Lectures: MWF 9:00-9:50 in HUMANTS A51.
Textbook: Differential equations (second edition) by John Polking, Albert Boggess, and David Arnold.
Instructor: Monica Visan, 6167 Math Sciences Building.
Office Hours: Tu 1:30-2:30pm and Fri 1:30-2:30pm in 6167 Math Sciences Building.
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 so far, 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. 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: