Math 274 - Final Exam - F 2018
Wednesday 12 Dec 2018, 2:00-3:50
The following information will be given.
You are responsible for all prerequisite information, this is a partial list.
The exam is written to take about 55 minutes. You will have 110 minutes to complete the exam.
The exam focuses on the material covered since Exam 3.
- Chapter 7 - Although there are no explicit questions covering the material from Chapter 7, the mechanics (matrix multiplication, computing determinants, etc.) and language (nullspace, singular matrix, etc.) has been used in Chapters 8 and 9.
- 8.1 - Know how to convert higher order equations to systems of first order equations.
- 8.2 - Understand the relationship between solutions x(t), y(t), and the phase plane solution x,y.
- 8.3 - Understand equilibrium points and nullclines in the phase plane. Be able to sketch nullclines with direction arrows. Be able to sketch solution curves based on nullcline information.
- 8.4 - Understand how to set up a two interconnected tank mixing problem.
- 8.5 - Understand Linear Dependence/Independence, the Wronskian, and the meaning of a Fundamental Solution Set.
- 9.1, 9.2 - Be able to find general solutions to homogeneous planar systems. Be able to find solutions to initial value problems.
- 9.3, 9.4, 9.7 - Be able to classify equilibria behavior based on eigenvalues, trace, and determinant. Be able to sketch and interpret half-line solutions. Be able to classify equilibria as stable or unstable.
- 10.1 - Be able to combine the Chapter 8 ideas of nullclines and equilibria with Chapter 9 ideas of classification of equilibria via linearization using the Jacobian.
There may, or may not, be questions involving some of the major concepts from the semester.
- What does it mean for a function to be a solution to a differential equation?
- How do we solve a first order separable equation (Section 2.2)?
- How do we classify harmonic motion (Section 4.4)?