MATH 351, Review for Midterm 2

Test topics

1. Linear equations of second order: examples with damped mass-spring system and electrical circuits (1.3.6, Example 1.14, pp.24-25)
2. Initial-value problem, existence/uniqueness; superposition principle, general solution, linear independence and the Wronskian (lecture notes, or Sections 3.2, 3.3, also Boyce-DiPrima, Theorem 3.3.2)
3. Homogeneous linear equations with constant coefficients (3.2)
4. Inhomogeneous linear equations with constant coefficients. Method of undetermined coefficients (3.3)
5. Method of variation of parameters (3.4.4)
6. Cauchy-Euler equations (3.4.1)
7. Power series solutions (3.4.2)
8. Reduction of order (3.4.3)
9. Boundary-value problems (Examples 3.22, 3.23 in 3.5)
10. Higher-order equations (3.6)

Practice problems: see the list after Assignments 4, 5 and 6.