By Professor Dr. Dietrich Stauffer, Professor Dr. Friedrich W. Hehl, Dr. Nobuyasu Ito, Dipl.-Phys. Volker Winkelmann, Professor Dr. John G. Zabolitzky (auth.)

ISBN-10: 3540565302

ISBN-13: 9783540565307

ISBN-10: 3642781179

ISBN-13: 9783642781179

**Computer Simulation and laptop Algebra**. ranging from basic examples in classical mechanics, those introductory lectures continue to simulations in statistical physics (using FORTRAN) after which clarify intimately using machine algebra (by technique of Reduce). This 3rd version takes into consideration the newest model of lessen (3.4.1) and updates the outline of large-scale simulations to matters equivalent to the 170000 X 170000 Ising version. moreover, an advent to either vector and parallel computing is given.

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**Example text**

4) The fraction, called "mantissa" in this context, is between 0 and 1 in magnitude and is represented by a finite number of bits. Similarly, a finite number of bits is used for the exponent. This gives us a finite dynamic range of floating-point numbers, essentially given by the exponent range, and finite precision. Typically we have 32 bit word 8 bit exponent 64 bit word 16 bit exponent 24 bit mantissa accuracy ~ 10-6 48 bit mantissa accuracy ~ 10- 14 In some machines, the sign bit of the fraction goes into the exponent field, giving a little extra precision for a slightly reduced dynamic range.

97717 root at r= 1. 550000 3. 326234 -1. 326234} 49 Chapter 5 Statics and Dynamics of Strings We now turn to the configuration of a string stretched between two anchoring points, subject to a tension T, shown below. We assume that the problem is totally dominated by restoring forces due to the string tension T, and that any stiffness of the string can be neglected. This is of course totally opposed to the problem of a bar bending under stress, which is dominated by stiffness. In the latter case, tension can usually be neglected.

4) is still valid. We can discretize the desired solution on some suitable mesh and transform the differential equation into an algebraic equation. 9), and we arrive at an eigenvalue problem for a tri-diagonal matrix.

### Computer Simulation and Computer Algebra: Lectures for Beginners by Professor Dr. Dietrich Stauffer, Professor Dr. Friedrich W. Hehl, Dr. Nobuyasu Ito, Dipl.-Phys. Volker Winkelmann, Professor Dr. John G. Zabolitzky (auth.)

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