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Unformatted text preview: ME 530.343: Design and Analysis of Dynamic Systems Spring 2009 Lecture 1  Introduction to Dynamical Systems Monday, January 26, 2009 Today’s Objectives • get to know the teaching staff. • course policies • why take this course • math review Handouts: course information, questionnaire. Reading: Palm 1.1–1.3, 2.1–2.4 Teaching Staff • Instructor: Noah J. Cowan; Lab instructor: Allison Okamura. • Lab TA: Tricia Gibo • Session TA’s: TBD Course Policies 4 main components to the course: • Lectures – Meant to outline concepts. • Problem Sets – Almost every week. Put concepts to practice. This is important to be successful on exams. (25%) • Laboratories – Every other week. Minimal time investment, maximal learning. (20%) • Exams – two midterms (30% total), and one comprehensive final (25%) Course book: Systems dynamics by William J. Palm III. Course notes: I will distribute notes before each lecture. The notes will have blank spaces for you to fill in relevant material during class. The completed notes will be available on my website at the end of each week. Some of the material can also be found in the book. 1 Course website: http://www.me.jhu.edu/courses/530.343/ . Make sure you download the right notes. Why this course? • What are dynamical systems? – system: a collection of elements for which there are cause and effect relationships between variables. Even for elements where the cause and effect relationships are not apparent, or appear random, relationships can be established about the average behavior or fluctua tions (probabilistic systems). The elements can range from atoms and molecules (molecular systems) to oceans and planets. – dynamic: variables are timedependent. These systems are everywhere! • What will we do with them in this class? – Model: mathematical description of the relationship between variables. In general the mathematical description must be a simplification of the actual phenomena. Model is as much art as science. Design, in some sense, is modeling in reverse, and also has artistic aspects....
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 Complex Numbers, Cos, Complex number, adjacent hypotenuse sin

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