From Elementary Probability to Stochastic Differential Equations with MAPLE®

From Elementary Probability to Stochastic Differential Equations with MAPLE®
Author: Sasha Cyganowski
Publisher: Springer Science & Business Media
Total Pages: 323
Release: 2012-12-06
Genre: Mathematics
ISBN: 3642561446

This is an introduction to probabilistic and statistical concepts necessary to understand the basic ideas and methods of stochastic differential equations. Based on measure theory, which is introduced as smoothly as possible, it provides practical skills in the use of MAPLE in the context of probability and its applications. It offers to graduates and advanced undergraduates an overview and intuitive background for more advanced studies.

Random Differential Equations in Scientific Computing

Random Differential Equations in Scientific Computing
Author: Tobias Neckel
Publisher: Walter de Gruyter
Total Pages: 650
Release: 2013-12-17
Genre: Mathematics
ISBN: 8376560263

This book is a holistic and self-contained treatment of the analysis and numerics of random differential equations from a problem-centred point of view. An interdisciplinary approach is applied by considering state-of-the-art concepts of both dynamical systems and scientific computing. The red line pervading this book is the two-fold reduction of a random partial differential equation disturbed by some external force as present in many important applications in science and engineering. First, the random partial differential equation is reduced to a set of random ordinary differential equations in the spirit of the method of lines. These are then further reduced to a family of (deterministic) ordinary differential equations. The monograph will be of benefit, not only to mathematicians, but can also be used for interdisciplinary courses in informatics and engineering.

Theory and Numerics of Differential Equations

Theory and Numerics of Differential Equations
Author: James Blowey
Publisher: Springer Science & Business Media
Total Pages: 336
Release: 2001-08-28
Genre: Mathematics
ISBN: 9783540418467

A compilation of detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics. Each set of notes presents a self-contained guide to a current research area and has an extensive bibliography. In addition, most of the notes contain detailed proofs of the key results. The notes start from a level suitable for first year graduate students in applied mathematics, mathematical analysis or numerical analysis, and proceed to current research topics. The reader should therefore be able to quickly gain an insight into the important results and techniques in each area without recourse to the large research literature. Current (unsolved) problems are also described and directions for future research is given.

Ordinary Differential Equations

Ordinary Differential Equations
Author: Vladimir Igorevich Arnolʹd
Publisher: Universitext
Total Pages: 350
Release: 2006-06-19
Genre: Mathematics
ISBN:

Few books on Ordinary Differential Equations (ODEs) have the elegant geometric insight of this one, which puts emphasis on the qualitative and geometric properties of ODEs and their solutions, rather than on routine presentation of algorithms. From the reviews: "Professor Arnold has expanded his classic book to include new material on exponential growth, predator-prey, the pendulum, impulse response, symmetry groups and group actions, perturbation and bifurcation." --SIAM REVIEW

Algebraic Geometry

Algebraic Geometry
Author: Daniel Perrin
Publisher:
Total Pages: 284
Release: 2008
Genre: Mathematics
ISBN:

Aimed primarily at graduate students and beginning researchers, this book provides an introduction to algebraic geometry that is particularly suitable for those with no previous contact with the subject; it assumes only the standard background of undergraduate algebra. The book starts with easily-formulated problems with non-trivial solutions and uses these problems to introduce the fundamental tools of modern algebraic geometry: dimension; singularities; sheaves; varieties; and cohomology. A range of exercises is provided for each topic discussed, and a selection of problems and exam papers are collected in an appendix to provide material for further study.

Applied Stochastic Processes and Control for Jump Diffusions

Applied Stochastic Processes and Control for Jump Diffusions
Author: Floyd B. Hanson
Publisher: Society for Industrial and Applied Mathematics (SIAM)
Total Pages: 478
Release: 2007-11-22
Genre: Mathematics
ISBN:

This self-contained, practical, entry-level text integrates the basic principles of applied mathematics, applied probability, and computational science. It emphasises modelling and problem solving, and presents sample applications in financial engineering and biomedical modelling. Contains computational and analytic exercises and examples, with appendices provided on a supplementary Web page.