Mathematical Physics: Applied Mathematics for Scientists and Engineers

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 ConventionsDifferential and Integral Operations on Vector and Scalar FieldsCurvilinear Coordinate SystemsTensors in Orthogonal and Skewed SystemsThe Dirac FunctionComplex VariablesFourier SeriesFourier and Laplace TransformsDifferential EquationsSolutions to Laplace′s EquationIntegral Equations

Spis treści:
1. A Review of Vector and Matrix Algebra Using Subscript/Summation Conventions.
2. Differential and Integral Operations on Vector and Scalar Field s.
3. Curvilinear Coordinate Systems.
4. Introduction to Tensors.
5. The Dirac Delta–Function.
6. Introduction to Complex Variables.
7. Fourier Series.
8. Fourier Transforms.
9. Laplace Transforms.
10. Differential Equations.
11. Solutions to Laplace′s Equation.
12. Integral Equations.
13. Advanced Topics in Complex Analysis.
14. Tensors in Non–Orthogonal Coordinate Systems.
15. Introduction to Group Theory.
Appendix A. The Levi–Civita Identitiy.
Appendix B. The Curvilinear Curl.
Appendix C. The Double Integral Identity.
Appendix D. Green′s Function Solutions.
Appendix E. Pseudovectors and the Mirror Test.
Appendix F. Christoffel Symbols and Covariant Derivatives.
Appendix G: Calculus of Variation.
Errata List.
Bibliography.
Index.


Nota biograficzna:
Bruce Kusse is Professor of Applied and Engineering Physics at Cornell University, where he has been teaching since 1970. He holds a PhD from the MIT in electrical engineering with a specialty in plasma physics.
Erik Westwig is a software engineer with Palisade Corporation, New Jersey. He holds an MS in applied physics from Cornell University.


Okładka tylna:
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 mo ves 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 ConventionsDifferential and Integral Operations on Vector and Scalar FieldsCurvilinear Coordinate SystemsTensors in Orthogonal and Skewed SystemsThe Dirac FunctionComplex VariablesFourier SeriesFourier and Laplace TransformsDifferential EquationsSolutions to Laplace′s EquationIntegral Equations