Perturbation Methods, Bifurcation Theory and Computer Algebra - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbation Methods, Bifurcation Theory and Computer Algebra write by Richard H. Rand. This book was released on 2012-12-06. Perturbation Methods, Bifurcation Theory and Computer Algebra available in PDF, EPUB and Kindle. Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.
Perturbation Methods in Science and Engineering
Perturbation Methods in Science and Engineering - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Perturbation Methods in Science and Engineering write by Reza N. Jazar. This book was released on 2021-07-12. Perturbation Methods in Science and Engineering available in PDF, EPUB and Kindle. Perturbation Methods in Science and Engineering provides the fundamental and advanced topics in perturbation methods in science and engineering, from an application viewpoint. This book bridges the gap between theory and applications, in new as well as classical problems. The engineers and graduate students who read this book will be able to apply their knowledge to a wide range of applications in different engineering disciplines. The book begins with a clear description on limits of mathematics in providing exact solutions and goes on to show how pioneers attempted to search for approximate solutions of unsolvable problems. Through examination of special applications and highlighting many different aspects of science, this text provides an excellent insight into perturbation methods without restricting itself to a particular method. This book is ideal for graduate students in engineering, mathematics, and physical sciences, as well as researchers in dynamic systems.
Multiple Scale and Singular Perturbation Methods
Multiple Scale and Singular Perturbation Methods - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Multiple Scale and Singular Perturbation Methods write by J.K. Kevorkian. This book was released on 2012-12-06. Multiple Scale and Singular Perturbation Methods available in PDF, EPUB and Kindle. This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.
Vorticity and Turbulence
Vorticity and Turbulence - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Vorticity and Turbulence write by Alexandre J. Chorin. This book was released on 2013-12-01. Vorticity and Turbulence available in PDF, EPUB and Kindle. This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.
Weakly Connected Neural Networks
Weakly Connected Neural Networks - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Weakly Connected Neural Networks write by Frank C. Hoppensteadt. This book was released on 2012-12-06. Weakly Connected Neural Networks available in PDF, EPUB and Kindle. Devoted to local and global analysis of weakly connected systems with applications to neurosciences, this book uses bifurcation theory and canonical models as the major tools of analysis. It presents a systematic and well motivated development of both weakly connected system theory and mathematical neuroscience, addressing bifurcations in neuron and brain dynamics, synaptic organisations of the brain, and the nature of neural codes. The authors present classical results together with the most recent developments in the field, making this a useful reference for researchers and graduate students in various branches of mathematical neuroscience.
