This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
The book is organized into two main sections and a set of appendices. Part I addresses steady-state boundary value problems, starting with two-point boundary value problems in one dimension, followed by coverage of elliptic problems in two and three dimensions. It concludes with a chapter on iterative methods for large sparse linear systems that emphasizes systems arising from difference approximations. Part II addresses time-dependent problems, starting with the initial value problem for ODEs, moving on to initial boundary value problems for parabolic and hyperbolic PDEs, and concluding with a chapter on mixed equations combining features of ODEs, parabolic equations, and hyperbolic equations. The appendices cover concepts pertinent to Parts I and II. Exercises and student projects, developed in conjunction with this book, are available on the book痴 webpage along with numerous MATLAB m-files.
Readers will gain an understanding of the essential ideas that underlie the development, analysis, and practical use of finite difference methods as well as the key concepts of stability theory, their relation to one another, and their practical implications. The author provides a foundation from which students can approach more advanced topics and further explore the theory and/or use of finite difference methods according to their interests and needs.
Contents
Available July 2007 / Approx. xiv + 339 pages / Softcover / ISBN 978-0-898716-29-0
Given that scientific material can be hard to comprehend, sustained attention and memory retention become major reader challenges. Scientific writers must not only present their science, but also work hard to generate and sustain the interest of readers. Attention-getters, sentence progression, expectation-setting, and 杜emory offloaders・are essential devices to keep readers and reviewers engaged. The writer needs to have a clear understanding of the role played by each part of a paper, from its eye-catching title to its eye-opening conclusion. This book walks through the main parts of a paper; that is, those parts which create the critical first impression.
The unique approach in this book is its focus on the reader rather than the writer. Senior scientists who supervise staff and postgraduates can use the book to review drafts and to help with the writing as well as the science. Young researchers can find solid guidelines that reduce the confusion all new writers face. Published scientists can finally move from what feels right to what is right, identifying mistakes they thought were acceptable, and fully appreciating their responsibility: to guide the reader along carefully laid-out reading tracks.
Contents:
The Reading Toolkit:
Require Less from Memory
Sustain Attention to Ensure Continuous Reading
Reduce Reading Time
Keep the Reader Motivated
Bridge the Knowledge Gap
Set the Reader痴 Expectations
Set Progression Tracks for Fluid Reading
Create Reading Momentum
Control Reading Energy Consumption
Paper Structure and Purpose:
Title: The Face of Your Paper
Abstract: The Heart of Your Paper
Headings/Subheadings: The Skeleton of Your Paper
Introduction: The Hands of Your Paper
Introduction Part II: Popular Traps
Visuals: The Voice of Your Paper
Conclusion: The Smile of Your Paper
224pp Pub. date: Apr 2007
ISBN 978-981-270-473-3
ISBN 978-981-270-144-2(pbk)
This volume gives an interdisciplinary discussion on the topological aspects of general networks and critical systems for physicists, chemists, biologists, mathematicians, medical scientists, social scientists, and other related researchers. Subjects as diverse as the general properties of complex networks, complexity in social science, patterns in biological objects, and criticality in pure and applied physics are represented. The book is essential for researchers in a wide range of scientific and technological fields related to these areas.
Contents:
General Properties of Networks:
Physics of Network Security (Y-C Lai et al.)
Multi-State Interacting Particle Systems on Scale-Free Networks (N Masuda & N Konno)
Homotopy Reduction of Complex Networks (Y Hiraoka & T Ichinomiya)
Complexity in Social Science:
Innovation and Development in a Random Lattice (J Lahtinen)
Long-Tailed Distributions in Biological Systems: Revisit to Lognormals (N Kobayashi et al.)
Power Law Distributions in Two Community Currencies (N Kichiji & M Nishibe)
Patterns in Biological Objects:
Collective Movement and Morphogenesis of Epithelial Cells (H Haga & K Kawabata)
Indecisive Behavior of Amoeba Crossing an Environmental Barrier (S Takagi et al.)
Topological Analysis of Placental Arteries: Correlation with Neonatal Growth (H Yamada & K Yakubo)
Criticality in Pure and Applied Physics:
Droplets in Disordered Metallic Quantum Critical Systems (A H Castro Neto & B A Jones)
Importance of Static Disorder and Inhomogeneous Cooperative Dynamics in Heavy-Fermion Metals (O O Bernal)
Competition between Spin Glass and Antiferromagnetic Phases in Heavy Fermion Materials (S S・low)
and other papers
280pp (approx.) Pub. date: Scheduled Summer 2007
ISBN 978-981-270-736-9
(Volume 2)
This accessible book for beginners uses intuitive geometric concepts to create abstract algebraic theory with a special emphasis on geometric characterizations. The book applies known results to describe various geometries and their invariants, and presents problems concerned with linear algebra, such as in real and complex analysis, differential equations, differentiable manifolds, differential geometry, Markov chains and transformation groups. The clear and inductive approach makes this book unique among existing books on linear algebra both in presentation and in content.
Contents:
The Euclidean Structures of ?1, ?2 and ?3: The Euclidean Plane ?2
The Euclidean Space ?3
Readership: Upper-level undergraduates, graduate students and lecturers.
900pp (approx.) Pub. date: Scheduled Spring 2008
ISBN 978-981-270-775-8(pbk)