Mathematical Methods in Physics: Partial Differential Equations, Fourier Series, and Special Functions
This book is a text on partial differential equations (PDEs) of mathematical physics and boundary value problems, trigonometric Fourier series, and special functions. This is the core content of many courses in the fields of engineering, physics, mathematics, and applied mathematics. The accompanying software provides a laboratory environment that allows the user to generate and model different physical situations and learn by experimentation. From this standpoint, the book along with the software can also be used as a reference book on PDEs, Fourier series and special functions for students and professionals alike.
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apply assume Bessel functions boundary conditions boundary value problem coefﬁcients conduction consider const constant continuous converges coordinates corresponding cylinder deﬁned depend derivative described differential direction Dirichlet discussion edge eigenfunctions eigenvalues elastically energy equal Equation Example expansion expression external ﬁeld Figure Find ﬁrst ﬁxed force formula Fourier series function f given given by Equation gives graph harmonic heat homogeneous inﬁnite initial conditions initial temperature inside integral interval Laplace’s medium membrane method nonhomogeneous obtain orthogonal oscillations parameters partial sum particular periodic physical plate polynomials positive potential present Reading Exercise relation represents respectively result roots satisﬁes satisfy shown shows side solution solve speed string Sturm-Liouville Substituting surface temperature temperature distribution tion variables vector wave zero