advanced mathematical methods in science and engineering

... MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING MATHEMATICS AND MIND 5 1.3 MATHEMATICS AND MIND Almost, everywhere mathematics is a very useful and powerful language in expressing ... part of the learning process. In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics. In fact, the number ... naturally comes from the inner efficiency of our brain. Research on subjects like brain stimulators, hard wiring of our brain, and mind reading machines are all aiming at a faster and much more efficient...

Ngày tải lên: 22/03/2014, 13:20

... (2.27) MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING PREFACE xviii encountered special functions in science and engineering. This is also very timely, because during the first year of ... part of the learning process. In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics. In fact, the number ... naturally comes from the inner efficiency of our brain. Research on subjects like brain stimulators, hard wiring of our brain, and mind reading machines are all aiming at a faster and much more efficient...

Ngày tải lên: 27/06/2014, 05:20

... relevant links of interest to readers. S. BAYIN OD TU Ankam/TURKE Y April 2006 MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING Preface Courses on mathematical methods of physics ... in physics, which are also offered by most engineering departments. Considering that the audience in these coumes comes from all subdisciplines of physics and engineering, the content and ... the growing in- terest in interdisciplinary studies has brought scientists together from physics, chemistry, biology, economy, and finance and has increased the demand for these courses in which...

Ngày tải lên: 27/06/2014, 18:20

Ngày tải lên: 05/03/2014, 23:20

... definition, 429 Cauchy integral formula, 390 Griinwald definition differintegrals, 385 Laplace transforms, 396 484 Fractional derivatives MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING ... and Engineering 424 14.7.2 Fractional Fokker-Planck Equations 427 Problems 429 14.7.1 Continuous Time Random Walk (CTRW) 424 15 INFINITE SERIES 431 15.1 Convergence of Infinite ... Mathematical Methods: for Students of Physics and Related Fields, Springer Verlag, 2000. Hassani, S., Mathematical Physics, Springer Verlag, second edition, 2002. Hildebrand, F.B., Methods...

Ngày tải lên: 13/08/2014, 09:21

... part of the learning process. In a vast area like mathematical methods in science and engineering, there is always room for new approaches, new applications, and new topics. In fact, the number ... write x = fl in the generating function Equation (2.65) we find (2.85) Expanding the left-hand side by using the binomial formula and comparing equal powers oft, we obtain 9 (1) = 1 ... and for meticulously reading Chapters 1 and 9 with 14 and 20. I also thank Prof. N. K. Pak for many interesting and stimulating discussions, encouragement, and critical reading...

Ngày tải lên: 13/08/2014, 09:21

... that the value of the integral in Equation (3.38) can be obtained by expanding in powers of t and s and then by comparing the equal powers of tnsm with the left-hand side of Equation ... (4.52) 'I A This Page Intentionally Left Blank ORTHOGONALiTY OF LAGUERRE POLYNOMlALS 49 Interchanging the integral and the summation signs and integrating with re- spect to x gives ... are very useful in cosmology and quantum field theory in curved backgrounds. Both the spherical harmonics and the Gegenbauer poly- nomials are combinations of sines and cosines. Chebyshev...

Ngày tải lên: 13/08/2014, 09:21

... second kind. Note that N,(z) and Jm(z) are linearly independent even for the integer values of m. Hence it is common practice to take N,(z) and Jm(z) as the two linearly independent ... can obtain the following recursion relations and First by adding and then by subtracting these equations we also obtain the relations m Jm-l(X) = -Jm(IL.) + J:,(X) (6.52) X and (6.53) ... equations in physics and engineering can be solved by the method of separation of variables. This method helps us to reduce a second-order partial differential equation into a set of ordinary...

Ngày tải lên: 13/08/2014, 09:21

... exists a minimum value, mmin, thus determining X as X = mmin (9.143) To find mmin we equate the two expressions [Eqs. (9.141) and (9.143)] for X to obtain (9.144) mmin = -1. ... Cancelling m on both sides and noting that (9.166) (9.167) and using Equation (9.164) we finally write Similarly We now define the ladder operators L+ and L- for the m index of ... m=O which converges absolutely and uniformly in all subintervals free of points of discontinuity. At the points of discontinuity this series rep resents (as in the Fourier series) the arithmetic...

Ngày tải lên: 13/08/2014, 09:21

... axn and Adding the first two equations and subtracting the last one from the result and after some rearrangement of indices we obtain (10.197) I0 COORDINATES and TENSORS Starting with ... choosing three mutually orthogonal straight lines. A point is defined by giving its coordinates, (q,z2,q), or by using the position vector 163 188 COORDINATES AND TENSORS Hence aa and ... 1 0 - sin $ cosCp sin4cos$ cosdsin+ -sin4 cos~cos$ (10.93) Reversing the order we get cos $ (10.94) sin $ sin Cp - sin $ cos Cp R2R1 = 0 cos Cp sin 4 [ sin $ - cos...

Ngày tải lên: 13/08/2014, 09:21

... the four-potential is defined as A" = (4,T) and 224 CONTINUOUS GROUPS AND REPRESENTATIONS inhomogeneous Lorentz group and introduce its Lie algebra. An advanced treatment of spherical ... Groups with infinite number of elements like R(n) are called infinite groups. A group with finite number of elements is called a finite group, where the number of elements in a finite group ... +ae d (TaB) r2sinOaW +a (WE)] After simplifying, the Laplacian is obtained as r2sin6 dr 34 r2sin28 a4 ' (10.239) Here we have obtained a well-known formula in a rather straightfor-...

Ngày tải lên: 13/08/2014, 09:21

... properties that remain invariant under similarity transformations. One such 254 CONTINUOUS GROUPS AND REPRESENTATIONS Y’ Fig. 11.6 (z,y,z) and the (z‘,y’,z‘) coordinates we obtain (Fig. 11.6) ... 240 CONTINUOUS GROUPS AND REPRESENTATIONS induces the following change in a function f(v1, ~2): - f(V) = f Mff, P, Y)VI' (1 1.126) Taking the active view we define an operator ... the physical point of view a very important part of the group theory is representing each element of the group with a linear transformation acting in a vector space. We now introduce the...

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21

Ngày tải lên: 13/08/2014, 09:21