Exterior Analysis


Book Description

Exterior analysis uses differential forms (a mathematical technique) to analyze curves, surfaces, and structures. Exterior Analysis is a first-of-its-kind resource that uses applications of differential forms, offering a mathematical approach to solve problems in defining a precise measurement to ensure structural integrity. The book provides methods to study different types of equations and offers detailed explanations of fundamental theories and techniques to obtain concrete solutions to determine symmetry. It is a useful tool for structural, mechanical and electrical engineers, as well as physicists and mathematicians. - Provides a thorough explanation of how to apply differential equations to solve real-world engineering problems - Helps researchers in mathematics, science, and engineering develop skills needed to implement mathematical techniques in their research - Includes physical applications and methods used to solve practical problems to determine symmetry




Introduction to Real Analysis


Book Description

Developed over years of classroom use, this textbook provides a clear and accessible approach to real analysis. This modern interpretation is based on the author’s lecture notes and has been meticulously tailored to motivate students and inspire readers to explore the material, and to continue exploring even after they have finished the book. The definitions, theorems, and proofs contained within are presented with mathematical rigor, but conveyed in an accessible manner and with language and motivation meant for students who have not taken a previous course on this subject. The text covers all of the topics essential for an introductory course, including Lebesgue measure, measurable functions, Lebesgue integrals, differentiation, absolute continuity, Banach and Hilbert spaces, and more. Throughout each chapter, challenging exercises are presented, and the end of each section includes additional problems. Such an inclusive approach creates an abundance of opportunities for readers to develop their understanding, and aids instructors as they plan their coursework. Additional resources are available online, including expanded chapters, enrichment exercises, a detailed course outline, and much more. Introduction to Real Analysis is intended for first-year graduate students taking a first course in real analysis, as well as for instructors seeking detailed lecture material with structure and accessibility in mind. Additionally, its content is appropriate for Ph.D. students in any scientific or engineering discipline who have taken a standard upper-level undergraduate real analysis course.




Mathematical Analysis


Book Description




Elements of Real Analysis


Book Description

This book is an attempt to make presentation of Elements of Real Analysis more lucid. The book contains examples and exercises meant to help a proper understanding of the text. For B.A., B.Sc. and Honours (Mathematics and Physics), M.A. and M.Sc. (Mathematics) students of various Universities/ Institutions.As per UGC Model Curriculum and for I.A.S. and Various other competitive exams.




From the Conscious Interior to an Exterior Unconscious


Book Description

This striking Lacanian contribution to discourse analysis is also a critique of contemporary psychological abstraction, as well as a reassessment of the radical opposition between psychology and psychoanalysis. This original introduction to Lacan’s work bridges the gap between discourseanalytical debates in social psychology and the social-theoretical extensions of discourse theory. David Pavón Cuéllar provides a precise definition and a detailed explanation of key Lacanian concepts, and illustrates how they may be put to work on a concrete discourse, in this case a fragment of an interview obtained by the author from the Mexican underground Popular Revolutionary Forces (EPR). Throughout the book, Lacanian concepts are compared to their counterparts in psychology. Such a comparison reveals insuperable incompatibilities between the two series of concepts. The author shows that Lacan’s psychoanalytical terminology can neither be translated nor assimilated to the terms of current psychology. Among the notions in actual or potential competition with Lacanian concepts, the book deals with those proposed by semiology, Marxism, phenomenology, constructionism, deconstruction, and hermeneutics. Taking a stand on those theoretical positions, each chapter includes detailed discussion of the contribution of classical approaches to language; including Barthes, Bakhtin, Althusser, Politzer, Wittgenstein, Berger and Luckmann, Derrida, and Ricoeur. There is sustained reference in the body of the text to the arguments of Lacan and Lacanians, of Miller, Milner, Soler, and Žižek. At the same time, in the extensive notes accompanying the text, there is a systematic reappraisal and reinterpretation of debates and pieces of research work in social psychology, especially in a discursive and critical domain that has incorporated elements of psychoanalytic theory.




An Introduction to Real Analysis


Book Description

This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.




Exterior Differential Systems


Book Description

This book gives a treatment of exterior differential systems. It will in clude both the general theory and various applications. An exterior differential system is a system of equations on a manifold defined by equating to zero a number of exterior differential forms. When all the forms are linear, it is called a pfaffian system. Our object is to study its integral manifolds, i. e. , submanifolds satisfying all the equations of the system. A fundamental fact is that every equation implies the one obtained by exterior differentiation, so that the complete set of equations associated to an exterior differential system constitutes a differential ideal in the algebra of all smooth forms. Thus the theory is coordinate-free and computations typically have an algebraic character; however, even when coordinates are used in intermediate steps, the use of exterior algebra helps to efficiently guide the computations, and as a consequence the treatment adapts well to geometrical and physical problems. A system of partial differential equations, with any number of inde pendent and dependent variables and involving partial derivatives of any order, can be written as an exterior differential system. In this case we are interested in integral manifolds on which certain coordinates remain independent. The corresponding notion in exterior differential systems is the independence condition: certain pfaffian forms remain linearly indepen dent. Partial differential equations and exterior differential systems with an independence condition are essentially the same object.




Structural Analysis and Design of Tall Buildings


Book Description

As software skills rise to the forefront of design concerns, the art of structural conceptualization is often minimized. Structural engineering, however, requires the marriage of artistic and intuitive designs with mathematical accuracy and detail. Computer analysis works to solidify and extend the creative idea or concept that might have started o







Finite Element Exterior Calculus


Book Description

Computational methods to approximate the solution of differential equations play a crucial role in science, engineering, mathematics, and technology. The key processes that govern the physical world?wave propagation, thermodynamics, fluid flow, solid deformation, electricity and magnetism, quantum mechanics, general relativity, and many more?are described by differential equations. We depend on numerical methods for the ability to simulate, explore, predict, and control systems involving these processes. The finite element exterior calculus, or FEEC, is a powerful new theoretical approach to the design and understanding of numerical methods to solve partial differential equations (PDEs). The methods derived with FEEC preserve crucial geometric and topological structures underlying the equations and are among the most successful examples of structure-preserving methods in numerical PDEs. This volume aims to help numerical analysts master the fundamentals of FEEC, including the geometrical and functional analysis preliminaries, quickly and in one place. It is also accessible to mathematicians and students of mathematics from areas other than numerical analysis who are interested in understanding how techniques from geometry and topology play a role in numerical PDEs.