Topics Covered
Topics covered in Math 216 generally include the following:
- First Order Equations, including solution of linear and separable equations, qualitative analysis of autonomous first-order equations, stability of critical points of autonomous first-order equations, and the existence and uniqueness of solutions.
- Systems of Linear First Order Equations, including existence and uniqueness of solutions, conversion between higher-order linear equations and systems, solution of constant-coefficient linear systems using linear algebra and eigenvalues, and analysis of the stability of critical points in the phase plane.
- Higher Order Linear Equations, including existence and uniqueness of solutions, solution of homogeneous and nonhomogeneous constant coefficient linear systems, including the method of undetermined coefficients and variation of parameters, oscillatory solutions and forced oscillations, gain and resonance.
- Use of Laplace Transforms to solve linear equations, including the definition of the transform, transform rules, and the use of the transform to solve linear constant-coefficient linear equations and systems with discontinuous and impulse forcing.
- Analysis of Nonlinear Autonomous Systems of First Order Equations by linearization at critical points, and qualitative analysis of phase space.
Sample Materials
The course materials for the course are determined by the course coordinator, and therefore subject to change. They do seek to build students’ understanding of the course material, its connection to real-world applications, and fundamental skills that are intrinsic to the material. The following are samples of the work expected of students in recent semesters.
- Sample written homework: homework sample 1, sample 2.
- Sample lab: Prelab, Part A, Part B.
- Sample exams: sample 1, sample 2.
Of course, the work that is expected in the current semester will be different from these samples, and they should not be considered to be either indicative of the types of assignments that are in use in the current semester or a model for the questions that will appear in assessments there.
