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Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.
This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus.
This textbook provides a rigorous approach to tensor manifolds in several aspects relevant for Engineers and Physicists working in industry or academia. With a thorough, comprehensive, and unified presentation, this book offers insights into several topics of tensor analysis, which covers all aspects of n-dimensional spaces. The main purpose of this book is to give a self-contained yet simple, correct and comprehensive mathematical explanation of tensor calculus for undergraduate and graduate students and for professionals. In addition to many worked problems, this book features a selection of examples, solved step by step. Although no emphasis is placed on special and particular problems of Engineering or Physics, the text covers the fundamentals of these fields of science. The book makes a brief introduction into the basic concept of the tensorial formalism so as to allow the reader to make a quick and easy review of the essential topics that enable having the grounds for the subsequent themes, without needing to resort to other bibliographical sources on tensors. Chapter 1 deals with Fundamental Concepts about tensors and chapter 2 is devoted to the study of covariant, absolute and contravariant derivatives. The chapters 3 and 4 are dedicated to the Integral Theorems and Differential Operators, respectively. Chapter 5 deals with Riemann Spaces, and finally the chapter 6 presents a concise study of the Parallelism of Vectors. It also shows how to solve various problems of several particular manifolds.
Provides a concise overview of the core undergraduate physics and applied mathematics curriculum for students and practitioners of science and engineering Fundamental Math and Physics for Scientists and Engineers summarizes college and university level physics together with the mathematics frequently encountered in engineering and physics calculations. The presentation provides straightforward, coherent explanations of underlying concepts emphasizing essential formulas, derivations, examples, and computer programs. Content that should be thoroughly mastered and memorized is clearly identified while unnecessary technical details are omitted. Fundamental Math and Physics for Scientists and Engineers is an ideal resource for undergraduate science and engineering students and practitioners, students reviewing for the GRE and graduate-level comprehensive exams, and general readers seeking to improve their comprehension of undergraduate physics. Covers topics frequently encountered in undergraduate physics, in particular those appearing in the Physics GRE subject examination Reviews relevant areas of undergraduate applied mathematics, with an overview chapter on scientific programming Provides simple, concise explanations and illustrations of underlying concepts Succinct yet comprehensive, Fundamental Math and Physics for Scientists and Engineers constitutes a reference for science and engineering students, practitioners and non-practitioners alike.
Calculus for Engineering Students: Fundamentals, Real Problems, and Computers insists that mathematics cannot be separated from chemistry, mechanics, electricity, electronics, automation, and other disciplines. It emphasizes interdisciplinary problems as a way to show the importance of calculus in engineering tasks and problems. While concentrating on actual problems instead of theory, the book uses Computer Algebra Systems (CAS) to help students incorporate lessons into their own studies. Assuming a working familiarity with calculus concepts, the book provides a hands-on opportunity for students to increase their calculus and mathematics skills while also learning about engineering applications. - Organized around project-based rather than traditional homework-based learning - Reviews basic mathematics and theory while also introducing applications - Employs uniform chapter sections that encourage the comparison and contrast of different areas of engineering
This book gives a practical overview of Fractional Calculus as it relates to Signal Processing
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.
Quarternionic calculus covers a branch of mathematics which uses computational techniques to help solve problems from a wide variety of physical systems which are mathematically modelled in 3, 4 or more dimensions. Examples of the application areas include thermodynamics, hydrodynamics, geophysics and structural mechanics. Focusing on the Clifford algebra approach the authors have drawn together the research into quarternionic calculus to provide the non-expert or research student with an accessible introduction to the subject. This book fills the gap between the theoretical representations and the requirements of the user.
Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice evident in the narrative, the figures, and the questions interspersed in the narrative is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope. This book is an expanded version of Calculus: Early Transcendentals by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections.