33B (Lect. 1), Differential Equations

Enrolment questions, PTE #, etc: See the math office in 6356 Math Sciences Building.

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.


Bring student ID to both midterms and the final.
No calculators, notes, or books will be permitted in any exam.
There will be no make-up 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:

Student Math Center

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: