chapter Profilogue -- chapter 1 Introduction: Review of Direct, Semi-inverse and Inverse Eigenvalue Problems -- chapter 2 Unusual Closed-Form Solutions in Column Buckling -- chapter 3 Unusual Closed-Form Solutions for Rod Vibrations -- chapter 4 Unusual Closed-Form Solutions for Beam Vibrations -- chapter 5 Beams and Columns with Higher-Order Polynomial Eigenfunctions -- chapter 6 Influence of Boundary Conditions on Eigenvalues -- chapter 7 Boundary Conditions Involving Guided Ends -- chapter 8 Vibration of Beams in the Presence of an Axial Load -- chapter 9 Unexpected Results for a Beam on an Elastic Foundation or with Elastic Support -- chapter 10 Non-Polynomial Expressions for the Beam’s Flexural Rigidity for Buckling or Vibration -- chapter 11 Circular Plates.