Homework problems contain all the main types of possible exam questions. Here is a few review problems to make sure you haven't overlooked an important topic:Ĥ.Rev: 3, 4, 6, 7, 9, 11, 13, 22, 25, 26, 32 5.Rev: 2, 3, 5, 6, 11, 12, 17, 18 6.Rev: 3, 4, 7, 8, 15 (find the formula for the coefficients, and write out explicitly the first few terms) 19, 20. Indicial equation recurrence relations in Frobenius method.Solutions near regular singualr point: the Frobenius method.Singular points regular singular points.Recurrence relations obtaining a few first terms of the series, or finding a formula for the coefficients. ![]() Radius of convergence of a power series solution: distance to the closest singular point in the complex plane.Series solutions of differential equations analytic functions ordinary and singular points.Examples of buckling of a thin vertical column and a rotating string.Eigenvalue problem for a second-order equation with different types of boundary conditions: eigenvalues and eigenfunctions.Fourth-oder linear model of beams different types of boundary conditions.Steady state and transient solutions resonance.Overdamped, underdamped, critically damped cases, depending on the roors of the auxiliary equation.Modeling: mass/spring systems, with damping and external forces.Nonlinear equations substitution u=y' applied to 2 cases of nonlinear equations.3 Different cases of solutions of Cauchy-Euler, depending on the roots of the auxiliary equation.Cauchy-Euler differential equations form of auxiliary equations for the Cauchy-Euler equations.Variation of parameters: the method and the determinant formulas for the solutions.Determinants for 2X2 and 3X3 matrices determinant expansion along a row or column.Method of undetermined coefficients (superposition approach).3 Different cases of homogeneous solutions, depending on the roots of the auxiliary equation. ![]()
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