Differential Equations and Population Dynamics I: Introductory Approaches
English | 2022 | ISBN: 3030981355 | 466 Pages | PDF True | 15 MB
Part I focuses on linear systems. Beginning with some modeling background, it considers existence, uniqueness, stability of solution, positivity, and the Perron-Frobenius theorem and its consequences.

English | January 10, 2012 | ASIN: B006VPAWHE | MP3 | M4B | 8h 22m | 227 MB
Author: Chip Conley

English | 2022 | ISBN: 978-3030889449 | 818 pages | pdf, epub | 201.57 MB
The greatly expanded and updated 3rd edition of this textbook offers the reader a comprehensive introduction to the concepts of logic functions and equations and their applications across computer science and engineering. The authors' approach emphasizes a thorough understanding of the fundamental principles as well as numerical and computer-based solution methods. The book provides insight into applications across propositional logic, binary arithmetic, coding, cryptography, complexity, logic design, and artificial intelligence.

English | 2021 | ISBN: 147045114X, 978-1470465407 | 553 pages | True PDF | 7.76 MB
This graduate-level introduction to ordinary differential equations combines both qualitative and numerical analysis of solutions, in line with Poincaré's vision for the field over a century ago. Taking into account the remarkable development of dynamical systems since then, the authors present the core topics that every young mathematician of our time―pure and applied alike―ought to learn. The book features a dynamical perspective that drives the motivating questions, the style of exposition, and the arguments and proof techniques. The text is organized in six cycles. The first cycle deals with the foundational questions of existence and uniqueness of solutions. The second introduces the basic tools, both theoretical and practical, for treating concrete problems. The third cycle presents autonomous and non-autonomous linear theory. Lyapunov stability theory forms the fourth cycle. The fifth one deals with the local theory, including the Grobman–Hartman theorem and the stable manifold theorem. The last cycle discusses global issues in the broader setting of differential equations on manifolds, culminating in the Poincaré–Hopf index theorem. The book is appropriate for use in a course or for self-study. The reader is assumed to have a basic knowledge of general topology, linear algebra, and analysis at the undergraduate level. Each chapter ends with a computational experiment, a diverse list of exercises, and detailed historical, biographical, and bibliographic notes seeking to help the reader form a clearer view of how the ideas in this field unfolded over time.

Published 06/2022
MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz, 2 Ch
Genre: eLearning | Language: English + srt | Duration: 13 lectures (13h 41m) | Size: 5.27 GB

MP4 | Video: h264, 1280x720 | Audio: AAC, 44.1 KHz
Language: English | Size: 1.46 GB | Duration: 4h 53m
Review Solving Linear and Absolute Value Equations and Inequalities in One Variable.

English | 2022 | ISBN: 1685075924, 978-1685075927 | 364 pages | True PDF | 8.64 MB
The laws of nature are written in the language of partial differential equations. Therefore, these equations arise as models in virtually all branches of science and technology. Our goal in this book is to help you to understand what this vast subject is about. The book is an introduction to the field suitable for senior undergraduate and junior graduate students. Introductory courses in partial differential equations (PDEs) are given all over the world in various forms. The traditional approach to the subject is to introduce a number of analytical techniques, enabling the student to derive exact solutions of some simplified problems. Students who learn about computational techniques in other courses subsequently realize the scope of partial differential equations beyond paper and pencil. Our book is significantly different from the existing ones. We introduce both analytical theory, including the theory of classical solutions and that of weak solutions, and introductory techniques of ill-posed problems with reference to weak solutions. Besides, since computational techniques are commonly available and are currently used in all practical applications of partial differential equations, we incorporate classical finite difference methods and finite element methods in our book.

English | 2022 | ISBN: 1470464918 | 647 pages | True PDF | 16.71 MB
While partial differential equations (PDEs) are fundamental in mathematics and throughout the sciences, most undergraduate students are only exposed to PDEs through the method of separation of variations. This text is written for undergraduate students from different cohorts with one sole purpose: to facilitate a proficiency in many core concepts in PDEs while enhancing the intuition and appreciation of the subject. For mathematics students this will in turn provide a solid foundation for graduate study. A recurring theme is the role of concentration as captured by Dirac's delta function. This both guides the student into the structure of the solution to the diffusion equation and PDEs involving the Laplacian and invites them to develop a cognizance for the theory of distributions. Both distributions and the Fourier transform are given full treatment.

English | 2022 | ISBN: 1032014458, 978-1032014456 | 284 pages | True PDF | 7.52 MB
Mathematical Modelling with Differential Equations aims to introduce various strategies for modelling systems using differential equations. Some of these methodologies are elementary and quite direct to comprehend and apply while others are complex in nature and require thoughtful, deep contemplation. Many topics discussed in the chapter do not appear in any of the standard textbooks and this provides users an opportunity to consider a more general set of interesting systems that can be modelled. For example, the book investigates the evolution of a "toy universe," discusses why "alternate futures" exists in classical physics, constructs approximate solutions to the famous Thomas-Fermi equation using only algebra and elementary calculus, and examines the importance of "truly nonlinear" and oscillating systems.
Features

Principles of Partial Differential Equations by Alexander Komech
English | PDF(True) | 2009 | 165 Pages | ISBN : 1441910956 | 3.2 MB
This concise book covers the classical tools of PDE theory used in today's science and engineering: characteristics, the wave propagation, the Fourier method, distributions, Sobolev spaces, fundamental solutions, and Green's functions. The approach is problem-oriented, giving the reader an opportunity to master solution techniques.