Review of Principles Of Applied Mathematics: Transformation And Approximation by James P. Keener
If you are looking for a comprehensive and rigorous introduction to the classical methods of applied mathematics, you might want to check out Principles Of Applied Mathematics: Transformation And Approximation by James P. Keener. This book, which is available in mobi format for easy download, covers topics such as function spaces, integral equations, differential operators, calculus of variations, complex variable theory, transform and spectral theory, partial differential equations, inverse scattering transform, asymptotic expansions, and perturbation methods. The book is suitable for beginning graduate students in applied mathematics, science, and engineering, and can be used as a one-year course in applied mathematical techniques.
One of the strengths of this book is that it shows how two areas of classical applied mathematics - spectral theory of operators and asymptotic analysis - are useful for solving a wide range of applied science problems. The book also blends several new topics, such as wavelength analysis, multigrid methods, and homogenization theory, into the mix to illustrate the modern applications of these methods. The book is updated to reflect the developments of the last twenty years and includes extensive corrections by the author.
The book is well-written and organized, with clear explanations and examples. The exercises at the end of each chapter are challenging and helpful for reinforcing the concepts. The book also provides references to further reading and research for those who want to explore more. The book assumes some background in linear algebra, calculus, and ordinary differential equations, but does not require any prior knowledge of functional analysis or complex analysis.
Overall, Principles Of Applied Mathematics: Transformation And Approximation by James P. Keener is a valuable resource for anyone who wants to learn the foundations and applications of classical applied mathematics. The book is available in mobi format for easy download from here or here.
Applied mathematics is not just a collection of techniques, but also a way of thinking and reasoning about problems that arise in various domains. Applied mathematicians use mathematical models to describe and analyze phenomena, and to make predictions and recommendations. They also develop new methods and tools to solve challenging problems that require mathematical insight and creativity.
Some examples of the applications of applied mathematics are:
Fluid mechanics: the study of fluids (liquids and gases) and their interactions with forces and boundaries. Fluid mechanics is important for understanding phenomena such as weather, ocean currents, blood flow, aerodynamics, and lubrication.
Cryptography: the science of secure communication using codes and ciphers. Cryptography is essential for protecting information and privacy in the digital age, as well as for ensuring the integrity and authenticity of data.
Numerical analysis: the study of algorithms and methods for approximating solutions of mathematical problems using computers. Numerical analysis is crucial for solving problems that are too complex or too large to be solved analytically or exactly.
Optimization: the study of finding the best or most efficient solution to a problem under given constraints. Optimization is widely used in engineering, economics, management, and science for designing systems, allocating resources, scheduling tasks, and making decisions.
These are just a few examples of the many areas where applied mathematics plays a vital role. Applied mathematics is an exciting and dynamic field that offers many opportunities for research, innovation, and collaboration. a474f39169