Logistics

Line number:	25616
Times and place	Tu Thu   3:00 - 4:15 in PVW 159
Reference texts:	(highly recommended) M. Spivak, A Comprehensive Introduction to Differential Geometry, vol. I and II, available directly from Publish or Perish Publ., at the campus bookstore, and at various online-bookstores. (to be made available online) Instructor's notes Additional references
Instructor:	Matthias Kawski
Contact info:	e-mail:	kawski@asu.edu (preferred mode of contact)
	office location:	Goldwater Center room 354
	office hours:	Tu Thu 1:15 - 2:30 and by appointment
	office phone:	(480) 965 3376 (very unreliable)
	home phone:	(480) 893 0107

Content, goals and objectives This course is the first part of a new two-semester sequence. It is intended to cover in a novel way fundamental topics of differential geometric control theory, understood to be in a distinguished intersection of applied and pure mathematics (in the spirit of this book's title). The plan is that the sequence covers the following topics (catalogue descriptions): APM 581 Geometry and Control of Dynamical Systems I Differential systems on manifolds, tangent bundle, Lie algebra tools, controllability, observability, feedback and stabilization, topological constraints. Prereqs: 501-504 or equivalent or consent of instructor. APM 582 Geometry and Control of Dynamical Systems II Hamiltonian systems, variational principles, tools from symplectic geometry and Lie groups, continuous symmetries, reduction, geometry of the Pontryagin Maximum Principle, curvature. Prereqs: 501-504 or equivalent or consent of instructor. However, it is expected that in this first run, various modifications may be made to accommodate the needs of the participating students, several of whom are only able to take the first course. Likely this will take the form of stronger emphasis on geometry in the first semester, and more control in the second. In particular, this first course likely will include some coverage of curvature and connections. Since the formal perequisites APM 501 - 504 are completely new, the class will accommodate various preparations. Typally this includes a strong background in analysis at least at the level of MAT 371 (Advanced calculus), and preferrably a second course in differential equations. Formally, the main required technical tool is the (finite dimensional) implicit function theorem. This sequence of courses shall provide a comprehensive introduction to differential geometry and differential geometric control theory which prepares the student for advanced special topics courses and research in these areas. This sequence shall also serve students with diverse mathematics, engineering backgrounds and career plans who simply want to broaden their backgrounds. Aside from acquiring a working knowledge of the topics, a major objective is the development of a deep understanding of the meaning of thinking geometrically, the value of intrinsic properties and coordinate-free descriptions, an appreciation of the very precise language and notation of modern differential geometry, the interplay between topology, geometry, and algebra, and the intellectual challenges posed by distinguishing feature of control theory by routinely asking inverse questions. Expectations, policies and grading: The following are default policies and are subject to change provided all participants agree. Students are expected to regularly attend class -- it is the students' responsibility to master any missed material. Students are expected to take notes, and rewrite them as needed -- the instructor will, in turn, provide type-set classnotes to complement (but not replace) students' notes for most (but not necessarily all) classes. Students are expected to prepare each class by reading course materials and work out examples. Expect that any falling behind very quickly becomes unrecoverable due to the nature of the course. Students are expected to regularly (weekly or biweekly) hand in written homework. Students are expected to actively participate in the class. Homework: Suggested exercises will be included in the class-notes. Students are expected to work at least one-half of these suggested exercises, and hand them in usually no later than one week after the corresponding material has been discussed in class. for the highest credit, students are expected to work more of the harder and more theoretical exercises, and utilize more sophisticated arguments. Collaboration between students is strongly encouraged -- but it is each student's responsibility to demonstrate her/his personal level of mastery. As default policy, there shall be one one-hour in-class midterm exam, and a two-hour in-class final examination -- taken to be individually. If in-class participation and homework are of high quality (and all participants agree), there may be no need for some or all of the in-class examinations, and they may be partially or completely replaced by homework and projects/presemtations. All homework and exams must be well presented, using complete sentences, correct grammar and punctuation. All work must include justifications of all major steps. Unreadable and poorly organized work will be rejected for zero credit. Students are not expected to type-set their homework. Generally, homework will not be graded on any "point-system", but rather verbal feedback will be provided about the quality of the work (e.g. meet, exceed, or does not meet expectations). Students are strongly encouraged to regularly come to the instructor's office (hours) to discuss individual performance and learning goals and objectives. comments and explanations. University rules and deadlines for withdrawals will be enforced (e.g. to earn a W the student must have a passing standing at the time of the request).