625.717.81 - Advanced Differential Equations: Partial Differential Equations

Applied and Computational Mathematics
Spring 2023


This course presents practical methods for solving partial differential equations (PDEs). The course covers solutions of hyperbolic, parabolic, and elliptic equations in two or more independent variables. Topics include Fourier series, separation of variables, existence and uniqueness theory for general higher-order equations, eigenfunction expansions, numerical methods, Green’s functions, and transform methods. MATLAB, a high-level computing language, is used in the course to complement the analytical approach and to motivate numerical methods.


Course Structure

The course materials are divided into modules which can be accessed by clicking Modules on the course 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 days (Wed - Tue). You should regularly check the Calendar for assignment due dates.

Course Topics

• Recognize three basic types of partial differential equations.
• Apply Fourier Series and Transforms for solutions to partial differential equations.
• Solve Sturm-Liouville boundary value problems and apply Green's Functions to solve boundary value problems.
• Demonstrate the application of various analytic methods to the solutions of hyperbolic, parabolic, and elliptic partial differential equations.

Course Goals

The goal of this course is to provide the student with an understanding of solutions to and applications of partial differential equations.


Textbook is required

Haberman, R. (2013). Applied partial differential equations: With Fourier series and boundary value problems (5th Edition). Upper Saddle River, N.J: Pearson Prentice Hall.

ISBN-10: 0321797051
ISBN-13: 978-0321797056

Student Coursework Requirements

Discussion (10% of Final Grade Calculation)

There will be weekly discussion required – focused on asking questions on material

Homework (40% of Final Grade Calculation)

There will be ten homework assignments throughout the semester representing 40% of your final grade. Assignments will provide instructive examples that are both analytic and numerical.

Quizzes (30% of Final Grade Calculation)

There will be three quizzes throughout the semester representing 30% of your final grade. The quizzes will cover major sections of the course.

Final Exam (20% of Final Grade Calculation)

There will be one cumulative final exam worth 20% of your final grade. Exam will be take-home. Any materials may be used to help complete the exam.

Working together on homework assignments is encouraged but the assignments must be completed individually. Students may not collaborate on quizzes or the exam.

Grading Policy

Student assignments are due according to the dates in the Calendar and Assignments items.I aim to post grades within 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.

Score RangeLetter Grade
100-98= A+
97-94= A
93-90= A−
89-87= B+
86-83= B
82-80= B−
79-77= C+
76-73= C
72-70= C−
69-67= D+
66-63= D
<63= F

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 (https://ep.jhu.edu/student-services/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. 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 Student Disability Services at Engineering for Professionals, 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 following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

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.