Mathematics of Physics and EngineeringAimed at scientists and engineers, this book is an exciting intellectual journey through the mathematical worlds of Euclid, Newton, Maxwell, Einstein, and Schrodinger-Dirac.While similar books present the required mathematics in a piecemeal manner with tangential references to the relevant physics and engineering, this textbook serves the interdisciplinary needs of engineers, scientists and applied mathematicians by unifying the mathematics and physics into a single systematic body of knowledge but preserving the rigorous logical development of the mathematics.The authors take an unconventional approach by integrating the mathematics with its motivating physical phenomena and, conversely, by showing how the mathematical models predict new physical phenomena. |
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algebra approximation assume boundary conditions called cartesian coordinate system cartesian coordinates center of mass coefficients complex numbers components conclude consider constant continuously differentiable convergence coordinate system corresponding curl curve defined definition Denote density dipole domain G eigenvalues electric equal example EXERCISE finite force formula Fourier series Fourier transform function f gravitational heat equation Hint implies initial conditions inner product integral linear mathematical mathematician matrix Maxwell's equations motion operator ordinary differential equations orthogonal partial differential equations physical piece-wise smooth plane point mass polynomial position vector power series problem proof properties quantum computer radius real number relative result ro(t rotation satisfies scalar field Show singular solution space speed surface tensor Theorem tion unit vector variables vector field velocity Verify wave equation zero