Meeting time: Tue, Thur., 9:30 am- 10:45 am
Location: Olsen 109
Time: Tue 2:00pm-3:30pm, Wed 9:30am-11:00am
or by appointment (minhyung_cho@uml.edu)
Many physical systems can be described mathematically by one or more differential equations. Examples include mechanical oscillators, electrical circuits, and chemical reactions, to name just three. In this course you will learn what a differential equation is, and you will learn techniques for solving some common types of equations. You will also learn techniques for obtaining information about the solutions of equations which cannot be solved analytically. Finally, you will learn how differential equations can be used to describe physical phenomena, and you will use your knowledge of differential equations to analyze these phenomena. These skills will be useful to you in your other science and engineering courses and in your career.
Main textbook: Class handout (lecture notes)
Optional: Boyce, DiPrima, Meade, Elementary Differential Equations and Boundary Value Problems, 11th edition, Wiley
Homework will be assigned every Thursday and due on following Thursday at 9:29 AM. HW must be either hand-written or typed up (Latex or Word) and show all of your work (writing a list of answers is not sufficient). Please staple HWs. You are encouraged to collaborate with classmates, but your final write-up must reflect your understanding and you must acknowledge collaborators. 1 or 2 random problems will be graded. Homework solutions will be posted. No late homework will be accepted.
There will be two in-class midterms and one cumulative final exam.
Midterm I: 2/19
Midterm II: 3/31
Final : TBA
The Centers for Learning and Academic Support Services (CLASS) provide tutoring services, including an online searchable tutoring schedules are available that include resources on all campuses. A tutoring request form is also available if there are no tutors listed for the class for which you need help.
Mathematics Department tutoring Center: Southwick 310, Mon-Fri 10:00 am-5:00 pm
Academic dishonesty is prohibited in all programs of the University and sanctions may be imposed on any student who commits an act of academic dishonesty. Details on UML policy can be found at
http://www.uml.edu/Catalog/Undergraduate/Policies/Academic-Integrity.aspx. Note in particular that any incident which results in some action being taken must be reported to the Provost’s Office.
Generative AI tools, such as chatbots, image generators, or code generators, to complete assignments, exams, or any other academic work are not allowed
Using any online tutoring services during exams will result in an academic dishonesty report to the Provost office with FX grade (F with a permanent record) recommendation
Student-athletes must adhere to the Athletic Academic Policy.
If you are registered with Disability Services and will require course accommodations, please notify me via the Accommodate semester request process as soon as possible so that we might make appropriate arrangements. It is important that we connect to discuss the logistics of your accommodations; please speak to me during office hours or privately after class as I respect and want to protect your privacy. If you need further information or need to register for academic accommodations, please visit the Disability Services Website.
Additionally, Student Disability Services supports software for ALL students (not just those registered with their office). The university has literacy software that allows you to read on-screen text aloud, research and check written work, and create study guides. You can download the software from the IT Software webpage on the UML assistive technologies website.
Your personal health and well-being are important to all of us at the university. I’m available to talk about your stresses or concerns related to your coursework in my class.
Here are some resources to support your well-being:
Counseling Services provide crisis intervention, assessment, referrals, short term individual counseling and group therapy. Call to book an appointment at (978) 934-6800.
UMatter2 is a university-wide initiative to support students and promote mental health. They can be reached at (978) 934-6671. You will find information at that website on how to access Togetherall, an online community which is a peer-to-peer platform dedicated to mental health support.
Centers for Learning and Academic Support Services (CLASS) provides advising services including goal setting, course selection, SIS functions, changing majors/minors and course deletions. (978) 934-2936 or Advisement@uml.edu.
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The Office of Multicultural Affairs (OMA) supports and advocates for students while leading diversity-related programming. At the same time working to create an inclusive environment for LGBTQ+ individuals via the LGBTQ+ Resource Center. Contact (978) 934-4336 or Multicultural_Affairs@uml.edu
UMass Lowell recognizes the importance of mutual trust between students and faculty. Neither faculty nor students may record video or audio of a course or private conversation without all parties’ consent. Massachusetts is a two-party consent state, which means it is illegal to record someone without their permission. Recordings of classroom lectures are the intellectual property of the instructor. Instructors have the right to prohibit audio and video recording of their lectures, unless the requesting student is registered with Disabilities Services and recording of class sessions is an approved accommodation. In addition, sharing of or selling recordings of classroom activity, discussions or lectures with any other person or medium without permission of the instructor is prohibited.
| Date | Topic | Homework |
|---|---|---|
| 1/20 (Tue) | 1. Introduction | |
| 1/22 (Thur) | 1. Introduction 2. First order Differential Equations: 2.1. Integrating factor 2.2. Separation |
HW 1 (Due 1/29 Thur), HW 1 solution |
| 1/27 (Tue) | Snow Day | |
| 1/29 (Thur) | 2. First order Differential Equations: 2.1. Integrating factor 2.2. Separation |
HW 2 (Due 2/5 Thur) |
| 2/3 (Tue) | 2. First order Differential Equations: 2.4. Modeling with 1st order Eqs. 2.5. Autonomous Eqs and Population Dynamics |
|
| 2/5 (Thur) |
2. First order Differential Equations: 2.5. Autonomous Eqs and Population Dynamics 2.6. Existence and Uniqueness |
|
| 2/10 (Tue) |
2. First order Differential Equations: 2.6. Existence and Uniqueness 2.7. Euler's method |
|
| 2/12 (Thur) | 2. First order Differential Equations: 2.7. Euler's method with MATLAB Review |
|
| 2/19 (Thur) | Exam 1 | |
| 2/24 (Tue) | 3. Second order Differential Equations: 3.1. Homogeneous Eqs with Constant Coefficients |
|
| 2/26 (Thur) |
3. Second order Differential Equations: 3.1. Homogeneous Eqs with Constant Coefficients |
|
| 3/3 (Tue) | 3. Second order Differential Equations: 3.1. Homogeneous Eqs with Constant Coefficients - real distinct roots 3.2. Wronskian |
|
| 3/5 (Thur) |
3. Second order Differential Equations: 3.2. Wronskian 3.3. Complex Roots 3.4. Repeated Roots |
|
| 3/17 (Tue) | 3. Second order Differential Equations: 3.4. Repeated Roots |
|
| 3/19 (Thur) | 3. Second order Differential Equations: 3.5. Method of Undertermined Coefficients |
|
| 3/24 (Tue) |
3. Second order Differential Equations: 3.5. Method of Undertermined Coefficients 3.6. Mechinical vibrations | |
| 3/26 (Thur) |
3. Second order Differential Equations: 3.6. Mechanical vibrations 3.7. Forced vibrations |
|
| 3/31 (Tue) | Exam 2 | |
| 4/2 (Thur) |
4. Series Solutions of 2nd order linear equations 4.1. Review of power series |
|
| 4/7 (Tue) |
4. Series Solutions of 2nd order linear equations 4.1. Review of power series 4.2. Power series solutions |
|
| 4/9 (Thur) |
4. Series Solutions of 2nd order linear equations 4.2. Power series solutions |
|
| 4/14 (Tue) |
5. The Laplace Transform 5.1 Definition of the Laplace transform |
|
| 4/16 (Thur) | 5. The Laplace Transform 5.1 Definition of the Laplace transform |
|
| 4/21 (Tue) | 5. The Laplace Transform 5.2 Solutions of initial value problems |
|
| 4/23 (Thur) | 5. The Laplace Transform 5.2 Solutions of initial value problems |
|
| 4/28 (Tue) |
6. Partial Differential Equations and Fourier Series 6.1 Two-point boundary value problems |
|
| 4/30 (Thur) |
6. Partial Differential Equations and Fourier Series 6.1 Two-point boundary value problems 6.2 Fourier Series |
|
| TBA | Final Exam (Time and Location: TBA) |