What sets this volume apart from other mathematics texts is 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. This expanded second edition contains a new appendix on the calculus of variation -- a valuable addition to the already superb collection of topics on offer.
This is an ideal text for upper-level undergraduates in physics, applied physics, physical chemistry, biophysics, and all areas of engineering. It allows physics professors to prepare students for a wide range of employment in science and engineering and makes an excellent reference for scientists and engineers in industry. Worked out examples appear throughout the book and exercises follow every chapter. Solutions to the odd-numbered exercises are available for lecturers at www.wiley-vch.de/textbooks/.Content:
Chapter 1 A Review of Vector and Matrix Algebra Using Subscript/Summation Conventions (pages 1โ17):
Chapter 2 Differential and Integral Operations on Vector and Scalar Fields (pages 18โ43):
Chapter 3 Curvilinear Coordinate Systems (pages 44โ66):
Chapter 4 Introduction to Tensors (pages 67โ99):
Chapter 5 The Dirac ??Function (pages 100โ134):
Chapter 6 Introduction to Complex Variables (pages 135โ218):
Chapter 7 Fourier Series (pages 219โ249):
Chapter 8 Fourier Transforms (pages 250โ302):
Chapter 9 Laplace Transforms (pages 303โ338):
Chapter 10 Differential Equations (pages 339โ423):
Chapter 11 Solutions to Laplace's Equation (pages 424โ490):
Chapter 12 Integral Equations (pages 491โ508):
Chapter 13 Advanced Topics in Complex Analysis (pages 509โ561):
Chapter 14 Tensors in Non?Orthogonal Coordinate Systems (pages 562โ596):
Chapter 15 Introduction to Group Theory (pages 597โ638):