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MATH 225–01: Introduction to Differential Equations

Spring 2023 Course information

Textbook and course content

Textbook: Stanley J. Farlow, An Introduction to Differential Equations and their Applications, available at the UMBC Bookstore, Amazon, and elsewhere.

This excellent and very affordable paperback book is a black-and-white reproduction of the original 1994 color hardcover edition which is no longer in print. There has been only a single edition of this book, and as is a common occurrence with first editions, it suffers from more than the expected number of typos/errors. I maintain an errata website where readers from all over the country report errors that they spot in the book. If you spot an unreported error, be sure to let me know and I will add you to that website with due acknowledgment.

Beware! The electronic version of the book brings in a large number of additional errors due to poor optical scanning. Stay away from the e-book!

We will cover much of

Chapter 1:

Introduction to differential equations

Chapter 2:

First-order differential equations

Chapter 3:

Second-order differential equations

Chapter 5:

The Laplace transform

Chapter 6:

Systems of differential equations

Calculus II (Math 152) is a prerequisite. A knowledge of Multivariable Calculus (Math 251) and Linear Algebra (Math 221) will give you an edge but is not a prerequisite; I will fill in the missing details as needed.

Course Goals/Objectives

The subject of this is course is an introduction to ordinary differential equations and their applications. It's pretty much a natural continuation of calculus, so if you liked calculus, you will like this course. In this course you will learn:

• What differential equations are.
• How they arise in applications.
• Their classification into recognizable types, such as first order separable, or second order linear constant coefficient homogeneous, etc.
• Solution techniques for various types.
• Applications, applications, applications …

Weekly homework and quizzes

I will put homework assignments on this web page shortly after each class. I will not collect homework but I expect that you do your best to solve them all. There will be a 10-minute quiz at the beginning of the class every Wednesday (except for the first week of classes and the week of Exams 1 and 2). The quiz questions will be identical to, or slight variations of, some of the homework problems assigned on the Monday and Wednesday of the previous week. I will return the graded quizzes to you on the following Monday.

There won't be make-up quizzes; please don't ask for exceptions. However the two lowest quiz grades will be dropped to accommodate unanticipated events.

Exams and grading

Exams 1 and 2 will cover approximately the first third and second third of the course; they will be given in the regularly scheduled class times.

The Final Exam will be comprehensive—it will cover the entire course—however it will put much greater emphasis on the material toward the later parts of the course.

Your course grade will be calculated according to the weights attached to various components as shown in the adjacent table. Letter grades will be determined according to:

if { grade ≥ 85: A}
else if { grade ≥ 75: B}
else if { grade ≥ 65: C}
else if { grade ≥ 55: D}
else F

I will make and grade the exams in a fair and reasonable way, but sorry, no "curving" in this course.

Homework assignments

Tutoring available

Tutoring service is available for this course. Go to Math and Science Tutoring Center for more information.

Student Disability Services (SDS)

Services for students with disabilities are provided for all students qualified under the Americans with Disabilities Act of 1990, the ADAA of 2009, and Section 504 of the Rehabilitation Act who request and are eligible for accommodations. The Office of Student Disability Services is the UMBC department designated to coordinate accommodations that would allow for students to have equal access and inclusion in their courses.

UMBC Honors Code

By enrolling in this course, each student assumes the responsibilities of an active participant in UMBC's scholarly community in which everyone's academic work and behavior are held to the highest standards of honesty. Cheating, fabrication, plagiarism, and helping others to commit these acts are all forms of academic dishonesty, and they are wrong. Academic misconduct could result in disciplinary action that may include, but is not limited to, suspension or dismissal.

The PDF document UMBC Policy for Undergraduate Student Academic Conduct spells out the official academic integrity policies for undergraduates.