625.604.81 - Ordinary Differential Equations

Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

Topics discussed in the course include methods of solving first-order differential equations, existence and uniqueness theorems, second-order linear equations, power series solutions, higher order linear equations, systems of equations, non-linear equations, Sturm-Liouville theory, and applications. The relationship between differential equations and linear algebra is emphasized in this course. Applications of differential equations in physics, engineering, biology, and economics are presented. This course covers morematerial at greater depth than the standard undergraduate-level ODE course.

Course Goals

The goal of this course is to provide the student with an understanding of the solutions and applications of ordinary differentialequations. The course serves as an introduction to both nonlinear differential equations and provides a prerequisite for further study in those areas.

Course Learning Outcomes (CLOs)

• Solve first and second order linear homogeneous and non-homogeneous differential equations.
• Solve second order equations using power series methods.
• Solve separable boundary value problems.
• Apply differential equations to problems in engineering, physics, biology and economics.

Textbooks

Required

Boyce, W. E., & DiPrima, R. C. (2012). Elementary Differential Equations and Boundary Value Problems (10th ed). Hoboken, NJ:John Wiley & Sons. ISBN-13: 978-0-470-45831-0.

Textbook information for this course is available online through the appropriate bookstore website: For online courses, search the MBS website at http://ep.jhu.edu/bookstore.

Optional 

Additionally, any of the following texts or other texts that you may have from previous courses may be useful for this course if you find yourself struggling with specific skills:

• Calculus book from undergrad course
• Linear Algebra/Matrix Theory text
• Schaum’s outline “Mathematical Handbook”
• Also the website http://www.sosmath.com may be helpful to recall other facts from calculus or linear algebra.

Required Software

MATLAB

The use of Matlab is encouraged for solving linear systems and for some graphing capability for specialized problems. There are two Matlab apps: dfield for plotting direction fields and pplane for plotting phase portraits of systems of differential equations.

The MATLAB Total Academic Headcount (TAH) license is now in effect. This license is provided at no cost to you. Send an email to software@jhu.edu to request your license file/code. Please indicate that you need a standalone file/code. You will need to provide your first and last name, as well as your Hopkins email address. You will receive an email from Mathworks with instructions to create a Mathworks account. The MATLAB software will be available for download from the Mathworks site.

Student Coursework Requirements

It is expected that each module will take approximately 7–10 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 3–4 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 2–3 hours per week), and writing assignments (approximately 2–3 hours per week).

This course will consist of the following basic student requirements:

Preparation and Participation (counted as part of the Assignment for each module)

You are responsible for carefully reading all assigned material and being prepared for discussion. The majority of readings are from the course text. Additional reading may be assigned to supplement text readings.

Post your initial response to the discussion questions by the evening of Day 4 for that module week. Posting a response to the discussion question is part one of your grade for module discussions (i.e., Timeliness).

Part two of your grade for module discussion is your interaction (i.e., responding to classmate postings with thoughtful responses) with at least two classmates (i.e., Critical Thinking). Just posting your response to a discussion question is not sufficient; we want you to interact with your classmates. Be detailed in your postings and in your responses to your classmates' postings. Feel free to agree or disagree with your classmates. Please ensure that your postings are civil and constructive.

I have also set-up Discussion areas where you may post questions or respond to questions posted by other students

I will monitor module discussions and will respond to some of the discussions as discussions are posted. In some instances, I will summarize the overall discussions and post the summary for the module.

Evaluation of preparation and participation is based on contribution to discussions. Preparation and participation is evaluated by the following grading elements:

1. Timeliness (50%)
2. Critical Thinking (50%)

 Preparation and participation is graded as follows:

100–90 = A—Timeliness [regularly participates; all required postings; early in discussion; throughout the discussion]; Critical Thinking [rich in content; full of thoughts, insight, and analysis].

89–80 = B—Timeliness [frequently participates; all required postings; some not in time for others to read and respond];Critical Thinking [substantial information; thought, insight, and analysis has taken place].

79–70 = C—Timeliness [infrequently participates; all required postings; most at the last minute without allowing for response time]; Critical Thinking [generally competent; information is thin and commonplace].

Assignments

Homework assignments will be provided for most modules. The assignment will be 5-6 problems assigned from either the text or by me. These problems will be relevant to material covered in the module. Include a cover sheet with your name and assignment identifier. Also include your name and a page number indicator (i.e., page x of y) on each page of your submissions. Each problem should have the problem statement, assumptions, computations, and conclusions/discussion delineated. Provide appropriate figures and tables as needed. Also make sure that you only post one document. Posting 14 separate pages will not be acceptable. You may want to post and appendix to a homework set and that would be acceptable.

All assignments are due according to the dates in the Calendar. Late submissions will only be accepted by prior approval from me. Otherwise there will be a deduction in your grade for that set. Doesn’t mean that submitting one minute past midnight will result in a deduction. I will be reasonable about time of submission. Posting 3 or more days late will result in a grade deduction. Consistently late will be cause for a grade reduction.

Any questions or concerns on the grading should be submitted to me. Each homework will be worth 25 total points. Each problem is worth 5 points and will be graded using the following rubric:

• 5 points – Correct answer and appropriate method (there maybe more than one correct method).
• 4 points – Appropriate method but incorrect answer, minor problem such as sign error or brain fade.
• 3 points – Appropriate method, incorrect answer, major problem such as not being able to solve quadratic or do simple integral or applying correct method incorrectly.
• 2 points – Incorrect method, the majority of work is done correctly – example applying undetermined coefficients when it cannot be used.
• 0-1 points – Incorrect method, answer is essentially wrong.
• 1-9 points – Incomplete work – grade based on amount of problem solved.

Part of the homework grade will be to participate in the discussion question as indicated in Part 1 above. This will be worth 10 points out of the 100 of the homework grade. These points are award based on participation not on correctness.

Exams

There will be two exams assigned with due dates provided on the Calendar. The midterm exam will be available in Module 7 and cover material provided in Modules 1 through 7. Material covered in Modules 1 through 7 may be relevant and needed in the final exam. Students will have one week to complete the midterm exam. The exam will be due by 11:59PM on the date provided in the Calendar. Late exams will not be graded and the student will receive a failing grade. The exam will be worth 200 points and be comprised of 5 or 6 problems. Problems may contain multiple parts and there may be some latitude in which problems are solved by the student. Explicit instructions on the exam will be provide when the exams are assigned.

The final exam will be available as the last module and cover material provided in Modules 8 through 13. Students will have one week to complete the final exam. The exam will be due by 11:59PM on the date provided in the calendar. Late exams will not be graded and the student will receive a failing grade for the course. The final exam is worth 200 points and will be comprised of 5 problems with multiple parts to each problem. The student may have some latitude as to which part is solved.

Exams will be graded using the following rubric:

• 100% - Full points - Correct answer and appropriate method (there maybe more than one correct method).
• 100%-80% - Appropriate method but incorrect answer, minor problem such as sign error or brain fade.
• 80%-60% - Appropriate method, incorrect answer, major problem such as not being able to solve quadratic or do simple integral or applying correct method incorrectly.
• 60%-40% – Incorrect method, the majority of work is done correctly – example applying undetermined coefficients when it cannot be used.
• 40%-0 – Incorrect method, answer is essentially hosed up.
• 90%-10% - Incomplete work – grade based on amount of problem solved.

Grading Policy

Assignments are due according to the dates posted in your Canvas course site. You may check these due dates in the Calendar or the Assignments in the corresponding modules. I will post grades one week after assignment due dates.

A grade of “A” indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of exams, assignments and discussion in every week.

A grade of “B” indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

Course grades will be determined using a weighted average of the following items. 

Item	Points
12 Assignments	35%
10 Discussions	10%
Midterm Exam	25%
Final Exam	30%
Total	100%

Final grades will be determined by the following criteria:
 

Score Range	Letter Grade
100-98	= A+
97-94	= A
93-90	= A−
89-87	= B+
86-83	= B
82-80	= B−
79-70	= C
<70	= F

Student Generative AI (GenAI) Use

This course follows the EP Guidance on Student Generative AI and is designated as a YELLOW (Restricted / Guided Use) course. Generative AI tools may be used in limited ways to support learning, but they may not replace your own reasoning or problem-solving. All submitted work must reflect your independent understanding, and you are responsible for ensuring that your use of AI complies with both this policy and university academic integrity standards.

Tools such as ChatGPT, Claude, and Gemini may be used for conceptual clarification, generating practice problems, or improving the presentation of your own work (e.g., grammar or LaTeX formatting). You may also use AI to help identify errors in your reasoning after making a genuine attempt. However, you may not use AI to generate solutions, proofs, or substantive parts of graded assignments, nor may you use it on assessments intended to measure your individual understanding unless explicitly permitted.

Any use of generative AI must be disclosed. You are required to include a brief statement identifying the tool used, the purpose of its use, and how it contributed to your work, along with representative prompts where appropriate. Failure to disclose AI use will be treated as a violation of academic integrity.

You are expected to critically evaluate any AI-generated content, as such tools may produce incorrect or misleading results. You must be able to explain and justify all aspects of your submitted work. The instructor reserves the right to request clarification or verification of authorship. In all cases, generative AI may assist your learning, but it may not substitute for your own intellectual effort.

Academic Policies

Deadlines for Adding, Dropping, and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar. Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course. 

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students. This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Our courses are designed with a proactive approach to accessibility to minimize the need for disability disclosure and accommodation requests, but we recognize that you may need additional support. Students with disabilities (including those with psychological conditions, medical conditions, and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.  For further information or to start the process of requesting accommodations, please contact EP Student Disability Services at ep-disability-svcs@jhu.edu. 

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. For a full description of the code please visit the Student Conduct Code website.

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team (EP-Registration@exchange.johnshopkins.edu) in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.