16.001 | Fall 2021 | Undergraduate

Unified Engineering: Materials and Structures


Course Meeting Times

Lectures: 1 hour / session, 5 sessions / week

Recitations: 1 hour / session, 2 sessions / week


18.02 Calculus II: Multivariable Calculus and 8.01 Physics I: Classical Mechanics


16.002 Unified Engineering II: Signals and Systems and 18.03: Differential Equations 


In the MIT Department of Aeronautics and Astronautics and Unified Engineering (Unified), aerospace engineering is taught within the context of the CDIO (Conceive-Design-Implement-Operate) framework. Our goal is to educate future leaders in the field who can contribute to the development of new products in a modern, team-based environment. In addition to learning the disciplinary material and acquiring the technical foundations of aerospace engineering, you will begin learning skills that will enable you to become an effective aerospace engineer.

Course Objectives

The basic objective of Unified is to give a solid understanding of the fundamental disciplines of Aerospace Engineering and to give insight into their interrelationships and applications. In the fall, these disciplines are Materials and Structures (16.001) and Signals and Systems (16.002). In the spring, the disciplines are Fluid Dynamics (16.003) and Thermodynamics (16.004). This course 16.001 is the first course in the Unified series.

The second objective of Unified is to guide you toward an understanding of the fundamental skills, knowledge, and sensitivities that are the traits of a successful engineer. These include the skills necessary to work successfully in a group (including technical and graphical communication) and those of self-education (reading, research, and experimentation). Professional engineers have the knowledge and confidence to make estimates of poorly known parameters, create conceptual models of systems, assess the applicability of various models and their resulting solutions to encountered problems, and design new solutions to meet technical challenges. Aerospace systems in particular are very unforgiving; one can do 99.5% of the job well, but it is the error in the remaining 0.5% that may cause a major accident or failure. Aerospace engineers are known for their attention to detail and, while we do not expect perfection, we do expect that all work carried out as part of Unified Engineering be done with care and as well as possible given the time constraints of the course.

  1. Separate but Unified: While the disciplines have separate course numbers and will receive separate letter grades, Unified is nonetheless taught with a significant amount of unification. This includes the structure (assignments, quizlets, exams) as well as the grading policy of the individual courses. As such, the contents of this section apply equally to 16.001–16.004. Also, we will have topics that are not specifically about a single discipline, but yet will be taught by one of the disciplinary faculty. This is, in particular, true for some of the labs which often bring together more than one discipline and/or involve some aspect of design.
  2. Teaching Methods: The Unified Engineering Team is firmly committed to helping you learn. This commitment takes many forms, including a process of continuous improvement in our teaching effectiveness. During this semester, the faculty will be exploiting teaching methods proven to increase students’ learning. These methods include presenting information to the student in the context of a compelling challenge or problem, stressing active versus passive learning in the classroom, enhancing feedback to the student, providing multiple opportunities for hands-on learning, etc.
  3. Learning and Grades: Learning is a lifelong endeavor, whereas learning for grades is often quite temporary (i.e. the material often is not remembered as time after an exam increases). Further, while pursuing learning for a lifetime ability, one tends to acquire an understanding that is demonstrated in typical assessment activities, such as exams, and thereby one achieves the grades representative of the learning level desired and as expressed in the definition of grades at MIT (see below). We strongly encourage you to view all activities within Unified as opportunities for learning with the final goal of having you prepared for your career after Unified.


S. Crandall, N. Dahl, et al., An Introduction to the Mechanics of Solids (In SI Units), McGraw-Hill, 1978. ISBN: 9781259006531.

M. F. Ashby and D. R. H. Jones, Engineering Materials 1: An Introduction to Their Properties and Applications, Pergamon Press, 1980. ISBN: 9780080261393.

R. Hibbeler, Engineering Mechanics: Statics (any recent edition), Pearson. ISBN: 9780132915540. [Free eBook from the Internet Archive] [Additional information and access via Open Library]

R. Hibbeler, Mechanics of Materials (any recent edition), Pearson. ISBN: 9780134319650.

The following books are also useful:

M. F. Ashby and D. R. H. Jones, Engineering Materials 2: An Introduction to Microstructures and Processing, Pergamon Press, 1986. ISBN: 9780080325323.

M. F. Ashby, Materials Selection in Mechanical Design, Pergamon Press, 1992. ISBN: 9780750627276.

W. Bickford, Mechanics of Solids: Concepts and Applications, Irwin, 1993. ISBN: 9780256114256.

Assignments, Quizlets, and Exams 

  • Problem Sets: A sample homework solution is provided illustrating the proper way to write up a problem solution. Doing homework helps to engage with the concepts and material taught in class on a deeper level. To enhance the learning process, we strongly suggest that you first try to solve the problems by yourself.
  • Quizlets [not available to OCW users]: Each week there will be a quizlet on the material covered in the past week. This will be a combined 50-minute exam. The questions will cover examples, previous homework questions, and recitation questions from the past week. Please note that the order of the subjects will not be the same from week to week. The quizlet problem will be drawn from (1) problems from any past problem set for which the solutions have been posted, (2) problems worked in lecture or recitation, or (3) problems included in assigned reading for which solutions have been made available. The quizlet problems will be identical to the problems from (1), (2), and (3) except possibly for some simplifications (to allow for solving the problem in the allotted quizlet time). When taking the quizlet, you will not have any materials available to you (e.g. no “cheat sheets”). For equations, etc. that we would not expect you to know from memory, they will be provided with the quizlet. 
  • Labs: Labs will often require working on a team of two or more Unified students. The lab report details and submission procedure will be specified for each lab. 
  • Exams: There will be an in-class 2-hour midterm and a final exam for each course.

Academic Honesty

A fundamental principle of academic integrity is that you must fairly represent the source of the intellectual content of the work you submit for credit. In the context of Unified Engineering, this means that if you consult other sources (such as fellow students, TAs, faculty, literature, old problems from prior years) in the process of completing homework, system problems, and labs, or any other assignment, you must acknowledge the sources in any way that reflects true ownership of the ideas and methods you used.

Doing homework helps to engage with the concepts and material taught in class on a deeper level. To enhance the learning process, we strongly suggest that you first try to solve the problems by yourself and then discuss challenges in groups or in office hours if necessary. Discussion among students and office hours to digest the material and the homework problems or to prepare for laboratories or exams is considered useful in the educational process and copies of problems and exams of previous years will be made available by the instructors on the Unified website. Collaboration on homework is allowed unless otherwise directed as long as all references (both literature and people) used are named clearly at the end of the assignment. Word-by-word copies of someone else’s solution or parts of a solution handed in for credit will be considered cheating unless there is a reference to the source for any part of the work that was copied verbatim. Failure to cite the contribution of another student to your homework solution will be considered cheating. Official Institute policy regarding academic honesty can be found in the MIT Bulletin Course and Degrees Issue under “Academic Procedures and Institute Regulations.” The Academic Integrity Handbook, a guide for students published by the Office of the Dean for Undergraduate Education, contains additional information that may be helpful. 

Unified Study Group Guidelines

Study groups are considered an educationally beneficial activity. However, at the end of each problem on which you collaborated with other students, you must cite the students and the interaction. The purpose of this is to acknowledge their contribution to your work. Some examples follow:

  1. You discuss concepts, approaches, and methods that could be applied to a homework problem before either of you start your written solution. This process is encouraged. You are not required to make a written acknowledgment of this type of interaction.
  2. After working on a problem independently, you compare answers with another student, which confirms your solution. You must acknowledge that the other student’s solution was used to check your own. No credit will be lost due to this comparison if the acknowledgment is made.
  3. After working on a problem independently, you compare answers with another student, which alerts you to an error in your own work. You must state at the end of the problem that you corrected your error on the basis of checking answers with the other student. No credit will be lost due to this comparison if the acknowledgment is made and if no direct copying of the correct solution is involved.
  4. You and another student work through a problem together, exchanging ideas as the solution progresses, but you each write up your own solution. Each of you must state at the end of the problem that you worked jointly. No credit will be lost due to this cooperation if the acknowledgment is made.
  5. You copy all or part of a solution from a reference such as a textbook or the homework archive available on the Unified website. You must cite the reference. Partial credit will be given since there is some educational value in reading and understanding the solution. However, this practice is strongly discouraged and should be used only when you are unable to solve the problem without assistance.
  6. You copy verbatim all or part of a solution from another student. This process is not considered academically dishonest if the acknowledgment is made. However, you will receive no credit for verbatim copying from another student as you have not made any intellectual contribution to the work you are submitting for credit.


The rules of the MIT faculty define grades in terms of the degree of mastery of course material. These definitions are listed in the Bulletin and will be applied in this course. The following is the MIT policy on assigning grades to students.

Passing Grades: Undergraduate and graduate students who satisfactorily complete the work of a subject by the end of the term receive one of the following grades:

  • A: Exceptionally good performance demonstrating a superior understanding of the subject matter, a foundation of extensive knowledge, and skillful use of concepts and/or materials.
  • B: Good performance demonstrating the capacity to use the appropriate concepts, a good understanding of the subject matter, and an ability to handle the problems and materials encountered in the subject.
  • C: Adequate performance demonstrating an adequate understanding of the subject matter, an ability to handle relatively simple problems, and adequate preparation for moving on to more advanced work in the field. 
  • D: Minimally acceptable performance demonstrating at least partial familiarity with the subject matter and some capacity to deal with relatively simple problems, but also demonstrating deficiencies serious enough to make it inadvisable to proceed further in the field without additional work.

Use of letter grades on submitted work and participation: The work you submit and overall participation in Unified will receive a numeric grade based on the MIT grade point scale as described below. Specifically, you will receive grades for:

  • each individual problem on a problem set
  • each exam
  • lab assignments

The mapping from numerical to letter grades is as follows: 5 = A, 4 = B, 3 = C, 2 = D, 0 = F. +/- modifiers are set at 0.2 grade points. For example, your grade on a midterm might be a 4.4.  This grade is between an A- (4.8) and B+ (4.2). 

Weights will be assigned to the individual problems on problem sets. Most problems will be of equal unit weight value; however, particularly long and/or challenging problems could be given increased weight value (e.g. a weight of 2 would be twice the default problem value). Using these weights, a weighted overall grade point for homework will be determined.

Unified course grade: The Unified course grade will be defined based on your “Unified grade point average” with a weighting of 20% for problem sets and labs, 20% for quizlets, 25% for the midterm, and 35% for the final exam. Specifically, the final course letter grades will be assigned using this numeric Unified grade point average, as well as considering the distribution of your grades throughout the semester. At a minimum, you will receive a course letter grade that is equal to the maximum letter grade that your numeric course grade is above. For example, if your numeric course grade is 4.3, you would at least receive a B+ for your course letter grade.

Course Info

As Taught In
Fall 2021
Learning Resource Types
Lecture Notes
Problem Sets with Solutions
Exams with Solutions
Online Textbook