| Description |
1 online resource (xviii, 857 pages) : illustrations |
| Series |
Dover books on mathematics |
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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 |
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2.7 Review and Fallacies in Algebra2.8 Summary; 3 Fractions-Rational 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 Exponents-An 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 |
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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 Equations-Straight 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 Degree-Conics; 6.1 Strategy; 6.2 Circles; 6.3 Completing the Square |
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6.4 A More General Form of the Second-Degree 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 Functions-Missing 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 |
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7.10 On the Formal Differentiation of Functions7.11 Summary; 8 Geometric Applications; 8.1 Tangent and Normal Lines; 8.2 Higher Derivatives-Notation; 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 Functions-Place Holders |
| Summary |
This text focuses on the most widely used applications of mathematical methods, including those related to probability and statistics. The 4-part 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. : Prentice-Hall, ©1985 |
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Includes index |
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Print version record |
| Subject |
Mathematics.
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Mathematics
|
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MATHEMATICS -- Calculus.
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Mathematics
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| Form |
Electronic book
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| ISBN |
9780486138879 |
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0486138879 |
|
9781621986058 |
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1621986055 |
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