If you’re looking for a comprehensive guide to bridge the gap between introductory calculus and advanced mathematical physics, Mathematical Physics by Bruce R. Kusse and Erik A. Westwig is the perfect resource. Published by WILEY-VCH, this textbook is a result of a sequence of courses offered at Cornell University, specifically designed to cover intermediate and advanced topics in applied mathematics necessary for science and engineering students. Whether you are an undergraduate or a graduate student, this book will equip you with the essential mathematical tools needed to solve complex physical problems.
Why This Book is Essential for Science and Engineering Students
The authors, Bruce R. Kusse and Erik A. Westwig, created this book to address the lack of intermediate-level textbooks that could serve as a transition from basic calculus to advanced mathematical methods. Originally intended for junior undergraduates in Applied Physics at Cornell University, Mathematical Physics has gained popularity among students from various engineering disciplines, as well as those studying physics, chemistry, astronomy, and biophysics. Its pedagogical approach, combined with a focus on practical applications, makes it a valuable resource for anyone needing to reinforce their mathematical foundation.
Topics Covered in the Book
This book covers a wide range of topics, starting from intermediate concepts and gradually progressing to more advanced subjects. The material is presented in a clear and approachable manner, with an emphasis on applications that are directly relevant to solving real-world physical problems. The topics covered include:
- Linear Algebra and Tensors: Introduction to matrices, determinants, eigenvalues, and tensors with applications to physics.
- Curvilinear Coordinate Systems: Understanding different coordinate systems and their importance in solving physical problems.
- Complex Variables: Exploration of complex numbers, functions, and their applications in engineering and physics.
- Fourier Series and Transforms: Study of Fourier series, Fourier transforms, and their use in signal processing and heat conduction problems.
- Laplace Transforms: Application of Laplace transforms in solving differential equations and modeling dynamic systems.
- Differential Equations: Techniques for solving ordinary and partial differential equations commonly encountered in physics.
- Dirac Delta-Functions and Solutions to Laplace’s Equation: Introduction to special functions and their role in electrostatics and other fields.
- Advanced Topics: Including contravariance and covariance in nonorthogonal systems, branch cuts, Riemann sheets, the method of steepest descent, and group theory.
Each chapter is rich with illustrations, examples, and exercises, making complex topics more accessible. The book’s structure, based on how the material was taught in Cornell’s AEP 321/322 courses, ensures a logical progression of concepts, from fundamental to advanced levels.
Benefits of Studying This Book
By studying Mathematical Physics, you will:
- Gain a solid understanding of both intermediate and advanced topics in applied mathematics.
- Develop the mathematical tools necessary to tackle complex physical and engineering problems.
- Benefit from a teaching-oriented approach that prioritizes clarity and application over formal proofs.
- Prepare yourself for more advanced studies in physics, engineering, and related fields.
- Use this book as both a teaching tool and a reference guide for future studies.
This book is an invaluable resource for students looking to excel in the applied sciences and engineering fields. Its emphasis on practical application ensures that you will be well-equipped to handle the mathematical challenges that come with solving real-world problems.