**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:**Wednesday, January 30th, in class.**Midterm 2:**Wednesday, February 20th, in class.**Final:**Monday, March 18th, 11:30am-2:30pm.

**Midterm 1:** will cover the material presented in
the first 9 lectures; see the table below. You can find a practice midterm
here.

- If you are enrolled in discussion sections A, B, C, or D, you will take the exam in HUMANTS A51.
- If you are enrolled in discussion sections E or F, you will take the exam in BOELTER 3400.
- Please go directly to the rooms you are assigned to.

**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.

- If you are enrolled in discussion sections A, B, C, or D, you will take the exam in HUMANTS A51.
- If you are enrolled in discussion sections E or F, you will take the exam in BOELTER 3400.
- Please go directly to the rooms you are assigned to.

**Final:** will cover all the material
presented this quarter. You can find a practice final here.

- If you are enrolled in discussion sections A, B, C, or D, you will take the exam in HUMANTS A51.
- If you are enrolled in discussion sections E or F, you will take the exam in PAB 1-425.
- Please go directly to the rooms you are assigned to.

**Homework:** There will be weekly homework. It is due *in class*. Further information is given below.

- No late homework will be accepted.
- The reader will grade three problems each out of five points.
- Up to five further points will be awarded based on the proportion of the remaining problems that are completed.
- Write your name, ID number, and TA section at the top of the first page.
- Staple your pages!
- Homework will be returned in TA section.
- The weakest homework score will be omitted.
- While you may collaborate on the homework, the final version needs to
be written in your own words. The loaning or copying of solutions is
**strictly forbidden**.

**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:**

- Homework 1 is due on Friday, January 11th, in class.
- Homework 2 is due on Friday, January 18th, in class.
- Homework 3 is due on Friday, January 25th, in class.
- Homework 4 is due on Friday, February 1st, in class.
- Homework 5 is due on Friday, February 8th, in class.
- Homework 6 is due on Friday, February 15th, in class.
- Homework 7 is due on Friday, February 22nd, in class.
- Homework 8 is due on Friday, March 1st, in class.
- Homework 9 is due on Friday, March 8th, in class.
- Homework 10 is due on Friday, March 15th, in class.