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Unformatted text preview: PMC 0045 PreCalculus for Engineering Foundation in Engineering ONLINE NOTES Topic 1 Prerequisites: Fundamental Concepts of Algebra FOSEE , MULTIMEDIA UNIVERSITY (436821T) MELAKA CAMPUS, JALAN AYER KEROH LAMA, 75450 MELAKA, MALAYSIA. Tel 606 252 3594 Fax 606 231 8799 URL: http://fosee.mmu.edu.my/~asd/ Mathematics Department (MD) Centre for Foundation Studies and Extension Education (FOSEE) PMC0045 PreCalculus for Engineering Topic 1 TOPIC 1: PREREQUISITES: FUNDAMENTAL CONCEPTS OF ALGEBRA References : 1. Sullivan, M. (2002), Algebra & Trigonometry , 6 th Ed., Prentice Hall. 2. Blitzer, R., Goh Wei Wei, et.al. (2005), Algebra & Trigonometry , Prentice Hall. Objectives : 1. Know the classification of numbers. 2. Graph sets of numbers, equations, inequalities, and absolute value. 3. Properties of real numbers. 4. Indices  Integer exponents; Laws of exponents. 5. Square roots and radicals, and their properties. Contents: 1.1 Real Numbers and Algebraic Expressions 1.2 Exponents 1.3 Radicals and Rational Exponents 1.4 Polynomials 1.5 Complex Numbers 1.1 REAL NUMBERS AND ALGEBRAIC EXPRESSIONS Classification of Numbers 1. Natural Numbers ( N ) {1, 2, 3, . . .} 2. Whole Numbers ( W ) {0, 1, 2, . . .} 3. Integers ( Z ) {. . ., 3, 2, 1, 0, 1, 2, 3, . . .} Consist of: positive integers {1, 2, 3, . . . } negative integers { . . , 3, 2, 1}  zero {0} 4. Rational Numbers ( Q )  numbers that can be expressed as a quotient of two integers. = b a Q a and b are integers, ≠ b may be represented as decimals: terminating, or nonterminating with repeating digits. ______________________________________________________________________________________ Mathematics Dept 2/ 10 PMC0045 PreCalculus for Engineering Topic 1 Example: 27 . ... 272727 . 11 3 , 375 . 8 3 , 2 = = = 5. Irrational Numbers  represented by decimals that neither repeats nor terminates. Example: ... 14159 . 3 , ... 414213 . 1 2 = = π 6. Real Numbers ( R )  all rational numbers together with all irrational numbers Equality 1. The reflexive Property: a a = 2. The symmetric property: If b a = , then a b = . 3. The principle of substitution: If b a = , we may substitute b for a in any expressions with a . Properties of Real Numbers For all the following properties, R c b a ∈ 2200 , , 1. Closure : b a + is a real number; ab is a real number. 2. Commutative Properties: a b b a a b b a ⋅ = ⋅ + = + ; 3. Associative Properties: ( 29 ( 29 c b a c b a c b a + + = + + = + + ( 29 ( 29 c b a c b a c b a ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ 4. Distributive Properties: ( 29 c a b a c b a ⋅ + ⋅ = + ⋅ ( 29 c b c a c b a ⋅ + ⋅ = ⋅ + 5. Identity Properties: a a a a a a = ⋅ = ⋅ = + = + 1 1 ; 0  additive identity; 1  multiplicative identity....
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 Spring '09
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 Real Numbers, Mathematics Dept

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