Syllabus
MA 2051 - Differential Equations
D-Term, Spring 2023
Department of Mathematical Sciences
Worcester Polytechnic Institute
D-Term, Spring 2023
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Department of Mathematical Sciences
Worcester Polytechnic Institute
Office: SL 405D
Phone: (508) 831-6664
e-mail: tilley@wpi.edu
Tilley Home Page
Office Hours: T: 12:00-12:50pm, R: 3:00-4:50pm, or by appointment
PLAs:
Darcy Milligan - DD10. MTC: R: 5:00pm-6:00pm
Krish Patel - DD06. MTC: F: 12:00pm-1:00pm
Justin Shen - DD07. MTC: R: 4:00pm-5:00pm
Textbook: An Introduction to Differential Equations and Their Applications, by Stanley J. Farlow, Dover. ISBN: 04864495X. NOTE: Although a very readable book, it does have typos which have been catalogued at UMBC. Students should be able to get electronic access to this text via the George C. Gordon Library.
Additional Resource: Exploring ODEs, by Nick Trefethen, Asgeir Birkisson, Toby Driscoll, SIAM
This is a first course in ordinary differential equations which requires the material in Calculus (MA 1021- MA 1024). The material in this course provides fundamental mathematical content for topics in science and engineering, since the mathematical models that describe many processes in these disciplines are ordinary differential equations. The objectives of this course center not only on the mathematical topics of differential equations, but also on the qualitative interpretation of the solutions to ordinary differential equations. The goal is for students to be proficient in the material covered, and at the end of the course, the student should be able to do
Solve separable differential equations by integration
Solve first-order linear differential equations by different methods, and qualitatively interpret their solutions
Find fundamental solutions to second-order linear constant-coefficient differential equations
Mathematically model fundamental processes from science and engineering using ordinary differential equations
Quantitatively and qualitatively interpret solutions to second-order linear constant-coefficient differential equations
Use Laplace Transforms to find solutions to linear constant-coefficient differential equations.
The class meets five times per week: 4 lectures (MTRF) and 1 discussion session (T). Students are responsible for any and all material discussed in lecture and in discussion. My expectations for these activities are:
Lectures: This is the first opportunity for a student to see the material, and my expectation of students after a lecture is to have an introduction of the material, not to demonstrate mastery. The goal is to give a high-level description of the main points of the topics, and to provide some examples illustrating the topic. Lectures will be in person, but videos of all lectures can be found through Echo 360 on the course Canvas site. For any WPI-defined significant weather event, the lecture will be given remotely (either through Echo 360 or through Zoom). Check the Canvas site for further details.
Discussion: Students have an opportunity to sit down and work through problems on a topic and have their individual questions addressed. It is through the discussion that the student can get major questions asked so that after discussion, the student can continue to work through the problems to develop mastery. Discussion sessions are not recorded.
Students are expected to spend an additional 8-10 hours per week studying outside of class: reading the text, organizing notes, and solving problems. In previous years, the average time, self-reported, spent outside of class on this class is 9 hours.
Grades are determined through WebWork and Exams. These are discussed in the Grade Breakdown page
All lectures (audio and video) are captured through course capture and can be found on the course Canvas page. NO recording of audio or video by students is allowed during lecture or during conference. Laptops, phones, and tables should be turned off during the lecture and conference sessions. If you take notes (typing/stylus only) using these devices during lecture, then you should sit in the back of the room, since screen activity is distracting to your neighbors.
Prior to the start of each exam, you must place all of your belongings (e.g., cell phone, study materials, etc.) in your backpack and under your desk, so that no items are visible during the exam. All exams this term are closed book, closed notes, and no electronic devices are permitted. You will be required to show your WPI ID when turning in your exam to verify your identity.
If you need course adaptations or accommodations because of a disability, or if you have medical information to share with me, please make an appointment with me as soon as possible. My office location and office hours are listed above. If you have not already done so, students who believe that they may need accommodations in this class are encouraged to contact the Office of Accessibility Services (OAS) as soon as possible to ensure that these accommodations are implemented in a timely fashion. The OAS is in Unity Hall, (508) 831-4908. Students who need accommodations for exams are required to make the arrangements to take these exams at the Exam Proctoring Center (EPC) on the day of the exam.
Final grades will be assigned as A,B,C,I or NR. In general, grades will be distributed approximately as follows:
A:
B:
C:
NR:
90-100%
80-89%
68-79%
other