Description 
1 online resource (xviii, 857 pages) : illustrations 
Series 
Dover books on mathematics 

Dover books on mathematics.

Contents 
Cover; Title Page; Copyright Page; Contents; Preface; I  Algebra and Analytic Geometry; 1 Prologue; 1.1 The Importance of Mathematics; 1.2 The Uniqueness of Mathematics; 1.3 The Unreasonable Effectiveness of Mathematics; 1.4 Mathematics as a Language; 1.5 What is Mathematics?; 1.6 Mathematical Rigor; 1.7 Advice to You; 1.8 Remarks on Learning the Course; References; 2 The Integers; 2.1 The Integers; 2.2 On Proving Theorems; 2.3 Mathematical Induction; 2.4 The Binomial Theorem; 2.5 Mathematical Induction Using Undetermined Coefficients; 2.6 The Ellipsis Method 

2.7 Review and Fallacies in Algebra2.8 Summary; 3 FractionsRational Numbers; 3.1 Rational Numbers; 3.2 Euclid's Algorithm; 3.3 The Rational Number System; 3.4 Irrational Numbers; 3.5 On Finding Irrational Numbers; 3.6 Decimal Representation of a Rational Number; 3.7 Inequalities; 3.8 ExponentsAn Application of Rational Numbers; 3.9 Summary and Further Remarks; 4 Real Numbers, Functions, and Philosophy; 4.1 The Real Line; 4.2 Philosophy; 4.3 The Idea of a Function; 4.4 The Absolute Value Function; 4.5 Assumptions About Continuity; 4.6 Polynomials and Integers; 4.7 Linear Independence 

4.8 Complex Numbers4.9 More Philosophy; 4.10 Summary; 5 Analytic Geometry; 5.1 Cartesian Coordinates; 5.2 The Pythagorean Distance; 5.3 Curves; 5.4 Linear EquationsStraight Lines; 5.5 Slope; 5.6 Special Forms of the Straight Line; 5.7 On Proving Geometric Theorems in Analytic Geometry; 5.8* The Normal Form of the Straight Line; 5.9 Translation of the Coordinate Axes; 5.10* The Area of a Triangle; 5.11* A Problem in Computer Graphics; 5.12 The Complex Plane; 5.13 Summary; 6 Curves of Second DegreeConics; 6.1 Strategy; 6.2 Circles; 6.3 Completing the Square 

6.4 A More General Form of the SecondDegree Equation 6.5 Ellipses; 6.6 Hyperbolas; 6.7 Parabolas; 6.8 Miscellaneous Cases; 6.9* Rotation of the Coordinate Axes; 6.10* The General Analysis; 6.11 Symmetry; 6.12 Nongeometric Graphing; 6.13 Summary of Analytic Geometry; II  The Calculus of Algebraic Functions; 7 Derivatives in Geometry; 7.1 A History of the Calculus; 7.2 The Idea of a Limit; 7.3 Rules for Using Limits; 7.4 Limits of FunctionsMissing Values; 7.5 The "Process; 7.6 Composite Functions; 7.7 Sums of Powers of x; 7.8 Products and Quotients; 7.9 An Abstraction of Differentiation 

7.10 On the Formal Differentiation of Functions7.11 Summary; 8 Geometric Applications; 8.1 Tangent and Normal Lines; 8.2 Higher DerivativesNotation; 8.3 Implicit Differentiation; 8.4 Curvature; 8.5 Maxima and Minima; 8.6 Inflection Points; 8.7 Curve Tracing; 8.8 Functions, Equations, and Curves; 8.9 Summary; 9 Nongeometric Applications; 9.1 Scaling Geometry; 9.2 Equivalent Ideas; 9.3 Velocity; 9.4 Acceleration; 9.5 Simple Rate Problems; 9.6 More Rate Problems; 9.7 Newton's Method for Finding Zeros; 9.8 Multiple Zeros; 9.9 The Summation Notation; 9.10 Generating Identities; 9.11 Generating FunctionsPlace Holders 
Summary 
This text focuses on the most widely used applications of mathematical methods, including those related to probability and statistics. The 4part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables 
Notes 
Originally published: Englewood Cliffs, N.J. : PrenticeHall, ©1985 

Includes index 

Print version record 
Subject 
Mathematics.


Mathematics


MATHEMATICS  Calculus.


Mathematics.

Form 
Electronic book

ISBN 
9780486138879 

0486138879 

9781621986058 

1621986055 
