mathematical methods in science and engineering by selcuk bayin pdf

... 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

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 ... Orthogonality and the Generating Function 75 5.3 Chebyshev Equation and Polynomials 75 5.3.1 Chebyshev Polynomials of the First Kind 75 5.3.2 Relation of Chebyshev and Gegenbauer...

Ngày tải lên: 13/08/2014, 09:21

... 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) ... polynomials of the first and second kinds are linearly independent, and they both satisfy the Chebyshev Equation (5.33). In terms of x the Chebyshev polynomials are written as and 96 BESSEL ... 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...

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 ... Proof of Equation (9.21) is accomplished by multiplying Equation (9.16) with O_(z,m) and by comparing it with the equation obtained by letting m-+m-l in Equation (9.17). This theorem says...

Ngày tải lên: 13/08/2014, 09:21

... 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 ... 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 ... followed by a rota- tion about the xl-axis as 1 0 - sin $ cosCp sin4cos$ cosdsin+ -sin4 cos~cos$ (10.93) Reversing the order we get cos $ (10.94) sin $ sin Cp - sin $ cos...

Ngày tải lên: 13/08/2014, 09:21

... P2)'I2 and obtained by interchanging with -d. = 3,'~. Inverse transformations are easily 10.10.14 Maxwell's Equations in Terms of Potentials The Electric and magnetic ... pseudo-Euclidean. In this line element c is the speed of light representing the maximum velocity in nature. An interesting property of the Minkowski spacetime is that two events connected by light ... 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...

Ngày tải lên: 13/08/2014, 09:21

... tensors. In this regard, D(') is generated by scalars, D(2) is generated by vec- tors, and d3) is generated by symmetric second-rank tensors wep. In general, D(") is generated by ... tensors. In this regard, D(l) is generated by scalars, D(2) is generated by vec- tors, and d3) is generated by symmetric second-rank tensors wap. In general, D(") is generated by completely ... 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)...

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