Mathematical Models of Physics Problems

Luis Alfredo Anchordoqui and Thomas Cantzon Paul
Department of Physics, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

Series: Physics Research and Technology, Mathematics Research Developments
BISAC: SCI040000

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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Details

This textbook is intended to provide a foundation for a one-semester introductory course on the advanced mathematical methods that form the cornerstones of the hard sciences and engineering. The work is suitable for first year graduate or advanced undergraduate students in the fields of Physics, Astronomy and Engineering.

While none of the subject matter was originally developed by the authors, the organization and presentation are unique and condensed. The rationale for this approach derives from the realization that as research-intensive fields rapidly increase our knowledge base, the time available to linger on any given topic inevitably shrinks. This text therefore employs a condensed narrative sufficient to prepare graduate and advanced undergraduate students for the level of mathematics expected in more advanced graduate physics courses, without too much exposition on related, but non-essential material. In contrast to the two semesters traditionally devoted to mathematical methods for physicists, the material in this book has been quite distilled, making it a suitable guide for a one-semester course. The assumption is that the student, once versed in the fundamentals, can master more esoteric aspects of these topics on his or her own if and when the need arises during the course of conducting research.

The book focuses on two core subjects: complex analysis and classical techniques for the solution of ordinary and partial differential equations. These topics are complemented with occasional terse reviews of other material, including linear algebra, to the extent required to ensure the book can be followed from end-to-end.

This textbook is designed to provide a framework for a roughly 12 week course, with 3 weeks devoted to complex variables, a 1 week refresher on linear algebra, followed by 5 and 3 weeks devoted to ordinary and partial differential equations, respectively. This schedule leaves time for a couple of exams. The narrative is complemented with ample problem sets, including detailed guides to solving the problems. (Imprint: Nova)

Preface

Chapter 1. Complex Analysis

Chapter 2. Elements of Linear Algebra

Chapter 3. Ordinary Differential Equations

Chapter 4. Partial Differential Equations

Appendices

Answers and Comments on the Exercises

References

Index

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