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Mathematical Physics
B. Kusse

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The second, corrected edition of this well-established mathematical text again puts its emphasis on mathematical tools commonly used by scientists and engineers to solve real-world problems. Using a unique approach, it covers intermediate and advanced material in a manner appropriate for undergraduate students. Based on author Bruce Kusse's course at the Department of Applied and Engineering Physics at Cornell University, Mathematical Physics begins with essentials such as vector and tensor algebra, curvilinear coordinate systems, complex variables, Fourier series, Fourier and Laplace transforms, differential and integral equations, and solutions to Laplace's equations. The book moves on to explain complex topics that often fall through the cracks in undergraduate programs, including the Dirac delta-function, multivalued complex functions using branch cuts, branch points and Riemann sheets, contravariant and covariant tensors, and an introduction to group theory. The book covers applications in all areas of engineering and the physical science, and features numerous figures and worked-out examples throughout the text. Many end-of-chapter exercises are provides; a free solution manual is available for lecturers. The topics are organized pedagogically, in the order they will be most easily understood. From the contents: A review of Vector and Matrix Algebra Using Subscript/Summation Conventions Differential and Integral Operations on Vector and Scalar Fields Curvilinear Coordinate Systems Tensors in Orthogonal and Skewed Systems The Dirac Function Complex Variables Fourier Series Fourier and Laplace Transforms Differential Equations Solutions to Laplace's Equation Integral Equations