numbers F,. In the first sentence of Sec. 1.] appear the words “are linear, have a finite number of degrees of freedom, and have properties independent of time.” The ...
... specified by n2 quantities m,,-, but require in addition the n numbers F,. In the first sentence of Sec. 1.] appear the words “are linear, have a finite number of degrees of freedom, and have properties independent of time.” The ...
Página 13
... specified relative to the position of the specified index (i in this case). Using this notation, one has as the rule for forming the product of two matrices ("7PM~ : mi.P.i (139) 1.6 Warnings The use of the same notation for matrix sums ...
... specified relative to the position of the specified index (i in this case). Using this notation, one has as the rule for forming the product of two matrices ("7PM~ : mi.P.i (139) 1.6 Warnings The use of the same notation for matrix sums ...
Página 23
... specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar (2-11) In this case, the evaluation of u(t) is straightforward. u(t) = eA'u(O) = e““s_1al + e“'s_2a2 + ' ~ - = ei'l'sla1 + e'lf'sja2 + ' - ' = e1"s_,~a,- (2.12) The ...
... specified initial conditions 14(0), “(0) = 5.1111 + 3.2% + ' ' ' = Saar (2-11) In this case, the evaluation of u(t) is straightforward. u(t) = eA'u(O) = e““s_1al + e“'s_2a2 + ' ~ - = ei'l'sla1 + e'lf'sja2 + ' - ' = e1"s_,~a,- (2.12) The ...
Página 25
... specified by all n elements. If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing the proof of the theorem. The problem is ...
... specified by all n elements. If A does have n linearly independent eigencolumns, it is possible to solve specifically for u in terms of the eigencolumns (see the next paragraph), thus completing the proof of the theorem. The problem is ...
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applied approximate arbitrary base vectors basis Bessel function boundary conditions Chap chapter coefficients column commute complete consider constant continuous systems contour corresponding cylindrical functions defined definition denoted determinant diagonal diagonalizable differential equation Dirac notation domain eigen eigencolumns eigenfunctions eigenvalue equation eigenvector elements evaluate expansion find finite number first follows formula Fourier given Green’s function Hence Hermitian matrix Hermitian operator infinite integral Introduction inverse Laplacian linear operator linearly independent lowest eigenvalue matrix McGraw-Hill Book Company membrane method multiplication nonsingular normal normal matrix Note number of degrees obtained orthonormality conditions perturbation plane procedure QUANTUM MECHANICS relations representation result Ritz method satisfies satisfy scattering solve specified spherical spherical harmonics string Substitution theorem theory tion trial functions vanish variable vector space verified wave write written yields York zero