Download An Introduction to Modern Mathematical Computing: With by Jonathan M. Borwein PDF

By Jonathan M. Borwein

Thirty years in the past mathematical, in preference to utilized numerical, computation was once tricky to accomplish and so particularly little used. 3 threads replaced that: the emergence of the non-public machine; the invention of fiber-optics and the ensuing improvement of the trendy net; and the construction of the 3 “M’s” Maple, Mathematica and Matlab.

We intend to cajole that Mathematica and different related instruments are worthy understanding, assuming in basic terms that one needs to be a mathematician, a arithmetic educator, a working laptop or computer scientist, an engineer or scientist, or someone else who wishes/needs to take advantage of arithmetic higher. We additionally desire to provide an explanation for find out how to develop into an "experimental mathematician" whereas studying to be higher at proving issues. to complete this our fabric is split into 3 major chapters via a postscript. those disguise hassle-free quantity idea, calculus of 1 and a number of other variables, introductory linear algebra, and visualization and interactive geometric computation.

Show description

Read or Download An Introduction to Modern Mathematical Computing: With Mathematica® PDF

Best counting & numeration books

Introducing Monte Carlo Methods with R

Computational ideas in line with simulation have now turn into an important a part of the statistician's toolbox. it truly is therefore the most important to supply statisticians with a realistic realizing of these equipment, and there's no larger technique to enhance instinct and abilities for simulation than to take advantage of simulation to unravel statistical difficulties.

Numerical Methods in Sensitivity Analysis and Shape Optimization

Sensitivity research and optimum form layout are key matters in engineering which were tormented by advances in numerical instruments at present on hand. This publication, and its supplementary on-line records, provides easy optimization ideas that may be used to compute the sensitivity of a given layout to neighborhood swap, or to enhance its functionality by means of neighborhood optimization of those information.

Mathematical Cardiac Electrophysiology

This ebook covers the most mathematical and numerical types in computational electrocardiology, starting from microscopic membrane types of cardiac ionic channels to macroscopic bidomain, monodomain, eikonal versions and cardiac resource representations. those complicated multiscale and nonlinear types describe the cardiac bioelectrical job from the mobilephone point to the physique floor and are hired in either the direct and inverse difficulties of electrocardiology.

Meshfree Methods for Partial Differential Equations VII

Meshfree equipment, particle tools, and generalized finite point tools have witnessed mammoth improvement because the mid Nineties. The turning out to be curiosity in those equipment is due partly to the truth that they're super versatile numerical instruments and will be interpreted in a couple of methods. for example, meshfree equipment might be seen as a ordinary extension of classical finite point and finite distinction easy methods to scattered node configurations with out mounted connectivity.

Additional info for An Introduction to Modern Mathematical Computing: With Mathematica®

Sample text

This technique works, but turns out to be about twice to three times as slow as using Npar. 64493 What we are seeing is an example of a case where obtaining decimal approximations of previous symbolic computations is simply not feasible. Sometimes we have to work purely numerically, and the reality is that numeric computations aren’t as bad as all that. We should, of course, be quite aware of the fact that numerical approximation can introduce errors in our calculations, and be on the lookout for them, but this should not and does not detract from the usefulness of symbolic computation.

Observe. In[89]:= a ~F~ b Out[89]= F [a, b] It should hopefully be expected, in light of the both pre- and postfix notation, that any function that can take exactly two inputs may be used in infix notation. Unfortunately, our previous example is not appropriate for infix notation; it does not have any functions that take two arguments. However, we have already seen a function which lends itself very nicely to infix notation, the Join function. In[90]:= {1, 2, 3} ~Join~ {3, 4, 5} Out[90]= {1, 2, 3, 3, 4, 5} We may chain these notations together, if we wish, and the results are fairly predictable.

This leaves us with two criteria, which we are able to express as a single criterion for the If function by using the && logical ‘and’ operator. We implement this approach using a loop similar to that used above. = n && (Divisors[m] // Total) - m == n, {n, m} // Print ], {n, 1, N} ]; ] Out[194]= {220, 284} Out[195]= {284, 220} Out[196]= {1184, 1210} Out[197]= {1210, 1184} Out[198]= {2620, 2924} Out[199]= {2924, 2620} Out[200]= {5020, 5564} Out[201]= {5564, 5020} Out[202]= {6232, 6368} Out[203]= {6368, 6232} To compute this with lists and cases, we first compute the list containing all candidate pairs of n, m where m is the sum of the proper divisors of m, and then apply a pattern to the Cases function which matches a list of 2 elements, with the elements named n and m, and choose those pairs which match our criteria, above.

Download PDF sample

Rated 4.79 of 5 – based on 23 votes