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Unformatted text preview: MATH1804 University Mathematics A Dr. YatMing Chan Department of Mathematics The University of Hong Kong First Semester 200910 Content Outline 1. PreCalculus Topics Sets, Functions and Graphs, Composite and Inverse Functions, Limits and Conti nuity. 2. Single variable Calculus Differentiation and its applications, Exponential and Logarithmic functions, L’Hˆ opit al’s rule, Taylor approximation, Integration, The Fundamental Theorem of Calculus, Techniques of Integraton, Improper Integrals. 3. Matrix algebra and Linear equations Matrices and their operations, Determinants, System of Linear equations, Eigen values and Eigenvectors. 4. Multivariable Calculus Functions of several variables, Partial Differentiation, Method of Lagrange Multi pliers, Double Integrals. Reference Books Main Reference 1. Class lecture notes — This course will follow closely with the lecture notes which can be downloaded from the course website. You are expected to have the relevant notes during the lectures. 2. Martin Anthony, Norman Biggs, Mathematics for Economics and Finance: Methods and Modelling , Cambridge University Press (1996) Suggested Readings 1. Adrian Banner, The Calculus Lifesaver: All the Tools You Need to Excel at Calculus , Princeton University Press (2007) 2. Raymond A. Barnett, Michael R. Ziegler, Calculus for business, economics, life sciences, and social sciences , Prentice Hall 3. George B. Thomas; as revised by Maurice D. Weir, Joel Hass and Frank R. Giordano, Thomas’ Calculus , 11th edition, Addison Wesley Ch1/MATH1804/YMC/200910 1 Chapter 1. Set Theory 1.1. Set notation One of the most fundamental concepts in modern mathematics is the theory of sets . A set is a collection of objects defined in a precise way such that any given object is either in or not in the set. Sets are conventionally denoted by capital letters. To define a set, we may either use any of the following methods: • Word description For example, let S be the set of currencies used in England, France, U.S.A. and Japan....
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 Spring '10
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