The audience consisted of academics from New York University and other universities, as well as practitioners from investment banks, hedge funds and asset-management firms.
The contributions to the 12th of FLINS conference cover state-of-the-art research, development, and technology for computational intelligence systems, both from the foundations and the applications points-of-view. The emphasis in this book is on theory and methods and differential equations as a part of analysis. Differential equations is worth studying, rather than merely some recipes to be used in physical science. The text gives substantial emphasis to methods which are generally presented first with theoretical considerations following.
Essentially all proofs of the theorems used are included, making the book more useful as a reference. The book mentions the main computer algebra systems, yet the emphasis is placed on MATLAB and numerical methods which include graphing the solutions and obtaining tables of values. Featured applications are easily understood. Complete explanations of the mathematics and emphasis on methods for finding solutions are included. Author : Steven J.
Miller Publisher: American Mathematical Soc. ISBN: Category: Management science Page: View: Read Now » Optimization Theory is an active area of research with numerous applications; many of the books are designed for engineering classes, and thus have an emphasis on problems from such fields. Covering much of the same material, there is less emphasis on coding and detailed applications as the intended audience is more mathematical.
There are still several important problems discussed especially scheduling problems , but there is more emphasis on theory and less on the nuts and bolts of coding. Why are we able to do a calculation efficiently? How should we look at a problem? As many of the key algorithms in the subject require too much time or detail to analyze in a first course such as the run-time of the Simplex Algorithm , there are numerous comparisons to simpler algorithms which students have either seen or can quickly learn such as the Euclidean algorithm to motivate the type of results on run-time savings.
Readers are also instructed in the extended potential theory in its three forms: the volume potential, the surface single-layer potential and the surface double-layer potential. Furthermore, the book presents the main initial boundary value problems associated with elliptic, parabolic and hyperbolic equations.
The second part of the book, which is addressed first and foremost to those who are already acquainted with the notions and the results from the first part, introduces readers to modern aspects of the theory of partial differential equations.
This field pertains to the design, analysis, and implementation of algorithms for the approximate solution of mathematical problems that arise in applications spanning science and engineering, and are not practical to solve using analytical techniques such as those taught in courses in calculus, linear algebra or differential equations. Topics covered include computer arithmetic, error analysis, solution of systems of linear equations, least squares problems, eigenvalue problems, nonlinear equations, optimization, polynomial interpolation and approximation, numerical differentiation and integration, ordinary differential equations, and partial differential equations.
For each problem considered, the presentation includes the derivation of solution techniques, analysis of their efficiency, accuracy and robustness, and details of their implementation, illustrated through the Python programming language. This text is suitable for a year-long sequence in numerical analysis, and can also be used for a one-semester course in numerical linear algebra.
Focusing on the modeling of real-world phenomena, it begins with a basic introduction to differential equations, followed by linear and nonlinear first order equations and a detailed treatment of the second order linear equations. After presenting solution methods for the Laplace transform and power series, it lastly presents systems of equations and offers an introduction to the stability theory.
To help readers practice the theory covered, two types of exercises are provided: those that illustrate the general theory, and others designed to expand on the text material. Detailed solutions to all the exercises are included. The book is excellently suited for use as a textbook for an undergraduate class of all disciplines in ordinary differential equations.
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