Syllabus
MA 2051 - Differential Equations
A-Term, Fall 2024
Department of Mathematical Sciences
Worcester Polytechnic Institute
A-Term, Fall 2024
Department of Mathematical Sciences
Worcester Polytechnic Institute
Instructor: Prof. B.S. Tilley
Department of Mathematical Sciences
Worcester Polytechnic Institute
Office: SH 419
Phone: (508) 831-6664
e-mail: tilley@wpi.edu
Replies within 24 hours on weekdays, 48 hours on weekends
Tilley Home Page
Office Hours: MR: 10:00-10:50am (SH 431)
F: 9:00-9:50am (SH 419)
TA: Evan Sayer
PLA: Lauren Braconnier
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 can get electronic access to this text via the George C. Gordon Library. See the course Canvas page for more details
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, 1:00-1:50 pm, UH 400
Discussion: Just one hour per week. Check your course schedule for your Discussion section. Students can only attend their assigned Discussion section.
AD07: T 4:00-4:50 pm, SH 301
AD08: T 12:00-12:50 pm, SH 301
AD09: T 3:00-3:50 pm, SH 301
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.
Students with approved academic accommodations should plan to submit their accommodation letters through the Office of Accessibility Services Student Portal. Should you have any questions about how accommodations can be implemented in this particular course, please contact me as soon as possible. Students who are not currently registered with the Office of Accessibility Services (OAS) but who would like to find out more information about requesting accommodations, documentation guidelines, and what the accommodated interactive process entails should plan to contact OAS either by email: AccessibilityServices@wpi.edu, by phone (508) 831-4908, or by stopping by the office on the 5th floor of Unity Hall.
There are two components that make up the final grade:
WebWorK (15% 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.
Three Exams: Closed book, closed notes, and no electronic devices are allowed.
Exam 1 (25% of Final Grade) The first exam (45 minutes) takes place on September 5, 2024 in lecture, and focuses on first-order initial value problems and their applications.
Exam 2 (25% of Final Grade) The second exam (45 minutes) takes place on September 19, 2024 in lecture, and focuses on homogeneous second-order initial value problems and their applications.
Final Exam (35% of Final Grade): This 45-minute exam takes place on October 10, 2024 in lecture, and focuses on nonhomogeneous second-order initial value problems, their applications, and Laplace Transforms.
Retake Exams: Students can retake either Exam 1 or Exam 2 on October 11, 2024 in lecture, but not both. The grade on the retake replaces the grade on the original exam.
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 this term are closed book, closed notes, and no calculators or 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