Introductory Analysis,9780395524329

Introductory Analysis

by ; ; ;
ISBN13: 9780395524329
ISBN10: 0395524326
Format: Hardcover
Pub. Date: 1990-11-01
Publisher(s): McDougal Littell/Houghton Mifflin
List Price: $84.26

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Table of Contents

Foundations of Real Analysis
Sets and Sentences
Sets
1(4)
Open Sentences
5(5)
Conditional Sentences
10(3)
Real Numbers
Addition and Multiplication Properties of Real Numbers
13(6)
Order and Inequalities
19(4)
Absolute Value
23(5)
Subsets of R
28(4)
Review and Testing
Summary
32(1)
Test
33(8)
Analytic Geometry
Coordinate Geometry and Lines
The Cartesian Coordinate System: Distance and Midpoints
41(5)
Lines
46(7)
Conic Sections
Circles
53(3)
Ellipses
56(7)
Hyperbolas
63(6)
Parabolas
69(4)
Conic Sections
73(3)
Intersections of Conic Section
76(4)
Review and Testing
Summary
80(1)
Test
81(8)
Sequences, Series, and Limits
Mathematical Induction
Mathematical Induction
89(5)
The Binomial Theorem
94(5)
Sequences and Series
Recursive Definitions: Sequences and Series
99(4)
Arithmetic Sequences
103(5)
Geometric Sequences and Series
108(6)
Limits and Sequences
Limits of Sequences
114(5)
Infinite Series
119(6)
The Axiom of Completeness
125(4)
Integral and Rational Exponents
129(4)
Review and Testing
Summary
133(2)
Test
135(3)
Cumulative Review
138(3)
Functions and Limits
Functions
Functions and Functional Notation
141(5)
The Algebra of Functions
146(5)
Composition and Inversion of Functions
151(6)
Limits of Functions
Limits and Their Properties
157(6)
Continuous Functions
163(4)
The Intermediate-Value Theorem
167(5)
Limits Involving Infinity
172(5)
Review and Testing
Summary
177(1)
Test
178(7)
Theory of Polynomial Equations
Complex Numbers
The Complex Field
185(4)
The Complex Plane
189(4)
Square Roots of Complex Numbers
193(3)
General Theory of Polynomials
Polynomials Over Fields
196(5)
The Fundamental Theorem of Algebra
201(4)
Polynomials with Real Coefficients
Conjugate Imaginary Roots
205(3)
Bounds For Real Roots; Descartes' Rule
208(3)
Finding Rational Roots
211(4)
Review and Testing
Summary
215(1)
Test
216(5)
Introduction to Differential Calculus
Differentiation
Derivatives of Functions
221(5)
Properties of Derivatives
226(4)
Notations for Derivatives
230(4)
The Chain Rule
234(4)
Applications
Using Derivatives in Graphing
238(4)
Concavity and the Second Derivative
242(3)
Applied Maxima and Minima
245(8)
Derivatives as Rates of Change
253(5)
Newton's Method
258(4)
Review and Testing
Summary
262(1)
Test
263(5)
Cumulative Review
268(3)
Trigonometric Functions and Triangle Solving
Circular Functions of Numbers
The Sine and Cosine Functions
271(6)
The Other Circular Functions
277(4)
Trigonometric Functions of Angles
Angles and Angle Measure
281(5)
The Trigonometric Functions
286(4)
Values of the Trigonometric Functions
290(2)
Solving Triangles
Right Triangles
292(4)
The Laws of Cosines and Sines
296(4)
Solving General Triangles
300(5)
Areas of Triangles
305(3)
Review and Testing
Summary
308(1)
Test
309(4)
Trigonometric Identities and Graphs
Trigonometric Identities
Identities in One Variable
313(5)
Trigonometric Addition Formulas
318(4)
Double-Angle and Half-Angle Formulas
322(4)
More Trigonometric Identities
326(4)
Trigonometric Equations
330(4)
Trigonometric Graphs
Periodicity and Other Properties
334(4)
Sine and Cosine Graphs
338(5)
More General Sine Curves
343(5)
Other Trigonometric Graphs
348(2)
Inverse Trigonometric Functions
350(5)
Review and Testing
Summary
355(2)
Test
357(4)
Applications of Trigonometry
Applications Involving Polar Coordinates
The Polar Coordinate System
361(4)
Graphs of Polar Equations
365(4)
Polar Form of Complex Numbers
369(3)
Powers and Roots of Complex Numbers
372(3)
Parametric Equations
375(5)
Calculus of Trigonometric Functions
Some Trigonometric Limits
380(4)
Derivatives of the Trigonometric Functions
384(4)
Rates and Extrema
388(5)
Review and Testing
Summary
393(1)
Test
394(5)
Exponential and Logarithmic Functions
Exponential Functions
Real Exponents
399(4)
Exponential Functions
403(5)
The Natural Exponential Function
408(4)
Logarithmic Functions
Logarithmic Functions
412(4)
Laws of Logarithms
416(6)
Derivatives
Derivatives of Exponential and Logarithmic Functions
422(5)
Exponential Growth and Decay
427(5)
Review and Testing
Summary
432(1)
Test
433(5)
Cumulative Review
438(3)
Vectors
Vectors
Introduction to Vectors
441(5)
Three-Dimensional Space
446(5)
The Norm of a Vector
451(3)
The Dot Product
454(3)
Basis Vectors
457(5)
Applications
Applications of Vectors
462(4)
Vectors and Proofs
466(3)
Vector Spaces
469(2)
Review and Testing
Summary
471(1)
Test
472(7)
Matrices, Determinants, and Systems of Linear Equations
Transformations and Matrices
Linear Transformations
479(6)
Matrices
485(5)
Matrices of Linear Transformations
490(3)
Rotation of Axes
493(4)
Systems of Linear Equations
Linear Systems I
497(4)
Linear Systems II
501(4)
Determinants
505(5)
The Inverse of a Matrix
510(5)
Cramer's Rule
515(3)
Review and Testing
Summary
518(1)
Test
519(6)
Further Vector Topics
Planes and Lines
The Cross Product
525(5)
Planes
530(4)
Lines
534(5)
Surfaces
Quadric Surfaces
539(6)
Cylindrical and Spherical Coordinates
545(4)
Review and Testing
Summary
549(2)
Test
551(3)
Cumulative Review
554(3)
Introduction to Integral Calculus
Antiderivatives and Definite Integrals
Antiderivatives
557(4)
Integration by Substitution
561(4)
Definite Integrals
565(3)
Applications of Integration
Areas of Plane Regions
568(6)
Volumes of Solids
574(6)
Work and Energy
580(4)
Review and Testing
Summary
584(1)
Test
585(4)
Probability and Statistics
Probability
Permutations
589(5)
Combinations
594(5)
Probability
599(4)
Compound Events
603(7)
Random Variables and Probability Distributions
610(6)
Statistics
Statistical Measures
616(5)
Variance and Standard Deviation
621(5)
Normal Distributions
626(6)
Confidence Intervals
632(3)
Correlation
635(4)
Review and Testing
Summary
639(2)
Test
641(5)
Using the Tables 646(1)
Tables 647(22)
Reference Materials 669(2)
Glossary 671(9)
Index 680(9)
Credits 689(1)
Appendix: The &epsis;-δ Definition of Limit 690

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