Cargando…
Beyond the Quadratic /
The quadratic formula for the solution of quadratic equations was discovered independently by scholars in many ancient cultures and is familiar to everyone. Less well known are formulas for solutions of cubic and quartic equations whose discovery was the high point of 16th century mathematics. Their...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge :
Cambridge University Press,
2013.
|
| Colección: | Classroom resource materials.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front cover ; copyright page ; title page ; Preface; Contents; Polynomials; Definitions; Multiplication and Degree; Factorization and Roots; Bounding the Number of Roots; Real Numbers and the Intermediate Value Theorem; Graphs; Quadratic Polynomials; Sums and Products; Completing the Square; Changing Variables; A Discriminant; History; Cubic Polynomials; Reduced Cubics; Cardano's Formula; Graphs; A Discriminant; History; Complex Numbers; Complex Numbers; Quadratic Polynomials and the Discriminant; Square and Cube Roots; The Complex Plane; A Geometric Interpretation of Multiplication.
- Euler's and de Moivre's FormulasRoots of Unity; Converting Root Extraction to Division; History; Cubic Polynomials, II; Cardano's formula; The Resolvent; The Discriminant; Cardano's Formula Refined; The Irreducible Case; Viète's Formula; The Signs of the Real Roots; History; Quartic Polynomials; Reduced Quartics; Ferrari's Method; Descartes' Method; Euler's Formula; The Discriminant; The Nature of the Roots; Cubic and Quartic Reprise; History; Higher-Degree Polynomials; Quintic Polynomials; The Fundamental Theorem of Algebra; Polynomial Factorization; Symmetric Polynomials.
- A Proof of the Fundamental TheoremReferences; Index; About the Author.