Methods of Mathematical Physics: Partial Differential Equations, Volume 2
Since the first volume of this work came out in Germany in 1937, this book, together with its first volume, has remained standard in the field. Courant and Hilbert's treatment restores the historically deep connections between physical intuition and mathematical development, providing the reader with a unified approach to mathematical physics. The present volume represents Richard Courant's final revision of 1961.
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Example Special Linear Systems with Constant Coefficients
mental Solution of the Heat Equation Poissons Integral
115 other sections not shown
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Methods of Mathematical Physics: Partial Differential Equations
Richard Courant,David Hilbert
Limited preview - 2008
according analytic apply arbitrary assume assumption boundary value problem bounded called Chapter characteristic characteristic curves coefficients complete condition cone consider const constant construct contains converges corresponding curves defined definition denote depend derivatives determined direction discontinuities domain easily elliptic equivalent example exists expression fact fixed formula function given hence holds homogeneous hyperbolic identically immediately independent variables initial value problem integral integral surface interior introduce leads limit linear manifold mean value theorem means method normal obtain operator origin parameter partial differential equation particular plane positive potential prescribed proof prove quantities quasi-linear region regular relation represents respect result satisfies second order single singular solution solved space sphere strip sufficiently tangent theorem theory tion transformation uniquely vanishes vector wave yields zero