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Methods of mathematics applied to calculus, probability, and statistics /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Mineola, N.Y. :
Dover Publications,
2004.
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| Edición: | Dover ed. |
| Colección: | Dover books on mathematics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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 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.
- 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.
- 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.
- 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.