search for books and compare prices
Tables of Contents for A Primer for Calculus
Chapter/Section Title
Page #
Page Count
Preface
vii
7
To the Student
xiv
3
A Note on Calculators
xvii
1 BASIC ALGEBRAIC CONCEPTS
1
62
1 The Real Number System
2
8
2 Order Properties and Absolute Value
10
4
3 The Arithmetic of Rational Numbers
14
8
4 Integral Exponents
22
7
5 Radicals and Fractional Exponents
29
5
6 The Arithmetic of Polynomials
34
8
7 Factoring
42
8
8 Rational Fractions
50
6
9 Other Fractional Expressions
56
7
Review Exercise Set
59
4
2 EQUATIONS AND INEQUALITIES OF THE FIRST AND SECOND DEGREE
63
54
1 Introduction
64
1
2 Linear Equations
65
4
3 Quadratic Equations
69
2
4 Completing the Square and the Quadratic Formula
71
5
5 Complex Numbers
76
6
6 Equations That Are Convertible to Linear or Quadratic Forms
82
7
7 Applications
89
11
8 Linear Inequalities
100
4
9 Inequalities and Absolute Value
104
3
10 Quadratic and Other Nonlinear Inequalities
107
10
Review Exercise Set
113
4
3 FUNCTIONS AND GRAPHS
117
58
1 The Cartesian Coordinate System and Graphs of Equations
118
11
2 The Function Concept
129
11
3 Graphs of Functions
140
10
4 Combinations of Functions
150
5
5 One-to-One Functions and Inverses
155
8
6 Variation
163
12
Review Exercise Set
169
3
Cumulative Review Exercise Set I (Chapters 1-3)
172
3
4 LINEAR AND QUADRATIC FUNCTIONS; INTRODUCTION TO CONIC SECTIONS
175
44
1 Introduction
176
1
2 Equations of Lines
176
12
3 Linear Functions
188
4
4 Quadratic Functions
192
12
5 Introduction to Conic Sections
204
15
Review Exercise Set
215
4
5 HIGHER-DEGREE POLYNOMIAL AND RATIONAL FUNCTIONS
219
50
1 Historical Note
220
1
2 The Remainder Theorem and the Factor Theorem
220
2
3 Synthetic Division
222
4
4 The Fundamental Theorem of Algebra and Its Corollaries
226
3
5 Rational Roots
229
10
6 Irrational Roots
239
6
7 Graphing Polynomial Functions
245
6
8 Rational Functions
251
9
9 Partial Fractions
260
9
Review Exercise Set
266
3
6 EXPONENTIAL AND LOGARITHMIC FUNCTIONS
269
34
1 The Exponential Function
270
8
2 Inverses of Exponential Functions
278
6
3 Properties of Logarithms
284
8
4 Applications of Exponential and Logarithmic Functions
292
11
Review Exercise Set
299
2
Cumulative Review Exercise Set II (Chapters 4-6)
301
2
7 THE TRIGONOMETRIC FUNCTIONS
303
46
1 Introduction
304
1
2 The Measurement of Angles
304
7
3 Some Special Angles
311
5
4 Trigonometric Functions of Angles
316
10
5 Trigonometric Functions of Real Numbers
326
4
6 Graphs of the Trigonometric Functions
330
8
7 The Inverse Trigonometric Functions
338
11
Review Exercise Set
347
2
8 TRIGONOMETRIC IDENTITIES AND EQUATIONS
349
36
1 Basic Trigonometric Identities
350
7
2 The Addition Formulas for Sine and Cosine
357
7
3 Double-Angle, Half-Angle, and Reduction Formulas
364
6
4 Further Identities
370
4
5 Trigonometric Equations
374
11
Review Exercise Set
382
3
9 THE SOLUTION OF TRIANGLES
385
36
1 Right Triangle Trigonometry
385
9
2 The Law of Sines
394
7
3 The Law of Cosines
401
5
4 Areas of Triangles
406
3
5 Vectors
409
12
Review Exercise Set
417
4
10 FURTHER APPLICATIONS OF TRIGONOMETRIC FUNCTIONS
421
30
1 Polar Coordinates
422
9
2 Parametric Equations
431
7
3 Trigonometric Form of Complex Numbers
438
13
Review Exercise Set
445
2
Cumulative Review Exercise Set III (Chapters 7-10)
447
4
11 SYSTEMS OF EQUATIONS AND INEQUALITIES
451
66
1 Linear Systems
452
12
2 Reduction to Triangular Form and the Use of Matrices
464
9
3 Determinants
473
6
4 Cramer's Rule
479
6
5 The Algebra of Matrices
485
5
6 Inverses of Matrices
490
6
7 Nonlinear Systems
496
6
8 Systems of Inequalities
502
4
9 Linear Programming
506
11
Review Exercise Set
512
5
12 THE CONIC SECTIONS
517
40
1 Introduction
518
1
2 The Locus of a Point
519
2
3 The Circle
521
3
4 The Parabola
524
7
5 The Ellipse
531
7
6 The Hyperbola
538
7
7 The General Second-Degree Equation and the Rotation of Axes
545
12
Review Exercise Set
555
2
13 SEQUENCES AND SERIES
557
1 Sequences
558
5
2 Arithmetic and Geometric Sequences
563
5
3 Series
568
6
4 Infinite Geometric Series
574
6
5 Mathematical Induction
580
6
6 Proof of the Binomial Theorem
586
Review Exercise Set
590
2
Cumulative Review Exercise Set IV (Chapters 11-13)
592
Answers to Selected Problems
AN-I
Index
IN-I