625.611.81 - Computational Methods
Description
As the need to increase the understanding of real-world phenomena grows rapidly, computer-based simulations and modeling tools are increasingly being accepted as viable means to study such problems. In this course, students are introduced to some of the key computational techniques used in modeling and simulation of real-world phenomena. The course begins with coverage of fundamental concepts in computational methods including error analysis, matrices and linear systems, convergence, and stability. It proceeds to curve fitting, least squares, and iterative techniques for practical applications, including methods for solving ordinary differential equations and simple optimization problems. Elements of computer visualization and Monte Carlo simulation will be discussed as appropriate. The emphasis here is not so much on programming technique, but rather on understanding basic concepts and principles. Employment of higher-level programming and visualization tools, such as MATLAB, reduces burdens on programming and introduces a powerful tool set commonly used by industry and academia. A consistent theme throughout the course is the linkage between the techniques covered and their applications to realworld problems. Prerequisite(s): Multivariate calculus and ability to program in MATLAB, FORTRAN, C++, Java, or other language. Courses in matrix theory or linear algebra as well as in differential equations would be helpful but are not required.
Instructor
Tatyana Sorokina
Course Structure
The course materials are divided into modules which can be accessed by clicking Course Modules on the menu. A module will have several sections including the lectures, quizzes, readings, discussions, and assignments. Each video lecture is followed by a short quiz. You will not be able to access the next lecture without taking the quiz. You will have one attempt to complete each quiz. Most modules run for a period of seven (7) days. The last module is devoted to presentations of final projects. You will be asked to watch and peer-review several projects. You should regularly check the Calendar and Announcements for assignment due dates.
Course Topics
- Matrices and Linear Systems
- Conditioning and Error
- Iterative Methods
- Polynomial Interpolation
- Bernstein-Bezier approach, and Bezier curves
- Polynomial Splines
- Computational methods for solving ODEs
- Linear Least Squares Methods
- Optimization for Linear Problems
Course Goals
To translate real-world problems into a mathematical problem, to find a way of solving the problem approximately or exactly, to estimate the error of the approximate solution, and to create an algorithm for the associated computational method.
Course Learning Outcomes (CLOs)
- Select and apply an appropriate computational method to solve a mathematical problem arising from a variety of applications
- Describe numerical algorithms on which computational methods are based
- Identify and explain mathematical ideas and concepts in the foundation of the algorithms
- Analyze different types of errors associated with computational methods
- Suggest ideas to improve existing algorithms or to create new ones
Textbooks
Required
Lyche T, Merrien J-L, (2014) Exercises in Computational Mathematics with MATLAB : Springer. Available at the JHU library in electronic format.
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
Rjabenʹkij, V. S., & Tsynkov, S. V. (2007). A theoretical introduction to numerical analysis. Boca Raton: CRC Press.
Required Software
MATLAB
You will need access to a recent version of MATLAB. 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.
Alternatively, you may choose to use Octave, or any software of your preference.
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 1–3 hours per week) as well as some outside reading, listening to the audio annotated slide presentations and completing quizzes (approximately 1.5–2 hours per week), and writing assignments (approximately 3–5 hours per week).
This course will consist of the following basic student requirements:
1. Discussions (12% of Final Grade Calculation, 1% each module except module 9 and module 14)
You are responsible for being prepared for discussion. The main part of your grade for module discussion is critical thinking. One or more meaningful posts (an initial post or a response to your peer) is required. 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.
2. Quizzes (12% of Final Grade Calculation, 1% each module except module 9 and module 14)
3. Assignments (36% of Final Grade Calculation, 12 % each module except module 9 and module 14)
Each module will contain a graded assignment that students will complete individually. Weekly assignments will vary depending on module learning objectives and will include a set of problems and/or a coding assignment. All assignments are due according to the dates in the Calendar. Late submissions will not be accepted.
Quantitative assignments are graded as follows:
- 100–90 = A—All parts of question are addressed; All assumptions are clearly stated; All intermediate derivations and calculations are provided; Answer is technically correct and is clearly indicated; Answer precision and units are appropriate.
89–80 = B—All parts of question are addressed; All assumptions are clearly stated; some intermediate derivations and calculations are provided; Answer is technically correct and is indicated; Answer precision and units are appropriate.
79–70=C—Most parts of question are addressed; Assumptions are partially stated; Few intermediate derivations and calculations are provided; Answer is not technically correct but is indicated; Answer precision and units are indicated but inappropriate.
- <70=F—Some parts of the question are addressed; Assumptions are not stated; Intermediate derivations and calculations are not provided; The answer is incorrect or missing; The answer precision and units are inappropriate or missing.
4. Course Project (25% of Final Grade Calculation)
A course project topic must be chosen by the student no later than by the Midterm Exam week. The students may work on the projects individually or in teams of at most three. Once you identified the topic of the project, please create a short project proposal and discuss it with me during Office Hours. The project must address the following components: statement of the problem, mathematical idea to solve the problem, computational method, algorithm, error analysis, stability analysis, code, discussion of the output of the code.
The final paper of the project is due by the end of Module 14. It should be at most six pages long not including the references. The format should be similar to a research paper. All projects are graded as follows:
100–90 = statement of the problem, mathematical ideas, computational method and algorithms are fully explained, theoretical and numerical error analysis and stability analysis are clearly addressed. An original code and a meaningful discussion of the output are attached.
89–80 = B— statement of the problem, mathematical ideas, computational method and algorithms are explained, theoretical or numerical error analysis and stability analysis are addressed. An original code and a discussion of the output are attached.
79–70 = C— statement of the problem, mathematical ideas, computational methods are explained. A code and a discussion of the output are attached.
<=70 =F — statement of the problem, mathematical ideas, computational methods are somewhat explained.
5. Midterm Exam (15% of Final Grade Calculation)
The midterm exam will be available in Module 9. You will have one week to complete the exam. You may use any course materials to complete the exam. Exams are graded as follows:
100–90 = A—All parts of question are addressed; full analysis has taken place.
89–80 = B—All parts of the question are addressed; some analysis has taken place.
79–70 = C—Majority of parts of the question are addressed; some analysis has taken place.
<=70= F—Some parts of the question are addressed
Final grades will be determined by the following weighting:
| Item | % of the final grade |
| Discussions | 12 |
| Quizzes | 12 |
| Midterm | 15 |
| Project | 25 |
| Assignments | 36 |
| Total | 100 |
Grading Policy
Assignments are due according to the dates posted in your Blackboard course site. You may check these due dates in the Course 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 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 Range | Letter 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.