The midterm is on Wednesday, December 2, 2009 in the regular classroom during the regular class time. The exam is closed-note and closed-book, and no calculators are allowed. Make sure to bring your student ID to the exam.

Midterm III Topics

• Introduction to Eigenvalues - Section 6.1
  • Finding the eigenvalues and corresponding eigenvectors for a square matrix
  • Eigenspaces and how to find a basis for the eigenspace of an eigenvalue
• Systems of Differential Equations - Chapter 7
  • Writing an n^th order equation as a system of first order equations - Sections 7.1-7.2
  • Determining if a set of solutions is linearly independent and forms a basis for the solution space (and then finding the general solution) - Sections 7.1-7.2
  • The eigenvalue method for linear systems - Sections 7.3 and 7.5
  • Finding the general solution and solving initial value problems for:
    • The case of distinct eigenvalues - Section 7.3
    • The case of complex conjugate eigenvalues - Section 7.3
    • The case of multiple eigenvalues - Section 7.5
      • algebraic multiplicity
      • geometric multiplicity
      • Finding a solution when algebraic multiplicity = geometric multiplicity
      • Finding a solution when algebraic multiplicity > geometric multiplicity
• Laplace Transforms - Chapter 10
  • Definition of the Laplace transform - Section 10.1
  • The inverse Laplace transform - Section 10.1
  • The Laplace transforms of the functions given in the table in lecture (a portion of the table in Figure 10.1.2 in Section 10.1)
  • Properties of the Laplace transform
    • Linearity - Section 10.1
    • Laplace transform of derivatives - Section 10.2
  • Using the above properties to determine the Laplace transform of a given function or to determine a function given its Laplace transform (i.e., find the inverse Laplace transform) - Sections 10.1-10.2
  • Using Laplace transform to solve initial value problems - Sections 10.2-10.3
  • Partial fractions and their use in determining inverse Laplace transforms - class notes and Section 10.3
  • Translation in the s-axis - Section 10.3