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Discusses the direction in which the field of differential equations, and its teaching, is going.
Written in a clear and accurate language that students can understand, Trench's new book minimizes the number of explicitly stated theorems and definitions. Instead, he deals with concepts in a conversational style that engages students. He includes more than 250 illustrated, worked examples for easy reading and comprehension. One of the book's many strengths is its problems, which are of consistently high quality. Trench includes a thorough treatment of boundary-value problems and partial differential equations and has organized the book to allow instructors to select the level of technology desired. This has been simplified by using symbols, C and L, to designate the level of technology. C problems call for computations and/or graphics, while L problems are laboratory exercises that require extensive use of technology. Informal advice on the use of technology is included in several sections and instructors who prefer not to emphasize technology can ignore these exercises without interrupting the flow of material.
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
The book is intended to serve as as a textbook for undergraduate and honors students. It will be useful to the engineering and management students, and other applied areas. It will also be helpful in preparing for competitive examinations like IAS, IES, NET, PCS, and other higher education exams. Key Features: Basic concepts presented in an easy to understand style, Notes and remarks given at appropriate places, clean and clear figures given for better understanding, includes a large number of solved examples, Exercise questions at the end of each chapter, Presentation of the subject in a natural way.
Modelling with Ordinary Differential Equations integrates standard material from an elementary course on ordinary differential equations with the skills of mathematical modeling in a number of diverse real-world situations. Each situation highlights a different aspect of the theory or modeling. Carefully selected exercises and projects present excellent opportunities for tutorial sessions and self-study. This text/reference addresses common types of first order ordinary differential equations and the basic theory of linear second order equations with constant coefficients. It also explores the elementary theory of systems of differential equations, Laplace transforms, and numerical solutions. Theorems on the existence and uniqueness of solutions are a central feature. Topics such as curve fitting, time-delay equations, and phase plane diagrams are introduced. The book includes algorithms for computer programs as an integral part of the answer-finding process. Professionals and students in the social and biological sciences, as well as those in physics and mathematics will find this text/reference indispensable for self-study.
Shell structures are key components in a very wide range of engineering enterprises. The theory of layered shells of revolution under the quasistatic action of loading and temperature is the subject of this book. The shells treated here are in general of an asymmetric sandwich structure. A linear theory is developed which allows for a transition to shells with less layers, that is two-layered and homogeneous structures.The first half of the book is concerned with orthotropic elastic shells. In particular, it includes the membrane theory of cylindrical, spherical and conical shells, and the bending theory of cylindrical shells, storage tanks and pressure-vessels. In each of the numerical examples considered, an attempt is made to map different regimes of structural behaviour.The second half of the book is devoted to viscoelastic shells. First the time-invariant hereditary theory is presented, describing the response of viscoelastic materials. According to the correspondence principle of this theory the actual viscoelastic shell may be replaced by a conjugate elastic one. In this way many of the results from the first half of the book can be put to good use even for viscoelastic shells. The time-dependent material characteristics are taken into account by means of the time-temperature principle.In an appendix (Part VI), the mathematical prerequisites are presented. With viscoelasticity comes the need to employ further mathematical disciplines; integral equations and integral transformations are usually encountered. Here, instead, a different concept has been chosen, the distributional concept of Laurent Schwartz, which allows many problems to be tackled in a simple formal way. In discussing the distribution theory, a level accessible to a technical reader has been maintained.The book is intended as a textbook for students and teachers of structural and aeronautical engineering. The book will also appeal to a broad range of practising engineers working in areas of aeronautical, civil, and mechanical engineering, as well as to those working for firms dealing with shell structures.