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Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus asound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations (PDEs) and the special functions introduced. Solving PDEs can't be done, however, outside of the context in which they apply to physical systems. The solutions to PDEs must conform to boundary conditions, a set of additional constraints in space or time to be satisfied at the boundaries of the system, that small part of the universe under study. The first volume is devoted to homogeneous boundary-value problems (BVPs), homogeneous implying a system lacking a forcing function, or source function. The second volume takes up (in addition to other topics) inhomogeneous problems where, in addition to the intrinsic PDE governing a physical field, source functions are an essential part of the system. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well. It is based on the assumption that it follows a math review course, and was designed to coincide with the second quarter of student study, which is dominated by BVPs but also requires an understanding of special functions and Fourier analysis.
This is an entry level text for a wide range of courses in computer science, medicine, health sciences, social sciences, business, engineering and science. Using the phenomenally successful approach of the bestselling Engineering Mathematics by the same authors, it takes you through the math step-by-step with a wealth of examples and exercises. It is an appropriate refresher or brush-up for sci-tech and business students whose math skills need further development. Offers a unique module approach that takes users through the mathematics in a step-by-step fashion with a wealth of worked examples and exercises. Contains Quizzes, Learning Outcomes and Can You? Checklists that guide readers through each topic and focus understanding. Ideal as reference or a self-learning manual.
Provides high-quality and thoroughly class-tested basic mathematics for the physical sciences This book set provides a thorough introduction to the essential mathematical techniques needed in the physical sciences. Carefully structured as a series of self-paced and self-contained chapters, it covers the basic techniques on which more advanced material is built. Starting with arithmetic and algebra, Basic Mathematics for the Physical Sciences then moves on to cover basic elements of geometry, vector algebra, differentiation and finally integration, all within an applied environment. The book handily guides readers through these different techniques with the help of numerous worked examples, applications, problems, figures, and summaries.
Essential Mathematics for Games and Interactive Applications, 2nd edition presents the core mathematics necessary for sophisticated 3D graphics and interactive physical simulations. The book begins with linear algebra and matrix multiplication and expands on this foundation to cover such topics as color and lighting, interpolation, animation and basic game physics. Essential Mathematics focuses on the issues of 3D game development important to programmers and includes optimization guidance throughout. The new edition Windows code will now use Visual Studio.NET. There will also be DirectX support provided, along with OpenGL - due to its cross-platform nature. Programmers will find more concrete examples included in this edition, as well as additional information on tuning, optimization and robustness. The book has a companion CD-ROM with exercises and a test bank for the academic secondary market, and for main market: code examples built around a shared code base, including a math library covering all the topics presented in the book, a core vector/matrix math engine, and libraries to support basic 3D rendering and interaction.
Market_Desc: · Physicists and Engineers· Students in Physics and Engineering Special Features: · Covers everything from Linear Algebra, Calculus, Analysis, Probability and Statistics, to ODE, PDE, Transforms and more· Emphasizes intuition and computational abilities· Expands the material on DE and multiple integrals· Focuses on the applied side, exploring material that is relevant to physics and engineering· Explains each concept in clear, easy-to-understand steps About The Book: The book provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference. This book helps readers gain a solid foundation in the many areas of mathematical methods in order to achieve a basic competence in advanced physics, chemistry, and engineering.
"More than ever before, modern social scientists require a basic level of mathematical literacy, yet many students receive only limited mathematical training prior to beginning their research careers. This textbook addresses this dilemma by offering a comprehensive, unified introduction to the essential mathematics of social science. Throughout the book the presentation builds from first principles and eschews unnecessary complexity. Most importantly, the discussion is thoroughly and consistently anchored in real social science applications, with more than 80 research-based illustrations woven into the text and featured in end-of-chapter exercises. Students and researchers alike will find this first-of-its-kind volume to be an invaluable resource."--BOOK JACKET.
Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.
Based on course material used by the author at Yale University, this practical text addresses the widening gap found between the mathematics required for upper-level courses in the physical sciences and the knowledge of incoming students. This superb book offers students an excellent opportunity to strengthen their mathematical skills by solving various problems in differential calculus. By covering material in its simplest form, students can look forward to a smooth entry into any course in the physical sciences.
Concise treatment of mathematical entities employs examples from the physical sciences. Topics include distribution theory, Fourier series, Laplace transforms, wave and heat conduction equations, and gamma and Bessel functions. 1966 edition.
Further Mathematics for the Physical Sciences Further Mathematics for the Physical Sciences aims to build upon the reader's knowledge of basic mathematical methods, through a gradual progression to more advanced methods and techniques. Carefully structured as a series of self-paced and self-contained chapters, this text covers the essential and most important techniques needed by physical science students. Starting with complex numbers, the text then moves on to cover vector algebra, determinants, matrices, differentiation, integration, differential equations and finally vector calculus, all within an applied environment. The reader is guided through these different techniques with the help of numerous worked examples, applications, problems, figures and summaries. The authors aim to provide high-quality and thoroughly class-tested material to meet the changing needs of science students. Further Mathematics for the Physical Sciences: * Is a carefully structured text, with self-contained chapters. * Gradually introduces mathematical techniques within an applied environment. * Includes many worked examples, applications, problems and summaries in each chapter. Further Mathematics for the Physical Sciences will be invaluable to all students of physics, chemistry and engineering, needing to develop or refresh their knowledge of basic mathematics. The book's structure will make it equally valuable for course use, home study or distance learning.