Fundamentals of College Mathematics

Fundamentals of College Mathematics
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Fundamentals of College Mathematics

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Publisher: Laxmi Publications
ISBN: 9789351380054
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Preface ....................................................................................................................................... v Syllabus ............................................................................................................................ vi vii
1
LOGIC AND SET THEORY
1 44
1.1 Definition and Examples of Propositions ....................................................................... 1 1.2 Compound or Complex Propositions ............................................................................ 2 1.3 Logical Connectives ........................................................................................................ 2 1.4 Tautology and Contradiction .......................................................................................... 6 1.5 Open Proposition and Quantifiers ................................................................................. 9 1.6 The Concept of a Set and the Underlying Set Operations .......................................... 20 Unit Exercise .......................................................................................................................... 41 Summary ............................................................................................................................... 43
2
THE REAL AND C OMPLEX N UMBER SYSTEMS
45 108
2.1 The Real Number System ............................................................................................. 45 2.1.1 The Natural Numbers, Principle of Mathematical Induction and the Well Ordering Principle ........................................................................................... 47 2.1.2 The Integers, Rational Numbers, and Irrational Numbers ........................... 60 2.1.3 Upper Bound, Lower Bound, lub, glb, Completeness Property of the Set of Real Numbers and the Archimedean Principle ............................. 77 2.2 Complex Number System ............................................................................................. 84 2.2.1 Definition of Complex Numbers and Underlying Operations ........................ 84 2.2.2 Polar Representation of Complex Numbers and the De Moivre s Formula .. 90 2.2.3 Extraction of Roots ........................................................................................... 98 Unit Exercise ........................................................................................................................ 105 Summary .............................................................................................................................. 108
3
FUNCTIONS
109 193
3.1 Review of Relations and Functions ............................................................................ 109 3.2 Real Valued Functions and Their Properties ............................................................ 118 3.3 Types of Functions One-to-One, Onto and Inverse of a Function .......................... 123
3.4 Polynomials, Zero s of Polynomials, Rational Functions, and Their Graphs ........... 130 3.5 Definitions and Basic Properties of Logarithmic, Exponential, Hyperbolic, Trigonometric Functions, and Their Graphs ............................................................. 140 Unit Exercise ........................................................................................................................ 189