Syllabus
MA 2051 - Differential Equations
D-Term, Spring 2024
Department of Mathematical Sciences
Worcester Polytechnic Institute
D-Term, Spring 2024
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: TBD
TA/PLAs:
Andrey Martemyanov
Aidan Cook
Sarah Roberge
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.
Students are responsible for all material described in the text in the sections covered in lecture. See the Lecture Schedule for more details.
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.
Collaborative learning and active engagement are expected. Collaborative learning meas that students collaborate together to learn the material in the course. Active engagement by students means that students accept the responsibility for their own learning of the material and do not perceive the instructor (professor/TA/PLA) as a source of all knowledge.
In order to meet these expectations, the classroom environment must be professional and supportive. Students are expected to treat each other with mutual respect, provide constructive feedback to other students, and to realize that as humans we all need guidance at times.
The class meets five times per week:
Lectures (MTRF, 2:00-2:50pm, AK 116)
Discussion: Just one hour per week
DD06: (T 10:00-10:50am, TA: Martemyanov) FL 311
DD07: (T 3:00-3:50pm, PLA: Cook) Portable Classroom
DD08: (T 4:00-4:50pm, PLA: Roberge) Portable Classroom
DD10: (M 9:00-9:50am, TA: Martemyanov) Portable Classroom
Students are responsible for any and all material discussed in lecture and in discussion. 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.
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 and quizzes are required to make the arrangements to take these exams at the Exam Proctoring Center (EPC) on the day of the exam.
There are three components that make up the final grade:
WebWorK (20% of Final Grade): There will be assignments using this online tool through the course Canvas site to understand your basic knowledge of the topics for that day's lecture. You receive full credit for correct answers, independent of the number of attempts made. Each problem is equally weighted (1 point per problem is a perfect score). These assignments need to be completed by their due date, typically within three days of the lecture.
Quizzes (20% of Final Grade): There are 4 quizzes given over the term,
These quizzes are based on the topics described on the Lecture Schedule. The quizzes are 20 minutes long and are problems that are considered fundamental. The quizzes are closed book, closed notes, and no electronic devices are allowed. The lowest score quiz is dropped before calculating this portion of the grade.
Two Exams: Closed book, closed notes, and no electronic devices are allowed.
Exam 1 (25% of Final Grade) The first exam takes place on March 22, 2024, and focuses on first-order initial value problems and their applications. Students have the option to retake this exam on May 1, 2024, however, the grade on the retake exam replaces the grade of the original exam.
Final Exam (35% of Final Grade): This exam takes place on April 30, 2024 in lecture, and will take 45 minutes. Problems for the final measure how well a student has synthesized different topics of the course.
Prior to the start of each exam or quiz, 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 and quizzes this term are closed book, closed notes, and no electronic devices are permitted.
Final grades will be assigned as A,B,C,I or NR. In general, grades will be distributed approximately as follows:
A: 90-100%
B: 80-89%
C: 68-79%
NR: other