imaginary parts of functions

Ngày tải lên: 30/08/2013, 08:10

... Young Asians are not so as their American counterparts. A. Rome B. Roman C. romantic D. romanticize 75. All of my students appreciate the ______ of English learning. A. importance B. important ... differently 10. All of us were _____ that he was successful in the final exam. A. surprising B. surprisingly C. surprise D. surprised 11. One recent ________ in medicine is the development of laser in ... achievements B. achievement C. achiever D. achieved 12. You have to be aware of the damage humans are doing to quicken the ________ of wildlife. A. extinct B. extinctive C. extinctions D. extinction 13....

Ngày tải lên: 27/10/2013, 10:11

Ngày tải lên: 01/11/2013, 16:20

Ngày tải lên: 01/11/2013, 16:20

... Integration of Functions 4.0 Introduction Numerical integration,which is also called quadrature, has a history extending back to the invention of calculus and before. The fact that integrals of elementary functions ... (4.0.3) Chapter 16 of this book deals with the numerical integration of differential equations. In that chapter, much emphasis is given to the concept of “variable” or “adaptive” choices of stepsize. ... the form of (4.0.2)–(4.0.3) and use the methods of Chapter 16. The quadrature methods in this chapter are based, in one way or another, on the obvious device of adding up the value of the integrand...

Ngày tải lên: 07/11/2013, 19:15

... f 3 + ···+f N−1 + 1 2 f N  +O  (b−a) 3 f  N 2  (4.1.11) Here we have written the error estimate in terms of the interval b − a and the number of points N instead of in terms of h. This is clearer, since one is usually holding a and b fixed ... amount that is the product of some numerical coefficient times h 3 times the value 134 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... as an additional power of N (since it is used only twice, not N times). This makes the resulting formula of degree one less than Simpson. 130 Chapter 4. Integration of Functions Sample page from...

Ngày tải lên: 07/11/2013, 19:15

Ngày tải lên: 12/12/2013, 00:03

... mode). S Correct the program. Software limit switches Function The software limit switches serve as limitations of the maximum traversing range of each in- dividual axis. 2 software limit switch pairs ... monitoring functions 2-24 SINUMERIK 802D, 802D base line 6FC5 697-2AA10-0BP2 (11.03) (DF) 2.2 Motion monitoring functions 2.2.1 Contour monitoring Function The principle of functioning of the contour ... (1st software limit switch minus) MD 36110: POS_LIMIT_PLUS (1st software limit switch plus) MD 36120: POS_LIMIT_MINUS2 (2nd software limit switch minus) MD 36130: POS_LIMIT_PLUS2 (2nd software...

Ngày tải lên: 13/12/2013, 01:16

... computation of first derivatives. • You must choose between methods that require storage of order N 2 and those that require only of order N,whereNis the number of dimensions. For moderate values of N ... then the new bracketing triplet of points is (a, b, x); 396 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN ... America). interpolationsof Brent’s method are of no advantage, and you might wish to use the simplest form of golden section search, as described in §10.1. • Forone-dimensional minimizationwithcalculation of the...

Ngày tải lên: 15/12/2013, 04:15

... this way is that, for most functions, the final square root is a number of order unity. Therefore, as a rule of thumb, it is hopeless to ask for a bracketing interval of width less than √  times ... in the larger of the two segments (z is positive only if w<1/2). But where in the larger segment? Where did the value of w itself come from? Presumably from the previous stage of applying our ... those of the so-called golden mean or golden section, whose supposedly aesthetic properties hark back to the ancient Pythagoreans. This optimal method of function minimization, the analog of the...

Ngày tải lên: 15/12/2013, 04:15

... are acceptable but 404 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 ... the value already evaluated only by an amount of order the roundofferror. Therefore in the code below you will find several tests and modifications of a potential new point, imposing this restriction. ... p = -p; q=fabs(q); 402 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992...

Ngày tải lên: 15/12/2013, 04:15

... consideration of multidimensional minimization, that is, finding the minimum of a function of more than one independent variable. This section stands apart from those which follow, however: All of the ... 408 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 ... d’s to an out -of- bracket value.d2=d1; if (dw != dx) d1=(w-x)*dx/(dx-dw); Secant method with one point. if (dv != dx) d2=(v-x)*dx/(dx-dv); And the other. Which of these two estimates of d shall we...

Ngày tải lên: 15/12/2013, 04:15

... consideration of multidimensional minimization, that is, finding the minimum of a function of more than one independent variable. This section stands apart from those which follow, however: All of the ... tetrahedron. (The simplex method of linear programming, 412 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright ... towards the low point. An appropriatesequenceof such stepswill alwaysconverge to a minimum of the function. described in §10.8,alsomakes useof thegeometrical conceptofasimplex. Otherwise it is completely...

Ngày tải lên: 15/12/2013, 04:15

... number of unknown parameters in f is equal to the number of free parameters in A and b,whichis 1 2 N(N+1),whichweseetobeoforderN 2 . Changing any one of these parameters can move the location of ... members of a set of vectors, they are said to be a conjugate set. If you do successive line minimization of a function along a conjugate set of directions, then you don’t need to redo any of those ... derivative matrix of the function is called the Hessian matrix of the function at P. 412 Chapter 10. Minimization or Maximization of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC...

Ngày tải lên: 15/12/2013, 04:15

... 136 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 ... READING: Abramowitz, M., and Stegun, I.A. 1964, Handbook of Mathematical Functions , Applied Mathe- matics Series, Volume 55 (Washington: National Bureau of Standards; reprinted 1968 by Dover Publications, ... fixed limits a and b, one can double the number of intervals in the extended trapezoidal rule without losing the benefit of previous work. The coarsest implementation of the trapezoidal rule is to average...

Ngày tải lên: 15/12/2013, 04:15

... RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992 by Cambridge University Press.Programs Copyright (C) 1988-1992 by Numerical Recipes Software. Permission ... while qsimp requires 8 calls (8 times as many evaluations of the integrand) and qtrap requires 13 calls (making 256 times as many evaluations of the integrand). CITED REFERENCES AND FURTHER READING: Stoer, ... “improper” if it has any of the following problems: • its integrand goes to a finite limitingvalue at finite upper and lower limits, but cannot be evaluated right on one of thoselimits(e.g., sin...

Ngày tải lên: 15/12/2013, 04:15

... it,j; b=sqrt(bb-aa); a=0.0; if (n == 1) { The rest of the routine is exactly like midpnt and is omitted. 142 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING ... Quadratures and Orthogonal Polynomials In the formulas of §4.1, the integral of a function was approximated by the sum of its functional values at a set of equally spaced points, multiplied by certain ... 146 Chapter 4. Integration of Functions Sample page from NUMERICAL RECIPES IN C: THE ART OF SCIENTIFIC COMPUTING (ISBN 0-521-43108-5) Copyright (C) 1988-1992...

Ngày tải lên: 15/12/2013, 04:15

... i.e., the computation of the coefficients a j , b j in (4.5.6); (ii) the determination of the zeros of p N (x),and the computation of the associated weights. For the case of the “classical” orthogonal polynomials, ... numerical stability is greatly improved if, instead of using powers of x as a set of basis functions to represent the p j ’s, one uses some other known set of orthogonal polynomials π j (x), say. Roughly ... { sig[k][l]=sig[k-1][l+1]+(alpha[l-1]-a[k-2])*sig[k-1][l]- b[k-2]*sig[k-2][l]+beta[l-1]*sig[k-1][l-1]; } a[k-1]=alpha[k-1]+sig[k][k+1]/sig[k][k]-sig[k-1][k]/sig[k-1][k-1]; b[k-1]=sig[k][k]/sig[k-1][k-1]; } free_matrix(sig,1,2*n+1,1,2*n+1); } As an example of the use of orthog, consider the problem [7] of generating orthogonal polynomials with the weight function W (x)=−log x on the interval (0, 1). A suitable set of π j ’s is the...

Ngày tải lên: 15/12/2013, 04:15

... Multidimensional Integrals Integrals of functions of several variables, over regions with dimension greater than one, are not easy. There are two reasons for this. First, the number of function evaluations ... Current values of x and y, and the pointer to your function func, are passed “over the head” of the intermediate calls through static top-level variables. 164 Chapter 4. Integration of Functions Sample ... entirely different approaches to doing the problem. The questions are: Is the shape of the boundary of the region of integration simple or complicated? Inside the region, is the integrand smooth...

Ngày tải lên: 15/12/2013, 04:15

Ngày tải lên: 15/12/2013, 04:15