Flight vehicles in the atmosphere and in space. Flight technologies, including structures, materials, propulsion, aerodynamics, vehicle dynamics, flight control, flight information systems and systems integration. An overview of aeronautics. Steady aircraft flight and performance. An overview of astronautics. Exposure to technologies including: computer aided design, manufacturing, simulation, composites, mechanisms, instrumentation and basic electronics. Embedded software development for data acquisition and processing, control and communications.

Individual and team projects. Includes analysis and numerical methods of solutions used for design of thin-walled Aerospace structures. Emphasis is placed on understanding behavior particular to thin-walled structures.

Topics include molecular and continuum concepts for fluids, first and second laws of thermodynamics, conservation laws for moving fluids, one-dimensional compressible flows, shocks and expansion waves, flows in nozzles, and two- and three-dimensional compressible flows.

Technical communications based upon the seminars. Directed Study Prerequisite: permission of instructor credits Study aspects of aerospace engineering that are not suitable for technical elective credit.

May be used for student team projects, pilot ground school, UROP or other academic studies that are directed by an Aerospace Engineering faculty member. Includes principles of analog and digital data acquisition, analysis of discrete measurement data, statistical assessment of hypotheses, design of experiments and similarity scaling of data. Emphasized development of skills for written communication and for working effectively in a team environment. Emphasis is on boundary-value problem formulation via simple examples, followed by the use of the finite-element method for solving problems in vehicle design.

Students learn how airfoils produce lift and how the pressure distribution about an airfoil can be calculated. Introduces the boundary-layer concept, how boundary layers lead to drag and what makes them prone to instability and turbulence or separation.

Effects of the wing planform shape on lift and drag. Introduction to airfoil design, high-lift devices and high-speed aerodynamics. Includes thermodynamic cycles as related to propulsion and the chemistry and thermodynamics of combustion. Students analyze turbojets, turbofans and other air-breathing propulsion systems.

Introduces liquid- and solid-propellant rockets and advanced propulsion concepts such as Hall thrusters and pulsed plasma thrusters. Students also learn about the environmental impact of propulsion systems and work in teams to design a jet engine. Nonlinear equations of motion.We strive to support our students and faculty on the front lines of learning and research and to steward our planet, our community, our campus.

To do this, the Department of Mathematics needs your support. Submit Site Search Search. Advising Extracurricular Activities Transfer Credit.

Programs Graduate Courses by Area Graduation. Giving Opportunities. Math T-Shirts. Let's Stay Connected Resources to stay in touch virtually with the math department community can be found here. Additional Contact Info Additional administrative staff contact information. University Covid Updates Click here for updates. Check out other resources below.

Michigan Math and Science Scholars A summer enrichment program for current high school students. Graduate Program Explore one of the world's top ranked mathematics graduate programs.

Michigan Center for Applied and Interdisciplinary Mathematics MCAIM has the broad aim of serving as the focal point for activities that integrate mathematics with the sciences across the University of Michigan. Undergraduate Program Discover the endless possibilities of an undergraduate mathematics degree here at the University of Michigan!

Previous Slide Next Slide. Secure Your Videoconferencing. Covid Updates. Well Being for Students. Math News and Info. Stacks Project WorkshopAugust ContinuUM Newsletters. Show your SUPPORT We strive to support our students and faculty on the front lines of learning and research and to steward our planet, our community, our campus.

Learn More Give Online. Events Apr. All Events. Click to call The BSE in Aerospace Engineering degree program has course requirements in several subjects listed below. Rules for Intellectual Breadth Electives, Technical Electives and General Electives selection are available here link to requirements document. Most AEROSP courses are offered every semester providing flexibility for students to plan their schedule according to their interests and needs, particularly in the junior and senior years.

Sample schedules are available for: aerospace programaeronautics trackand the astronautics track. Intellectual breadth 16 credits See the College of Engineering Bulletin for rules in selecting Intellectual Breadth courses that satisfy this requirement. A total of 7 credits of technical elective courses is required. The courses must be upper division that is level or above courses from engineering, mathematics, physical science, or other courses approved by an academic adviser, that are chosen to satisfy the following constraints:.

One course of 3 or more credits must be advanced mathematics or advanced science; this could include a course in astronomy, biology, chemistry, computer science, mathematics, or physics. Other courses can be selected if approved by an academic adviser. Aerospace Engineering students can earn directed study credit based on successful completion of pilot training activities according to the following procedures:. This exam is typically taken as part of a ground school course that covers basic knowledge required for a private pilot license.

Students requesting this credit must bring their FAA exam paperwork to the cognizant Aerospace Engineering faculty member for approval. More advanced FAA-issued ratings such as instrument, instructor, instrument instructor and multi-engine are acceptable but cannot be used to obtain additional credit.

Students eligible for this credit must either obtain their license while a University of Michigan student or maintain currency by completing a documented annual or biennial proficiency check after enrollment as a University of Michigan student. The cognizant faculty member for pilot training activities is currently Professor Carlos Cesnik. Inquiries should be directed to him.

See College of Engineering Bulletin for rules selecting general elective courses. Degree Requirements.Introduction to Ship Systems Prerequisite: none. Types, structures and purposes of ships. Ship compartmentation, propulsion systems, auxiliary power systems, interior communications and ship control.

Elements of ship design to achieve safe operations and ship stability characteristics. Course culminates with the student sailing a radio-controlled model sailboat around a course. Idealizations of marine structures including bars, beams, and frames; deflections due to bending and torsion.

Methods of structural analysis including equilibrium and strength requirements in consideration of stresses, forces and moments.

First law, second law of thermodynamics. System and control volume analyses. Energy and entropy. Heat transfer. Thermodynamic analysis of representative power producing cycles and refrigerators. Applications to marine systems. Engineering economics as applied in marine design decision making.

Overview of preliminary ship design with brief team design project. Hydrostatics, stability and trim of ships, boats, and marine platforms.

Loading, material and fabrication considerations. Hull primary bending and midship section analysis. Framing systems. Secondary and tertiary stresses in stiffened plate components.

### Illinois, University of - Urbana-Champaign (UIUC)

Energy methods. Introduction to Finite Element Analysis. Failure theories for buckling; combined stress states; brittle fracture and fatigue. Similitude and dimensional analysis, basic equations in integral form, continuity, and Navier-Stokes equations.Math is one of the more abstract and difficult sequences in the undergraduate program.

Its goal is to introduce students to the basic structures of modern abstract algebra groups, rings, fields, and modules in a rigorous way.

Emphasis is on concepts and proofs; calculations are used to illustrate the general theory. Exercises tend to be quite challenging. Students must have some previous exposure to rigorous proof-oriented mathematics and be prepared to work hard. The course covers basic definitions and properties of groups, fields, and vector spaces including homomorphisms, isomorphisms, subgroups, and bilinear forms.

Further topics are selected from: Sylow theorems; structure theorem for finitely-generated abelian groups; permutation representation; the symmetric and alternating groups; vector spaces over arbitrary fields; spectral theorem; and linear groups.

Submit Site Search Search. Advising Extracurricular Activities Transfer Credit. Programs Graduate Courses by Area Graduation. Giving Opportunities. Math T-Shirts. Undergraduates Undergraduate Math Courses [X] close. Undergraduates Undergraduate Math Courses. Prerequisites: Math, or Credit: 3 Credits Background and Goals: This course is an introduction to the modern qualitative theory of ordinary differential equations with emphasis on geometric techniques and visualization.

Much of the motivation for this approach comes from applications. Examples of applications of differential equations to science and engineering are a significant part of the course. There are relatively few proofs. Content: Geometric representation of solutions, autonomous systems, flows and evolution, linear systems and phase portraits, nonlinear systems, local and global behavior, linearization, stability, conservation laws, periodic orbits. Prerequisites: Math or ; and Math Credit: 3 credits.

A typical student entering this course has substantial experience in using complex mathematical calculus calculations to solve physical or geometrical problems, but is inexperienced at analyzing carefully the content of definitions and the logical flow of ideas which underlie and justify these calculations. Although the topics discussed here are quite distinct from those of calculus, an important goal of the course is to introduce the student to this type of analysis.

Much of the reading, homework exercises, and exams consist of theorems propositions, lemmas, etc. Mathor equivalent, required as background. Content: The initial topics include ones common to every branch of mathematics: sets, functions mappingsrelations, and the common number systems integers, rational numbers, real numbers, complex numbers.

These are then applied to the study of particular types of mathematical structures: groups, rings, and fields. These structures are presented as abstractions from many examples such as the common number systems together with the operations of addition or multiplication, permutations of finite and infinite sets with function composition, sets of motions of geometric figures, and polynomials.

Notions such as generator, subgroup, direct product, isomorphism, and homomorphism are defined and studied. Background and Goals: Many common problems from mathematics and computer science may be solved by applying one or more algorithms — well-defined procedures that accept input data specifying a particular instance of the problem and produce a solution.

Students entering Math typically have encountered some of these problems and their algorithmic solutions in a programming course.What are you learning? This is a first course in applied differential equations. We want you to get a solid, modern, understanding of the subject. Integrity It is very easy to cheat yourself and your fellow students as you work through your University courses.

## Math 417: Matrix Algebra

Please see the note about academic integrity on the syllabus. Canvas Site This website is the primary source of information about math We also have a canvas sitewhich provides an alternate entry point to this information, and will be used to submit lab assignments and provide other resources. Course Description Math is a 4 credit course on differential equations with supplementary coverage of complex numbers and matrix algebra.

It is intended for engineers and scientists who will be using differential equations in their work. Those looking for a more in-depth treatment should consider Math, or instead. Students considering a Math major should consult with a Math advisor before taking !

There should be a custom edition, ISBNwhich is discounted and includes the e-book. If you can't find that, please ask the course coordinator. This may be available only at bookstores affiliated with UM. Other formats of the text are also acceptable e. If you are having trouble finding it for that price locally, please try this link to the publisher.

The daily schedule is now updated. Please Note: Read this carefully. Labs have a handful of unexpected due datesthat depend on the day of the week you have lab. Differential Equations.

Winter Off-site Links:. Tutor List. Math Careers.

**My First Semester at the University of Michigan**

Quick Links. This Course. This course is many things; you may have heard that it is challenging, that it moves fast, or that it used to be much easier. These are all, from one perspective or another, correct. Most aspects of this course have been designed to help you learn.

The way we learn is by working on what is hard for us, so we want you to be in that space—in educational theory, it's called the zone of proximal development. Note: we do not expect you to struggle unproductively on your own. The point of taking a class is that we are all working toward the goal of you learning the material. It is very easy to cheat yourself and your fellow students as you work through your University courses.

This website is the primary source of information about math Math is a 4 credit course on differential equations with supplementary coverage of complex numbers and matrix algebra. Mathor Please note: we do not know how much this has changed from the 2nd edition. If you wish to work with the 2nd edition instead, you are responsible for ensuring that the material you are studying and problems you work are correct.An academic minor in Mathematics is not open to students with any concentration in Mathematics.

While the concentration will often be in a field that makes significant use of mathematics, such as a science or a quantitative social science, it may be in any area of study. Students wishing to pursue an academic minor in Mathematics must develop a specific plan for its completion in consultation with an advisor. Appointments are scheduled on-line at:. These all provide a thorough grounding in the calculus of functions of one variable. No more than one course may be elected from each of the three areas of category A.

The courses in category B must be selected from exactly two of the six listed areas. A student planning to take linear algebra and differential equations should note that not all of MATH, and will count toward the academic minor, whereas all of MATH, and will. All courses for the academic minor program must be completed with a grade of at least a C. While the concentration will often be in a field which makes significant use of mathematics, such as a science or a quantitative social science, it may be in any area of study.

Students wishing to pursue an academic minor in Mathematics must develop a specific plan for its completion in consultation with the Department's designated advisor. Appointments are scheduled on-line. Academic Minor Program: credits of courses, including either two courses from category A and three courses from category B, or one course from category A and four courses from category B.

A student planning to take linear algebra and differential equations should note that not all of MATH, and will count toward the academic minor, whereas all of MATHand will. Category A: Second-year courses:. Category B: Upper-level courses:. College of Literature, Science, and the Arts S. Mathematics Minor Effective Fall An academic minor in Mathematics is not open to students with any concentration in Mathematics.

Appointments are scheduled on-line at: www. Academic Minor Program credits of courses, including either two courses from category A and three courses from category B, or one course from category A and four courses from category B.

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