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Description
This book is the result of a sequence of two courses given in the School of Applied and Engineering Physics at Cornell University. The intent of these courses has been to cover a number of intermediate and advanced topics in applied mathematics that are needed by science and engineering majors. The courses were originally designed for junior level undergraduates enrolled in Applied Physics, but over the years they have attracted students from the other engineering departments, as well as physics, chemistry, astronomy and biophysics students. Course enrollment has also expanded to include freshman and sophomores with advanced placement and graduate students whose math background has needed some reinforcement.While teaching this course, we discovered a gap in the available textbooks we felt appropriate for Applied Physics undergraduates. There are many good introductory calculus books. One such example is Calculus andAnalytic Geometry by Thomas and Finney, which we consider to be a prerequisite for our book. There are also many good textbooks covering advanced topics in mathematical physics such as Mathematical Methods for Physicists by Arfken. Unfortunately, these advanced books are generally aimed at graduate students and do not work well for junior level undergraduates. It appeared that there was no intermediate book which could help the typical student make the transition between these two levels. Our goal was to create a book to fill this need.
Content:-
1. A Review of Vector and Matrix Algebra Using Subscript/Summation Conventions
2. Differential and Integral Operations on Vector and Scalar Fields
3. Curvilinear Coordinate Systems
4. Introduction to Tensors
5. The Dirac &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 Led-Cidta Identity
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 Variations
Errata List
Bibliography
Index
Author Details
"Bruce R. Kusse"
and
"Erik A. Westwig"
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