Focused on fluid mechanics modeling, this volume is structured into four chapters that include numerous exercises complete with solutions. It offers comprehensive references for further exploration of relevant topics, enhancing the reader's understanding and application of the material.
Mathematical Methods and Applications
Exploring nonlinear phenomena and instabilities, this book offers a comprehensive approach across various scientific fields. It begins with foundational topics in analysis and progresses through essential and advanced methods of ordinary differential equations, including visualization techniques like attractors and chaos. Subsequent chapters delve into perturbation theory, turbulence, and significant hydrodynamic instabilities. Rich in theoretical insights and practical examples, it serves as a valuable resource for students and professionals in mathematics, physics, chemistry, biology, and engineering.
Focusing on analytical modeling and visualization, this text explores elementary methods for curves, surfaces, and polyhedra using computer modeling. It features 2-D and 3-D animations, transformations, and differential geometry, supported by over 350 figures and numerous Maple programs. Designed for students and professionals with a background in analytical geometry, it offers a wealth of exercises and solutions, making it an ideal resource for both classroom use and self-study. The integration of traditional geometry with modern computer algebra systems enhances its practical application.
Focusing on Riemannian geometry, this monograph explores foliations with nonnegative mixed curvature and the geometry of submanifolds featuring rulings in spaces of nonnegative curvature. It presents a decomposition approach for foliated manifolds when leaf dimensions are large. The work is structured into two parts, encompassing seven chapters and three appendices, with the first part detailing foundational results on foliated smooth manifolds and emphasizing the significance of Riemannian curvature in understanding these structures.
This text on geometry is devoted to various central geometrical topics including: graphs of functions, transformations, (non-)Euclidean geometries, curves and surfaces as well as their applications in a variety of disciplines. This book presents elementary methods for analytical modeling and demonstrates the potential for symbolic computational tools to support the development of analytical solutions. The author systematically examines several powerful tools of MATLAB® including 2D and 3D animation of geometric images with shadows and colors and transformations using matrices. With over 150 stimulating exercises and problems, this text integrates traditional differential and non-Euclidean geometries with more current computer systems in a practical and user-friendly format. This text is an excellent classroom resource or self-study reference for undergraduate students in a variety of disciplines.
Extrinsic geometry describes those properties of foliations on Riemannian manifolds which can be expressed in terms of the second fundamental form of the leaves. The central topic of this book is Extrinsic Geometric Flow (EGF) on foliated manifolds.