Estimating Eigenvalues With A Posteriori/a Priori Inequalities (research Notes In Mathematics)

This Research Note Presents A Method For The Numerical Estimation Of Eigenvalues Which Is Easy To Understand, Practical To Implement And Effective In Its Results. It Is Developed With Complete Details Of How To Calculate Eigenvalues Associated With Vibrating Membranes And Plates, Waveguides, Sloshing Fluids And Stekloff Problems; However, This Flexible Technique Can Be Applied To A Variety Of Eigenvalue Problems. The Text Is Illustrated By A Number Of Simple Examples, Many Of Which Are Worked Out In Full. By Discussing Both Theoretical And Computational Aspects, This Book Is Of Use To Electrical And Mechanical Engineers As Well As Applied Mathematicians. Introduction -- A Posteriori And A Priori Inequalities -- Applying The Method Of A Posteriori-a Priori Inequalities -- Membrane Problems -- Eigenvalues In The Boundary Conditions -- Plate Problems -- Appendix A: 1. Lower Bounds For Dirichlet Eigenvalues -- 2. Some Formulas For Legendre Polynomials -- 3. Lower Bounds For The Neumann Eigenvalues -- 4. Bounds For The Sloshing Problem -- 5. The A Priori Inequality For The Clamped Plate -- 6. The A Priori Inequality For Orthotropic Plates -- 7. The A Priori Inequality For The Variable Thickness Plate -- 8. A Priori Inequalities For Cantilever Plates And Elastic Organ Pipes. J.r. Kuttler & V.g. Sigillito. Includes Index. Bibliography: P. 144-149.