535.641.85 - Mathematical Methods For Engineers

Course Structure

The course materials are divided into modules. Clicking “Modules” on the left menu can access the modules. 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. Typically, a module runs for a period of seven (7) days. See “Course Outline” for more details. Students should regularly check the Announcements for the newest information about the course.

Course Topics

• Linear Algebra (linear systems, vectors spaces, eigenvalues)
• Laplace Transforms
  
• Review of Ordinary Differential Equations
• Partial Differential Equations (Heat and Wave equations)
• Probability (Discrete and Continuous random variables)
• Statistics (Basic concepts, Confidence Intervals, Testing Hypothesis)

Course Goals

The main goal of this course is to provide the student with some mathematical methods which are essential to the solution of advanced problems encountered in Applied Physics and Engineering. The student will demonstrate understanding of methods covered in the course by solving problems assigned as homework and given on exams, and by presenting a paper illustrating a concrete application using some mathematical method taught in the course.

Course Learning Outcomes (CLOs)

• Solve systems of linear equations and solve eigenvalue problems.
• Solve problems requiring Laplace transforms and solve differential equations and systems of differential equations by using Laplace transforms.
• Apply Fourier analysis methods to solve problems on the representation of functions as Fourier series.
• Solve heat flow and wave motion problems similar to the ones covered in class and in the assignments.
• Be able to apply Probability and Statistics theory to Engineering problems, such as estimation of parameters to industrial quality control.
• Apply techniques learned to specific problems in engineering: vibrations, heat flow problems, and problems that require the use of eigenvalues.

Textbooks

1. Lecture Notes in Engineering Mathematics by George Nakos

(Lecture notes that are freely distributed by George Nakos to the students of the course)

2. Recommended but NOT required

Kreyszig, Erwin (2011). Advanced Engineering Mathematics (10th edition). John Wiley & Sons, Inc.

ISBN-10: 0470458364
ISBN-13: 978-0470458365

Note: Any form of the book is acceptable: Electronic form, hard copy new or used, international editions, etc. A student with an earlier edition of the book need not purchase the 10^th edition. This is because the course is strongly supported by the instructor’s notes.

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 1–2 hours per week), and writing assignments (approximately 3–4 hours per week).

This course will consist of the following basic student requirements:

Assignments (28% of Final Grade Calculation)

There are 11 assignments that consist of mathematical problems related to the material covered in the course. The assignments are the very important. They carry the most single item weight of your grade. They also point towards most of the types of questions in the exams. Please work diligently to submit very good assignment solutions.

When you submit your assignment for grading please:

1. Use the provided template.

2. Include your name and assignment identifier.

3. Submit in Canvas only one file in PDF format. The best way to achieve this is to use a scanner to scan your hard copy into one PDF file.

4. Avoid uploading one page at a time.

5. Your uploaded file name should be as follows: “YOUR LAST NAME_ASSIGNMENT_NUMBER”

6. Avoid emailing your assignments, unless it is absolutely necessary (for example, if Canvas would not upload your document).

7. Avoid uploading pictures of your assignment because they create big files that are hard to upload, download, or save.

8. If you need to insert extra pages please include your name and an extra page number indicator (i.e., extra page x of y).

9. Each problem should have the assumptions, computations, and conclusions/discussion delineated.

10. Your writing should be clear.

11. The computations should be presented in logical order and sequentially.

All assignments are due according to the dates in Modules and Course Outline.

With the exception of Assignment 11, late submissions will be accepted up to a maximum of three days after the day they are due. The grade for late submission is reduced by 10% for each day that the assignment is overdue (no exceptions without prior coordination with me). The only exception is Assignment 11: the due date is firm and no extensions will be allowed. The reason is that I would like to make the key to this assignment available as soon as possible so that you can prepare for the final exam.

Note: The lowest assignment grade will be dropped.

Each assignment consists of several problems, usually similar to the examples presented in the course. Each problem carries an indicated number of points.

Each problem is graded as follows:

1. The method is correct (50%).

2. The computation, graphs, if any, and final answer are correct (40%).

3. The presentation is clear and logical (10%).

Discussion Activities (Team) (5% of Final Grade Calculation)

Course (Team) Project (20% of Final Grade Calculation)

The course includes a mandatory project. The project consists of a written paper and a short presentation in Zoom. You are to work in teams of two. Each team submits one paper. Each student participates in the short presentation. If the course has an odd number of students, then one team will consist of three students. I prefer that you pick your partners for the project. If you cannot decide on a partner, then you will be assigned one by me.

The project topic is chosen solely by you from the broader area of “applications of engineering mathematics”. It is the responsibility of each team to find a project topic. The project should have engineering content. It should be a specific engineering problem, which is solved by using some of the mathematics covered in the course. The project does not need not be original or research work.

The project topic cannot be material that in essence we covered in the course. For example, in the notes we offer a deduction of the 1-dimensional wave equation. This topic is not appropriate for a project.

The project is submitted in form of a written paper. The paper should be a Microsoft Word document with a minimum of 2,000 words not counting mathematical equations, graphs, references, or websites. Also, it should have a minimum of two references.

All projects should be compliant with the above guidelines.

Each project is evaluated by the following grading elements:

1. Correctness: correct equations, proofs, graphs, & conclusions (40%).

2. Amount of work: strong evidence that the work is not superficial, routine, or trivial (40%).

3. Writing style: clear and concise writing with appropriate graphs, illustrations, etc. (10%).

4. Clarity of presentation (10%).

It is also understood that each team member participates equally in the work involved to produce the project. I reserve the right to lower the project grade of a student for whom there is evidence that he/she did not fully participate in all the work needed for the project.

The project grade distribution is as follows:

• First Draft 10%
  
• Final Paper 70%
• Presentation and comments on other teams work 20%

Exams (47% of Final Grade Calculation, combined from 23% for Midterm and 24% for Final)

The dates and times of the exams are in the Course Outline document. Also, you will be reminded, via an Announcement in Canvas, about the time interval when the exam will be available. Students may use the course notes, the course text, and their own notes to complete the exams. If you are unable to take the exam within the allocated time interval, please contact me to make some other arrangement.

The exams will consist mostly of assignment-like problems. The assessment of exams is similar to that of assignments. More precisely:

Each exam consists of several problems. Each problem carries an indicated number of points. Just as with the assignments, the student is requested to use the instructor’s template to answer the exam questions. The student is free to add extra pages, if there is need for extra space.

Each problem is graded as follows:

1. The method is correct (50%).

2. The computation, graphs, if any, and final answer are correct (40%).

3. The presentation is clear and logical (10%).

Each of the Midterm and the Final exams has two parts both of which must be completed within a period of 24 hours as follows:

Part 1 (20 points out of 100) Five multiple choice questions with time allowed: 40 minutes. This portion is only 40 minutes long. After 40 minutes this portion of the test will be unavailable. If you miss this time interval, you cannot be credited for this portion of the exam. This portion has only five multiple choice questions. Each question is worth 4 points. This part is computer-graded and there is no partial credit. For this part you only click your chosen answers and submit. You do not submit any documents. This portion can be started whenever you choose but it needs to be completed within 40 minutes and also within the 24 hour time frame specified in the course outline. Part 1 is a new recommendation of the school to have some multiple choice questions that are automatically graded. These questions may be randomly picked from a larger pool of equivalent questions so that, this part of the test is more individualized.

Part 2 (80 points out of 100) Five problems with sub-parts. Time allowed: 24 hours. These are the long answer questions. The questions are mostly, assignment-like. For this part you write your complete answers in one PDF file and you submit in Canvas in the appropriate slot just as you would submit any other assignment. This part of the final is the equivalent of an in-class 3-hour test. However, you may use extra time as mentioned above. 

Grading Policy

Student assignments are due according to the dates in the Calendar and Assignments items in the corresponding modules. I will post grades one week after assignment due dates.

A grade in the A range 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 in the B range 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. A grade below B− does not count towards graduate credit.

100-99.5 = A+
99.49-94 = A
93.99-90 = A−
89.99-87 = B+
86.99-83 = B
82.99-80 = B−
79.99-77 = C+
76.99-73 = C
72.99-70 = C−
69.99-67 = D+
66.99-63 = D

Final grades will be determined by the following weighting:

Item	% of Grade
Assignments	33%
Course Project	20%
Exams: Midterm (23%) and Final (24%)	47%

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.