Precalculus
A Prelude to Calculus
3rd Edition
Loose-leaf edition
576 pages
978-1-119-44333-9 (ISBN)
Description
Sheldon Axler's Precalculus: A Prelude to Calculus, 3rd Edition focuses only on topics that students actually need to succeed in calculus. This book is geared towards courses with intermediate algebra prerequisites and it does not assume that students remember any trigonometry. It covers topics such as inverse functions, logarithms, half-life and exponential growth, area, e, the exponential function, the natural logarithm and trigonometry.
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Other editions
Previous edition
Loose-leaf edition
11/2012
2nd Edition
Wiley
€124.06
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Person
Dr. Sheldon Axler is the dean of the College of Science and Engineering at San Francisco State University in California. He has received over a dozen awards, grants, and fellowships from different organizations including the M.I.T. Teaching Award, National Science Foundation ILI Grant, and the National Science Foundation Research Grants. He had published extensively in journals and has three other books to his name.
Content
About the Author v
Preface to the Instructor xv
Acknowledgments xxi
Preface to the Student xxiii
Chapter 0 The Real Numbers 1
0.1 The Real Line 2
Construction of the Real Line 2
Is Every Real Number Rational? 3
Problems 5
0.2 Algebra of the Real Numbers 6
Commutativity and Associativity 6
The Order of Algebraic Operations 7
The Distributive Property 8
Additive Inverses and Subtraction 9
Multiplicative Inverses and the Algebra of Fractions 10
Symbolic Calculators 13
Exercises, Problems, and Worked-out Solutions 15
0.3 Inequalities, Intervals, and Absolute Value 20
Positive and Negative Numbers 20
Inequalities 21
Intervals 23
Absolute Value 25
Exercises, Problems, and Worked-out Solutions 29
Chapter Summary and Chapter Review Questions 35
Chapter 1 Functions and Their Graphs 37
1.1 Functions 38
Definition and Examples 38
The Domain of a Function 41
The Range of a Function 42
Functions via Tables 44
Exercises, Problems, and Worked-out Solutions 45
1.2 The Coordinate Plane and Graphs 50
The Coordinate Plane 50
The Graph of a Function 52
Determining the Domain and Range from a Graph 54
Which Sets are Graphs of Functions? 56
Exercises, Problems, and Worked-out Solutions 56
1.3 Function Transformations and Graphs 63
Vertical Transformations: Shifting, Stretching, and Flipping 63
Horizontal Transformations: Shifting, Stretching, Flipping 66
Combinations of Vertical Function Transformations 68
Even Functions 71
Odd Functions 72
Exercises, Problems, and Worked-out Solutions 73
1.4 Composition of Functions 81
Combining Two Functions 81
Definition of Composition 82
Decomposing Functions 85
Composing More than Two Functions 85
Function Transformations as Compositions 86</
Preface to the Instructor xv
Acknowledgments xxi
Preface to the Student xxiii
Chapter 0 The Real Numbers 1
0.1 The Real Line 2
Construction of the Real Line 2
Is Every Real Number Rational? 3
Problems 5
0.2 Algebra of the Real Numbers 6
Commutativity and Associativity 6
The Order of Algebraic Operations 7
The Distributive Property 8
Additive Inverses and Subtraction 9
Multiplicative Inverses and the Algebra of Fractions 10
Symbolic Calculators 13
Exercises, Problems, and Worked-out Solutions 15
0.3 Inequalities, Intervals, and Absolute Value 20
Positive and Negative Numbers 20
Inequalities 21
Intervals 23
Absolute Value 25
Exercises, Problems, and Worked-out Solutions 29
Chapter Summary and Chapter Review Questions 35
Chapter 1 Functions and Their Graphs 37
1.1 Functions 38
Definition and Examples 38
The Domain of a Function 41
The Range of a Function 42
Functions via Tables 44
Exercises, Problems, and Worked-out Solutions 45
1.2 The Coordinate Plane and Graphs 50
The Coordinate Plane 50
The Graph of a Function 52
Determining the Domain and Range from a Graph 54
Which Sets are Graphs of Functions? 56
Exercises, Problems, and Worked-out Solutions 56
1.3 Function Transformations and Graphs 63
Vertical Transformations: Shifting, Stretching, and Flipping 63
Horizontal Transformations: Shifting, Stretching, Flipping 66
Combinations of Vertical Function Transformations 68
Even Functions 71
Odd Functions 72
Exercises, Problems, and Worked-out Solutions 73
1.4 Composition of Functions 81
Combining Two Functions 81
Definition of Composition 82
Decomposing Functions 85
Composing More than Two Functions 85
Function Transformations as Compositions 86</