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Chapter1(0211)

Chapter1(0211) - MATH0211 Basic Applicable Mathematics Dr...

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Unformatted text preview: MATH0211 Basic Applicable Mathematics Dr. Yat-Ming Chan Department of Mathematics The University of Hong Kong First Semester 2009-10 Content Outline 1. Pre-Calculus Topics Sets theory, Permutation and Combination, Functions and Graphs, Composite and Inverse Functions, Limit and Continuity 2. Single variable Calculus Differentiation and Rate of Change, Rules of Differentiation, Critical points, Max- ima and Minima, Integration, Definite and Indefinite Integrals, Integration by sub- stitutions 3. Matrix algebra Matrices and their operations, Determinants 4. Multivariable Calculus Functions of several variables, Partial Differentiation and Double Integration 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. Adrian Banner, The Calculus Lifesaver: All the Tools You Need to Excel at Calculus , Princeton University Press (2007) Suggested Readings 1. Raymond A. Barnett, Michael R. Ziegler, Calculus for business, economics, life sciences, and social sciences , Prentice Hall 2. Margaret L. Lial, Raymond N. Greenwell and Nathan P. Ritchey, Calculus with Applications , Pearson/Addison Wesley Ch1/MATH0211/YMC/2009-10 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. • Listing Elements of a set are listed within a pair of braces. Note that the ordering of elements within the braces does not matter. For example, S := { Pound, Euro, Dollar, Yen } . • Set-builder notation For example, S := { x : x is the currencies used in England, France, U.S.A. and Japan. } Example 1.1 Represent the set A = { x : 2 x- 5 = 0 } by listing. Solution . It is a set containing the element 5 / 2 , that is, A = { 5 / 2 } . 2 Example 1.2 Represent the set A = { x : x 2- 4 = 0 } by listing. Solution . It is a set containing the elements 2 and- 2 , that is, A = { 2 ,- 2 } . 2 Example 1.3 Represent the set S of all positive integers less than 6 by listing and by set-builder notation. Solution . The set S can be expressed as S = { 1 , 2 , 3 , 4 , 5 } , or S = { x : x is an integer and < x < 6 } . Ch1/MATH0211/YMC/2009-10 2 Definition 1.4 An object of a set is called an element of the set. If x is an element of a set S , then we write x ∈ S . The Greek symbol ∈ means “belongs to”. If x is NOT an element of S , then we write...
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Chapter1(0211) - MATH0211 Basic Applicable Mathematics Dr...

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