675.650.81 - Mathematics for Space Systems

Space Systems Engineering
Spring 2024


This course is designed to teach Mathematical Methods commonly employed for engineering Space Systems. The course will provide a solid technical foundation in mathematics so the students can apply this knowledge to this broad field. Topics will include select, applicable methods from vector calculus, linear algebra, differential equations, transform methods, complex variables, probability, statistics, and optimization. Various applications to real problems related to space systems and technical sub-disciplines will be used during the semester. No prior knowledge of advanced mathematics is assumed and important theorems and results from pure and applied mathematics are taught as needed during the course. Examples and relevant applications will be utilized throughout the course to further clarify the mathematical theory. Prerequisite(s): The course requires working knowledge of college calculus and algebra, or approval of the instructor.


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 (7) days, exceptions are noted on the Course Outline page. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

Course Goals

By the end of the course, you will be able to:

  1. Solve problems in Linear Algebra, Ordinary differential equations, Transform Methods, Optimization, Probability and Statistics by using the mathematical methods taught in the course.
  2. Mathematically formulate real world problems by using the techniques taught in the course.
  3. Develop a solid foundation in mathematics in order to take advanced courses in Space Systems, Control Systems, Physics, and Engineering which have a mathematical orientation.

Course Learning Outcomes (CLOs)



K.F. Riley, M.P. Hobson, and S.J. Bence, Mathematical Methods in Physics and Engineering: A Comprehensive Guide, Cambridge University Press, 3rd Edition, 2006.

Kreyzig, Advanced Engineering Mathematics, Wiley, 10th Edition, 2011.


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:

G. Arfken and H. Weber, Mathematical Methods for Physicists: A Comprehensive Guide, Academic Press, 7th Edition, 2012.

John Dettman, Mathematical Methods in Physics and Engineering, Dover Publications, 2011.

B. Demidovich and G. Yankovsky, Problems in Mathematical Analysis, English Translation, Mir Publishers, 1989.

Sheldon Axler, Linear Algebra Done Right, Springer, 2nd Edition, 2004.

R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 2nd Edition, 2012.B

W. Boyce and R. DiPrima, Elementary Differential Equations and Boundary Value Problems, Wiley, 8th Edition, 2004.

S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 1st Edition, 2004

J. Brown and R. Chruchill, Complex Variables and Applications, McGraw Hill, 7th Edition, 2003.

Sheldon Ross, A First Course in Probability, 9th Edition, Pearson, 2012.

D. Bertsekas and J. Tsitsiklis, Introduction to Probability, Athena Scientific, 2002.

V. Zohatgi and E. Saleh, An Introduction to Probability and Statistics, Wiley, 2000.

Student Coursework Requirements

It is expected that each module will take approximately 7–12 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 3–6 hours per week).

This course will consist of following basic components:

Module Lectures (0% of Final Grade Calculation)

The material covered in each module will be presented in the Module Lectures. Additional material maybe assigned in the reading assignments. You are responsible for listening to the course lecture videos. Please feel free to contact the instructor for additional clarifications regarding the material presented in the course lectures. Problem Assignments and Exams will be constructed from the material presented in the course lectures and the reading assignments. 

Problem Assignments (35% of Final Grade Calculation)

There will be weekly homework assignments based on the material covered in the modules. Each homework assignment will have 4-6 problems of varying difficulty. The students will have one week to finish each assignment. Students are encouraged to collaborate on these assignments but should write their own final solution. Some assignments might also have a small computing (Matlab or software of your choice) component.  

All assignments are due according to the dates in the Calendar. Please contact the instructor if you are unable to complete an assignment by its submission date due to exceptional circumstances.

Exams (60% of Final Grade Calculation, combined from 30% for Midterm and 30% for Final)

There will be a Mid-Term and a Final-Exam. You will have 2hrs to complete each exam and their due dates and submission instruction will be provided before their release. You may use the course text and lecture notes to complete the exams.

The midterm examination will be given after the completion of Module 7. No collaboration will be allowed on this exam. This exam will cover the course material taught in the first seven modules. The students will be required to submit their answers via Canvas within the assigned time limits.

The final examination will be given after the completion of Module 14. This will cover the material covered in Modules 8-14.

Reading Assignments (0% of Final Grade Calculation)

There will be weekly reading assignments. These will not count towards a grade but are strongly recommended. There will be assigned readings from the course textbook and other reference texts. In addition, interesting applications of mathematical methods in real world problems will be made accessible to the students. The associated articles and papers will be posted on Canvas. 

Module Discussions (5% of Final Grade Calculation)

In this course, you are encouraged to ask questions about the content and concepts covered in this course. I want to help you master all topics in this course and I also encourage you to help one another. These discussions will help you collaborate with your peers in this course and in future endeavors. I will monitor discussions and will respond to some discussions as they are posted. These discussions will count towards 5% of final grade calculations..

Grading Policy

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

Final Grades will be determined by the following Grading system:


% of Grade

Module Discussions


Problem Assignments


Reading Assignments


Exam[s] (Midterm + Final)

60% (30% + 30%)


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.