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Vectors in 2 or 3 dimensions /
Vectors in 2 or 3 Dimensions provides an introduction to vectors from their very basics. The author has approached the subject from a geometrical standpoint and although applications to mechanics will be pointed out and techniques from linear algebra employed, it is the geometric view which is empha...
| Cote: | Libro Electrónico |
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| Auteur principal: | |
| Format: | Électronique eBook |
| Langue: | Inglés |
| Publié: |
London :
Arnold,
1995.
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| Collection: | Modular mathematics series.
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| Sujets: | |
| Accès en ligne: | Texto completo |
Table des matières:
- Front Cover; Vectors in 2 or 3 Dimensions; Copyright Page; Table of Contents; Series Preface; Preface; Chapter 1. Introduction to Vectors; 1.1 Vectors and scalars; 1.2 Basic definitions and notation; 1.3 Addition of vectors; Summary; Further exercises; Chapter 2. Vector Equation of a Straight Line; 2.1 The vector equation of a straight line; 2.2 The cartesian equations of a straight line; 2.3 A point dividing a line segment in a given ratio; 2.4 Points of intersection of lines; 2.5 Some applications; Summary; Further exercises; Chapter 3. Scalar Products and Equations of Planes.
- 3.1 The scalar product3.2 Projections and components; 3.3 Angles from scalar products; 3.4 Vector equation of a plane; 3.5 The intersection of two planes; 3.6 The intersection of three planes; Summary; Further exercises; Chapter 4. Vector Products; 4.1 Definition and geometrical description; 4.2 Vector equation of a plane given three points on it; 4.3 Distance of a point from a line; 4.4 Distance between two lines; 4.5 The intersection of two planes; 4.6 Triple scalar product; 4.7 Triple vector product; Summary; Further exercises.
- Chapter 5. The Vector Spaces IR2 and IR3, Linear Combinations and Bases5.1 The vector space IRn; 5.2 Subspaces of IRn; 5.3 Linear combinations; 5.4 Bases for vector spaces; 5.5 Orthogonal bases; 5.6 Gram-Schmidt orthogonalisation process; Summary; Further exercises; Chapter 6. Linear Transformations; 6.1 Linear transformations; 6.2 Linear transformations of IR2; 6.3 Some special linear transformations of IR2; 6.4 Combinations of linear transformations; 6.5 Fixed lines, eigenvectors and eigenvalues; 6.6 Eigenvectors and eigenvalues in special cases; 6.7 Linear transformations of IR3.
- 6.8 Special cases in IR3Summary; Further exercises; Chapter 7. General Reflections, Rotations and Translations in IR3; 7.1 Reflections; 7.2 Rotation; 7.3 Translations; 7.4 Isometries; 7.5 Combinations of reflections, rotations and translations; Summary; Further exercises; Chapter 8. Vector-valued Functions of a Single Variable; 8.1 Parameters; 8.2 Differentiation of vectors and derived vectors in IR3; 8.3 Curves in three dimensions; 8.4 Rules for differentiating vectors; 8.5 The Serret-Frenet equations of a curve in IR3; Summary; Further exercises.
- Chapter 9. Non-rectangular Coordinate Systems and Surfaces9.1 Polar coordinates in IR2; 9.2 Spherical polar coordinates in IR3; 9.3 Cylindrical polar coordinates in IR3; 9.4 Surfaces; 9.5 Partial differentiation; 9.6 Tangent planes; 9.7 Gradient, divergence and curl; 9.8 Further study; Summary; Further exercises; Answers to Exercises; Index.