625.719.8VL - Advanced Differential Equations: Numerical Solutions to Ordinary and Partial Differential Equations
Description
This course presents numerical methods for the solution of both ordinary and partial differential equations. The analytical focus examines concepts of stability and convergence as applied to numerical simulations to differential equations. For solutions to ordinary differential equations topics in Euler’s method and Runge-Kutta methods are considered and analyzed, as well as boundary value problems. For solutions to partial differential equations, both implicit and explicit methods are considered and studied. The majority of consideration will be given to finite difference methods but will include a brief introduction to finite element and discontinuous Galerkin methods. A critical eye will be given toward appropriate discretization and methods, pairing effective techniques to the defined problem. Course work will be divided between analysis and computer implementation through comprehensive projects. Numerical implementations are not required to be in any specific programming language. Some familiarity with programming with a higher-level language (Fortran, MATLAB, Python) will be necessary. Course Notes: This course will complement the development of solutions to differential equations learned in EN.625.717 and EN.625.718, which are largely analytical. EN.625.719 will develop numerical solutions where an analytical solution may be otherwise unavailable. While there is some overlap in the types of differential equations considered, the techniques used to develop solutions are quite different. Similarly, the general concepts of numerical analysis from EN.625.611 are used in this course but applied to a specific application.
Instructor
Kurt Stein
Instructor
Kurt Stein
Course Structure
The course will be divided into six modules, representing the twelve weeks of the course. A module will include an assignment, two lectures, and a discussion post.
The modules will be developed as the course progresses, to include readings, code snippets, and examples. The calendar will be accurate. Assignments will generally be due on the Monday at the start of the next module.
Students are encouraged to collaborate, discuss ideas, and work together. Assignments must be completed individually but help and collaboration with other students and the instructor is encouraged / necessary for the course.
Course Structure
The course will be divided into six modules, representing the twelve weeks of the course. A module will include an assignment, two lectures, and a discussion post.
The modules will be developed as the course progresses, to include readings, code snippets, and examples. The calendar will be accurate. Assignments will generally be due on the Monday at the start of the next module.
Students are encouraged to collaborate, discuss ideas, and work together. Assignments must be completed individually but help and collaboration with other students and the instructor is encouraged / necessary for the course.
Course Topics
- General numerical analysis
- Finite Difference Methods for Partial Differential Equations
- Yee Scheme, as applied to Maxwell Equations
- Finite Element Methods for Partial Differential Equations
- Euler Methods for Ordinary Differential Equations
- Taylor Methods for Ordinary Differential Equations
- Runge-Kutta Methods for Ordinary Differential Equations
Course Goals
This course presents a survey of numerical methods for the solution of both ordinary and partial differential equations. While the course will not have the depth of any dedicated course, the main concepts behind numerical solutions and analysis will be presented.
Course Goals
This course presents a survey of numerical methods for the solution of both ordinary and partial differential equations. While the course will not have the depth of any dedicated course, the main concepts behind numerical solutions and analysis will be presented.
Textbooks
1. Thomas, James William. Numerical partial differential equations: finite difference methods. Vol. 22. Springer Science & Business Media, 2013. JHU Library - Online Access
2. Whiteley, Jonathan. Finite Element Methods: A Practical Guide. Springer, 2017. JHU Library - Online Access
3. Griffiths, David Francis, and Desmond J. Higham. Numerical methods for ordinary differential equations: initial value problems. Vol. 5. London: Springer, 2010. JHU Library - Online Access
Textbooks
1. Thomas, James William. Numerical partial differential equations: finite difference methods. Vol. 22. Springer Science& Business Media, 2013. JHU Library - Online Access
2. Whiteley, Jonathan. Finite Element Methods: A Practical Guide. Springer, 2017. JHU Library - Online Access
3. Griffiths, David Francis, and Desmond J. Higham. Numerical methods for ordinary differential equations: initial value problems. Vol. 5. London: Springer, 2010. JHU Library - Online Access
Other Materials & Online Resources
EP students may access electronic versions of textbooks through the Sheridan Libraries. Instructions on how to searchfor available textbooks are accessible through this link: Browse Electronic Textbook Instructions
Required Software
Webcam, microphone (if provided with computer, this is usually adequate along with adequate lighting and no background sound interference). Standard MS suite applications recommended.
MATLAB or similar will be required for some assignments. While the class doesn't mandate a specific programming language, please keep this to a high-level language. MATLAB or Fortran is fine, Python is probably OK; COBOL is not likely to work. If you have concerns or a question, please review with the instructor.
Required Software
Webcam, microphone (if provided with computer, this is usually adequate along with adequate lighting and no background sound interference). Standard MS suite applications recommended.
MATLAB or similar will be required for some assignments. While the class doesn't mandate a specific programming language, please keep this to a high-level language. MATLAB or Fortran is fine, Python is probably OK; COBOL is not likely to work. If you have concerns or a question, please review with the instructor.
Student Coursework Requirements
Student Coursework Requirements
It is expected that each module will take approximately 10-12 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 2-3 hours per week), as well as some videos (1-2 hours) and assignments (approximately 5–6 hours per week).
This course will consist of five basic student requirements:
1. Assignments (40% of final grade)
Weekly assignments are from the Stogatz textbook. They are an opportunity for you to practice the content for each week. Instructor monitors and provides guidance as necessary. In addition, instructor is available via email or weekly synchronous office hours.
2. Discussion board assignments (10% of final grade)
Weekly discussion board assignments require you to think about real-world applications for the mathematical concepts you will be learning. You are required to respond to each discussion prompt as well as respond to at least two other students’ post.
3. Quizzes (30% of final grade)
There are three quizzes in the course, in modules 5, 8, and 11. Quizzes cover material from previous weeks that is practiced in the weekly assignments.
4. Final Exam (20% of final grade)
The final exam is in module 14. You have all week to complete the exam.
Grading Policy
Assignments are due according to the dates posted in the course site. Students may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will post no later than 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 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.
The following grades are used for this course: A+, A, A– (excellent), B+, B, B– (good), C (unsatisfactory), F (failure), I (incomplete). A grade of F indicates the student’s failure to complete or comprehend the course work.
A course for which an unsatisfactory grade (C or F) has been received may be retaken. The original grade is replaced with an R. If the failed course includes laboratory, both the lecture and laboratory work must be retaken unless the instructor indicates otherwise. A grade of W is issued to those who have dropped the course after the refund period but before the drop deadline. The transcript is part of the student’s permanent record at the university. No grade may be changed except to correct an error, to replace an incomplete with a grade, or to replace a grade with an R.
The Whiting School assumes that students possess acceptable written command of the English language. It is proper for faculty to consider writing quality when assigning grades.
For incomplete grades, please see the Graduate Programs catalogue for the Whiting School of Engineering.
Grading Policy
Assignments are due according to the dates posted in the course site. Students may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will post no later than 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 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.
The following grades are used for this course: A+, A, A– (excellent), B+, B, B– (good), C (unsatisfactory), F (failure), I (incomplete). A grade of F indicates the student’s failure to complete or comprehend the course work.
A course for which an unsatisfactory grade (C or F) has been received may be retaken. The original grade is replaced with an R. If the failed course includes laboratory, both the lecture and laboratory work must be retaken unless the instructor indicates otherwise. A grade of W is issued to those who have dropped the course after the refund period but before the drop deadline. The transcript is part of the student’s permanent record at the university. No grade may be changed except to correct an error, to replace an incomplete with a grade, or to replace a grade with an R.
The Whiting School assumes that students possess acceptable written command of the English language. It is proper for faculty to consider writing quality when assigning grades.
For incomplete grades, please see the Graduate Programs catalogue for the Whiting School of Engineering.
The course grading scale is the following:
100–98 = A+
97–94 = A
93–90 = A−
89–87 = B+
86–83 = B
82–80 = B−
79–70 = C
<70 = F
Course Policies
Assignments are due according to the dates posted in the Blackboard course site. Students may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will post no later than 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 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.
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.