The exam will be cumulative, covering all of the material from the first three exams, as well as the new material listed below. A few topics are not covered on the final exam. These omitted topics are listed below, as well.

Final Exam Topics

• All material from the first three exams, found at Midterm I Topics, Midterm II Topics, nad Midterm III Topics
• Material from Section 10.4
  • Convolution
  • The Convolution Theorem (products of Laplace transforms)
  • Using the Convolution Theorem to find Laplace transforms and inverse Laplace transforms
• Material from Section 10.5
  • The unit step function
  • Representing a discontinuous function using unit step functions
  • Using the theorem for translation on the t-axis to find Laplace transforms of piecewise continuous functions
  • Using the theorem for translation on the t-axis to find inverse Laplace transforms.
• The exam will not cover the following:
  • Exact first order differential equations - part of Section 1.6
  • Differential equations of order higher than two - part of Ch. 2
  • Solving systems of differential equations using the Laplace transform - Section 10.2