# Differential Equations - Math 23 (section 1)

Welcome to the Differential Equations Course webpage. This course is designed to provide an introduction to the theory and applications of differential equations.

## Homework Assignments

Problem Set Due Date Solution
HW1 April 4, 7pm HW1-S
HW2 April 11, 7pm HW2-S
HW3 April 18, 7pm HW3-S
HW4 April 25, 7pm HW4-S
HW5 May 2, 7pm HW5-S
HW6 May 9, 7pm HW6-S
HW7 May 17, 7pm HW7-S
HW8 May 24, 7pm

#### Homework Submission

Submit written homework by putting it in the homework boxes in the basement of Kemeny Hall (outside of the room 008), look for a box with label 'Math 23 HW'. Written homework will be graded on both the correctness of your solutions and the completeness, correctness, and clarity of your work and explanations. Explaining your work both demonstrates your understanding and helps your learning. Try to write so that another student in the class, who does not understand the material as well as you do and has not yet thought about this homework problem, would be easily able to understand your reasoning.

#### Class Acitvity Submission

Upload the week class activity as pdf or jpg file in the 'Assignment' section of Canvas.

## Visualizations

• Homework assignments: 20
• Class Activity: 10
• Midterm One: 20
• Midterm Two: 20
• Final Exam: 30

### Notes

Lecture Notes V4 - May 30 (incomplete)
Practice - Midterm 1 (solution)
Practice - Midterm 2 (solution)
Practice - Final Exam (solution)
More Practice - Final Exam

## Schedule

Week 1:
- introduction (1.1,1.2)
- classification (1.3)
- direction fields
- linear first order equations (2.1)
- integration factors (2.1)
Week 2:
- linear vs. non-linear ODEs (2.4)
- model building (2.3)
- separable equations (2.2)
- autonomous equations and population dynamics (2.5)
- Assignments: HW1 due
Week 3:
- second order constant coefficients equations; Wronskian (3.1,3.2)
- characteristic equation and complex roots (3.3)
- repeated roots and order reductions (3.4)
- Midterm 1, Friday April 14 (in class)
- Assignments:  HW2 Due
Week 4:
- method of undetermined coefficients and VoP (3.5,3.6)
- review of matrices (7.1,7.2)
- vibrations (3.7)
- Assignments: HW3 due
Week 5:
- systems of ODEs, existence uniqueness and solutions of of systems (7.3,7.4)
- constant coefficients (7.5,7.6)
- Assignments: HW4 due
Week 6:
- fundamental matrices (7.7)
- repeated eigenvalues (7.8)
- phase place (9.1)
- Midterm 2, Friday Mat 5 (in class)
- Assignments: , HW5 Due
Week 7:
- non homogenous linear systems (7.9)
- autonomous systems and stability (9.2)
- Assignments: HW6 Due
Week 8:
- competing species predator prey (9.4,9.5)
- Laplace transform and IVP (6.1,6.2)
- Assignments: HW8 Due
Final Exam: Friday, June 2, 2023 8:00 AM Kemeny Hall 6

## Accessibility Needs

Students with disabilities who may need disability-related academic adjustments and services for this course are encouraged to see me privately as early in the term as possible. Students requiring disability- related academic adjustments and services must consult the Student Accessibility Services office (Carson Hall, Suite 125, 646-9900). Once SAS has authorized services, students must show the originally signed SAS Services and Consent Form and/or a letter on SAS letterhead to me. As a first step, if students have questions about whether they qualify to receive academic adjustments and services, they should contact the SAS office. All inquiries and discussions will remain confidential.