Introduction -- Technical preliminaries: tensors, actions and functors -- Applied manifold geometry -- Applied bundle geometry -- Applied jet geometry -- Geometrical path integrals and their applications

This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator — “Human Biodynamics Engine”, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools — this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.

The topics covered are pure differential geometry, especially submanifolds and affine differential geometry, and applications of geometry to human vision, robotics, and gastro-entrology.

This book aims to present a new approach called Flow Curvature Method that applies Differential Geometry to Dynamical Systems. Hence, for a trajectory curve, an integral of any n-dimensional dynamical system as a curve in Euclidean n-space, the curvature of the trajectory ? or the flow ? may be analytically computed. Then, the location of the points where the curvature of the flow vanishes defines a manifold called flow curvature manifold. Such a manifold being defined from the time derivatives of the velocity vector field, contains information about the dynamics of the system, hence identifying the main features of the system such as fixed points and their stability, local bifurcations of codimension one, center manifold equation, normal forms, linear invariant manifolds (straight lines, planes, hyperplanes).In the case of singularly perturbed systems or slow-fast dynamical systems, the flow curvature manifold directly provides the slow invariant manifold analytical equation associated with such systems. Also, starting from the flow curvature manifold, it will be demonstrated how to find again the corresponding dynamical system, thus solving the inverse problem.

This is the first book on a newly emerging field of discrete differential geometry providing an excellent way to access this exciting area. It provides discrete equivalents of the geometric notions and methods of differential geometry, such as notions of curvature and integrability for polyhedral surfaces. The carefully edited collection of essays gives a lively, multi-facetted introduction to this emerging field.

Contents:Progress in Affine Differential Geometry — Problem List and Continued Bibliography (T Binder & U Simon)On the Classification of Timelike Bonnet Surfaces (W H Chen & H Z Li)Affine Hyperspheres with Constant Affine Sectional Curvature (F Dillen et al.)Geometric Properties of the Curvature Operator (P Gilkey)On a Question of S S Chern Concerning Minimal Hypersurfaces of Spheres (I Hiric( & L Verstraelen)Parallel Pure Spinors on Pseudo-Riemannian Manifolds (I Kath)Twistorial Construction of Spacelike Surfaces in Lorentzian 4-Manifolds (F Leitner)Nirenberg's Problem in 90's (L Ma)A New Proof of the Homogeneity of Isoparametric Hypersurfaces with (g,m) = (6, 1) (R Miyaoka)Harmonic Maps and Negatively Curved Homogeneous Spaces (S Nishikawa)Biharmonic Morphisms Between Riemannian Manifolds (Y L Ou)Intrinsic Properties of Real Hypersurfaces in Complex Space Forms (P J Ryan)On the Nonexistence of Stable Minimal Submanifolds in Positively Pinched Riemannian Manifolds (Y B Shen & H Q Xu)Geodesic Mappings of the Ellipsoid (K Voss)η-Invariants and the Poincaré-Hopf Index Formula (W Zhang)and other papers Readership: Researchers in differential geometry and topology. Keywords:Conference;Proceedings;Berlin (Germany);Beijing (China);Geometry;Topology;Submanifolds X;Differential Geometry;Dedication

Covering the main fields of mathematics, this handbook focuses on the methods used for obtaining solutions of various classes of mathematical equations that underlie the mathematical modeling of numerous phenomena and processes in science and technology. The authors describe formulas, methods, equations, and solutions that are frequently used in scientific and engineering applications and present classical as well as newer solution methods for various mathematical equations. The book supplies numerous examples, graphs, figures, and diagrams and contains many results in tabular form, including finite sums and series and exact solutions of differential, integral, and functional equations.

Teaching Electromagnetics: Innovative Approaches and Pedagogical Strategies is a guide for educators addressing course content and pedagogical methods primarily at the undergraduate level in electromagnetic theory and its applications. Topics include teaching methods, lab experiences and hands-on learning, and course structures that help teachers respond effectively to trends in learning styles and evolving engineering curricula. The book grapples with issues related to the recent worldwide shift to remote teaching. Each chapter begins with a high-level consideration of the topic, reviews previous work and publications, and gives the reader a broad picture of the topic before delving into details. Chapters include specific guidance for those who want to implement the methods and assessment results and evaluation of the effectiveness of the methods. Respecting the limited time available to the average teacher to try new methods, the chapters focus on why an instructor should adopt the methods proposed in it. Topics include virtual laboratories, computer-assisted learning, and MATLAB® tools. The authors also review flipped classrooms and online teaching methods that support remote teaching and learning. The end result should be an impact on the reader represented by improvements to his or her practical teaching methods and curricular approach to electromagnetics education. The book is intended for electrical engineering professors, students, lab instructors, and practicing engineers with an interest in teaching and learning. In summary, this book: Surveys methods and tools for teaching the foundations of wireless communications and electromagnetic theory Presents practical experience and best practices for topical coverage, course sequencing, and content Covers virtual laboratories, computer-assisted learning, and MATLAB tools Reviews flipped classroom and online teaching methods that support remote teaching and learning Helps instructors in RF systems, field theory, and wireless communications bring their teaching practice up to date Dr. Krishnasamy T. Selvan is Professor in the Department of Electronics & Communication Engineering, SSN College of Engineering, since June 2012. Dr. Karl F. Warnick is Professor in the Department of Electrical and Computer Engineering at BYU.