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Math 2250 - 002 Midterm #2 Review Chapter 4: Determine whether a set of vectors is linearly independent or linearly dependent. Describe the span of a finite set of vectors Find the specific solution to a homogenous linear DE with constant coefficients given a set of initial conditions. Use the method of undetermined coefficients to find the particular solution of a non-homogenous linear DE with constant coefficients. Use variation of parameters to find the particular solution of a non-homogeneous linear DE with constant coefficients. Fine the complimentary solution of a nonhomogeneous linear DE with constant coefficients. Given a mass-spring-dashpot system, or a pendulum system, find the o general solution o period of motion o frequency of motion o amplitude of motion o whether the system is over-damped, under-damped, or critically damped. Given a mass-spring-dashpot system with external forcing, find the o natural frequency o forcing frequency o general solution o transient solution o stable periodic solution o amplitude of stable periodic solution Vector addition, subtraction, scalar multiplication. Fall 2011 11/10/11 Determine whether a set of vectors is a subspace o Closed under addition o Closed under scalar multiplication Determine whether or not a finite set of vectors is a basis. Determine the dimension of a vector space. Determine the solution space of a linear system. Determine whether two functions are linearly independent. Chapter 5: Given two linearly independent solutions to a second order homogeneous DE, and a set of initial conditions, find a solution that satisfies the initial conditions using the principle of super position. Calculate the Wronskian of a set of functions. Use this information to determine whether the functions are linearly dependent or independent. Chapter 10: Find the Laplace Transform of a basic functions. Find the general solution for a homogeneous linear DE with constant coefficients. o Distinct Roots o Duplicated Roots o Complex Roots Find the inverse Laplace Transform of basic functions Apply the Laplace Transform to an IVP. Math 2250 - 002 Midterm #2 Review Practice Problems: Note: I would suggest trying out at least one of each type of problem. If you need the additional practice then work through additional examples of the same problem type. Problem types are separated by commas. Section 4.1: 13 - 18, 19 - 24, 29 - 32, 33 - 37 Section 4.2: 1 - 14, 15 - 18 Section 4.3: 9 - 16, 17 - 22 Section 4.4: 1 - 8, 12 - 14, 15 - 26 Section 4.7: 13 - 18 Section 5.1: 1 - 16, 20 - 26 Section 5.2: 7 - 12, 13 - 20 Section 5.3: 1 - 20, 21 - 26, 27 - 32 Section 5.4: 1 - 4, 8, 13, 14, 15 - 21 Section 5.5: 1 - 20, 31 - 40, 44 - 46, 47 - 56 Section 5.6: 1 - 6, 7 - 10, 11 - 14, 15 - 18 Section 10.1: 1 - 6, 11 - 22, 23 - 32 Section 10.2: 1 - 16, 17 - 24 Fall 2011 11/10/11