MATH 0090: Introductory
TENTATIVE DATES: June 23rd to August 8th, 2008
Professor Steven Miller (sjmiller AT math.brown.edu), Kassar House, Room 210, 863-1123
Webpage with many useful links and explanations and examples:
Homework problems here
Review sheet of all derivatives and rules
DESCRIPTION: Calculus, as one of the most important subject in mathematics, has far-reaching consequences and applications in many sciences. However, the main ideas involved in understanding calculus are often challenging. We will emphasize how to think about calculus problems, highlight the key steps of the proofs, and motivate the material with examples drawn from biology to computer science to economics to physics, to name just a few. Topics include limits, differentiation, maxima and minima, rational, trigonometric and exponential functions, as well as an introduction to integration with applications to area and volumes of revolution; additional topics will be determined by student interest.
IMPORTANT: It is essential that you have a solid grasp of high school algebra for this course. Over the years I have found many students' understanding of calculus is hindered by gaps in their ability to do basic algebra. As we will use algebra throughout the course, you must be familiar and comfortable with it at the start of the class. You should review your algebra. Any textbook is fine; one particularly good (and cheap!) one is Schaum's Easy Outlines: Precalculus (Based on Schaum's Outline of Precalculus by Fred Safier, Abridgement Editor: Kimberly S. Kirkpatrick). You should know the material from Chapters 1 2, 3, 4, 5, 6, and 8. You can also find algebra review online (see, for example, http://www.math.uakron.edu/~dpstory/mpt_home.html).
GENERAL: Homework is to be submitted on time, neatly written and stapled (if not, the homework may not be graded); Homework problems here. Working in groups is encouraged; everyone must submit their own assignment. If you work in groups, please write the name of everyone in your group on the first page. Grading policy: HW 20%, Midterm(s) 40%, Final 40%.
TEXTBOOK: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus, Adrian Banner, ISBN13: 978-0-691-13088-0. Webpage with many useful links and explanations and examples:
Introduction, Review, Definition of the Derivative
Derivatives of Simple Functions
Rules of Differentiation
Rules of Differentiation and Applications (Tangent Line)
Implicit Differentiation, Maximization and Minimization
The Chain Rule
Derivatives of trigonometric functions
Derivatives of logarithmic and exponential functions
LíHospitalís Rule and Newtonís Method
Areas, distances and integratals
The definite integral
The fundamental theorem of calculus
Applications of integration