Syllabus
MA 2051 - Differential Equations
B-Term: Fall 2021
Department of Mathematical Sciences
Worcester Polytechnic Institute
B-Term: Fall 2021
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Department of Mathematical Sciences
Worcester Polytechnic Institute
Office: SH 105A
TAs: Dane Johnson
Kiara Sanchez
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.
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.
Discussion: Students have an opportunity to sit down and work through problems on a topic with two instructors and have their individual questions addressed. It is through the conference that the student can get major questions asked so that after conference, the student can continue to work through the problems to develop mastery.
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 with disabilities 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 Daniels 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