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Unformatted text preview: 1 Introduction 1.1 Purpose and Objectives This document is intended to help you with the math skills that you will need for 16.06. The idea is to create an explicit linking of the mathematics courses that you took in freshman and sophomore year and the skills that you will need for 16.06. This document will provide you with a comprehensive list of mathematics resources should you need to do further review. Note that many of the engineering concepts and skills that we will be learning in 16.06 depend directly on the math you learned in 18.01, 18.02 and 18.03. In most cases, we will not be spending lecture time to review these math skills in class. It is therefore very important that you feel comfortable with the math so that you can focus on achieving the 16.06 learning objectives. 1.2 Document Overview This document is organized in a lecture-by-lecture format that reintroduces mathematical tools as they are used in class. Each section contains some math notes for selected topics as well as a list of references of where each concept was taught in the introductory math courses. Each set of notes will be given out before the corresponding lecture and you should review them before class. For each lecture, you will see a list of the math topics that arise in that lecture. For each topic, there is a list of the specific skills that you will require. Some specific examples are given and a list of resources is provided. If you do not feel comfortable with any of the skills that are listed, you should go back and review these resources. If there are specific math skills in with you feel particularly weak, we are willing to provide extra review during recitation sessions. Please communicate any requests to the faculty or teaching assistants. 1.3 Acknowledgments This work is supported by the Class of 1951 Fund for Excellence in Education, the Class of 1955 Fund for Excellence in Teaching, the Class of 1972 Fund for Educational Innovation, and the Class of 1999 Fund for Excellence in Student Learning. 2 Lecture 2: Introduction to Feedback Control Lecture 2 Math Topics Functions Linearization First-Order Ordinary Differential Equations Laplace Transforms 2.1 Functions Required Skills Understand the concept of an independent and dependent variables (ar- gument of a function) A function is a rule that defines how the elements of one set are transformed into the elements of another set (a set is a collection of a finite or infinite number of elements). For example, let us consider the set containing all people in the United States and the set of all positive integers with 9 or fewer digits. Then we can think about the Social Security Number system as providing a function from the first set to the second, because for every person we can define the value of our function to be his/her Social Security Number. The first set, the set con- taining all people in the United States, is called the domain of the function. [aa-math website] Another example is the function sin(...
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This note was uploaded on 11/06/2011 for the course AERO 100 taught by Professor Willcox during the Fall '03 term at MIT.
- Fall '03