Textbook: Differential Equations (second edition) by John
Polking, Albert Boggess, and David Arnold.
I find that A First Course In Differential Equations with
Applications (fourth edition) by Dennis G. Zill is a good source of
additional exercises.
Instructor: Monica Visan, 6167 Math Sciences Building.
Office Hours: Tu: 1:00-2:00pm and Wed: 2:30-3:30pm, or by appointment.
Exams:
Midterm 1: will cover the material presented in the first 9 lectures; see the table below. You can find a practice midterm here.
Midterm 2: will cover all the material presented up to that point, with emphasis on lectures 10 through 16; see the table below. You can find a practice midterm here.
Final: will cover all the material presented this quarter. You can find a practice final here.
Homework: There will be weekly homework. It is due in class on Fridays. It will be posted on this webpage the weekend before it is due. Further information is given below.
Grading: Homework: 10%; Midterm 1: 20%; Midterm 2: 20%; Final: 50%. No exceptions.
Teaching Assistants:
Syllabus: The following table will be updated as we progress through the course.
Lecture | Sections | Topics |
1 | 2.1 | First Order Differential Equations, Solutions, Initial Value Problems, Examples |
2 | 2.1 | Direction Fields, Euler's Method |
3 | 2.2, 2.4 | Separable Equations, Linear Homogeneous Equations |
4 | 2.4 | Linear Inhomogeneous Equations, x'(t) = f(t) x(t) + g(t) |
5 | 2.5 | Mixing Problems |
6 | 2.6 | Exact Differential Equations |
7 | 2.6 | Exact Differential Equations and Integrating Factors |
8 | 2.7 | Existence and Uniqueness |
9 | 2.9 | Autonomous Equations and Stability |
10 | 4.1 | Second Order Linear Equations, Existence and Uniqueness, the Wronskian |
11 | 4.1 | Fundamental Set of Solutions, Linear Independence |
12 | 4.3 | Second Order Constant Coefficient Equations |
13 | 4.3 | Higher Order Constant Coefficient Equations |
14 | 4.5 | The Method of Undetermined Coefficients |
15 | 4.5 | Undetermined Coefficients and Annihilators |
16 | 4.6 | Variation of Parameters |
17 | 9.1 | Linear Systems with Constant Coefficients: Existence and Uniqueness, Structure of the Solution Set |
18 | 9.2 | Eigenvalues and Eigenvectors, Fundamental Set of Solutions |
19 | 9.2 | 2 x 2 Systems: Distinct Real and Complex Eigenvalues |
20 | 9.2 | 2 x 2 Systems: One Real Eigenvalue of Multiplicity 2 |
21 | 9.3 | Phase Plane Portraits |
22 | 9.3 | Phase Plane Portraits |
23 | 9.4 | The Trace-Determinant Plane |
24 | 9.5 | Higher-Dimensional Systems |
25 | 9.6 | The Exponential of a Matrix |
26 | 9.6 | Continuation |
Homework Problems: