Mathematical Physics. Applied Mathematics for Scientists and Engineers. 2nd Edition

  • ID: 2180240
  • Book
  • 689 Pages
  • John Wiley and Sons Ltd
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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
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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 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

A. The Levi–Civita Identitiy

B. The Curvilinear Curl

C. The Double Integral Identity

D. Green′s Function Solutions

E. Pseudovectors and the Mirror Test

F. Christoffel Symbols and Covariant Derivatives

NEW APPENDIX: The Calculus of Variation

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"Any lecturer on mathematical methods is also looking for worked examples and numerous exercises. This book passes these tests admirably. [...] In summary, a welcome addition to the good books in this area."

Australian PHYSICS

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