Vectors in 2 or 3 dimensions:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
London
Arnold
1995
|
| Schriftenreihe: | Modular mathematics series
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 |
| Beschreibung: | Includes index 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 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 emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to mo |
| Beschreibung: | x, 134 pages : |
| ISBN: | 9780080572017 0080572014 0340614692 9780340614693 |
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| 245 | 1 | 0 | |a Vectors in 2 or 3 dimensions |c A.E. Hirst |
| 246 | 1 | 3 | |a Vectors in two or three dimensions |
| 264 | 1 | |a London |b Arnold |c 1995 | |
| 300 | |a x, 134 pages : | ||
| 336 | |b txt |2 rdacontent | ||
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| 490 | 0 | |a Modular mathematics series | |
| 500 | |a Includes index | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 | ||
| 500 | |a 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 emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to mo | ||
| 650 | 4 | |a Vector algebra | |
| 650 | 4 | |a Vector analysis | |
| 650 | 7 | |a MATHEMATICS / Vector Analysis |2 bisacsh | |
| 650 | 7 | |a Vector algebra |2 fast | |
| 650 | 7 | |a Vector analysis |2 fast | |
| 650 | 4 | |a Vector analysis | |
| 650 | 4 | |a Vector algebra | |
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Datensatz im Suchindex
| _version_ | 1804176599123230720 |
|---|---|
| any_adam_object | |
| author | Hirst, A. E. |
| author_facet | Hirst, A. E. |
| author_role | aut |
| author_sort | Hirst, A. E. |
| author_variant | a e h ae aeh |
| building | Verbundindex |
| bvnumber | BV043774312 |
| collection | ZDB-4-EBA |
| ctrlnum | (ZDB-4-EBA)ocn815471179 (OCoLC)815471179 (DE-599)BVBBV043774312 |
| dewey-full | 515/.63 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.63 |
| dewey-search | 515/.63 |
| dewey-sort | 3515 263 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV043774312 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:34:44Z |
| institution | BVB |
| isbn | 9780080572017 0080572014 0340614692 9780340614693 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029185372 |
| oclc_num | 815471179 |
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| owner_facet | DE-1046 DE-1047 |
| physical | x, 134 pages : |
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| publishDate | 1995 |
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| publisher | Arnold |
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| series2 | Modular mathematics series |
| spelling | Hirst, A. E. Verfasser aut Vectors in 2 or 3 dimensions A.E. Hirst Vectors in two or three dimensions London Arnold 1995 x, 134 pages : txt rdacontent c rdamedia cr rdacarrier Modular mathematics series Includes index 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 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 emphasised throughout. Properties of vectors are initially introduced before moving on to vector algebra and transformation geometry. Vector calculus as a means of studying curves and surfaces in 3 dimensions and the concept of isometry are introduced later, providing a stepping stone to mo Vector algebra Vector analysis MATHEMATICS / Vector Analysis bisacsh Vector algebra fast Vector analysis fast Vektorrechnung (DE-588)4062471-7 gnd rswk-swf Vektorrechnung (DE-588)4062471-7 s 1\p DE-604 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hirst, A. E. Vectors in 2 or 3 dimensions Vector algebra Vector analysis MATHEMATICS / Vector Analysis bisacsh Vector algebra fast Vector analysis fast Vektorrechnung (DE-588)4062471-7 gnd |
| subject_GND | (DE-588)4062471-7 |
| title | Vectors in 2 or 3 dimensions |
| title_alt | Vectors in two or three dimensions |
| title_auth | Vectors in 2 or 3 dimensions |
| title_exact_search | Vectors in 2 or 3 dimensions |
| title_full | Vectors in 2 or 3 dimensions A.E. Hirst |
| title_fullStr | Vectors in 2 or 3 dimensions A.E. Hirst |
| title_full_unstemmed | Vectors in 2 or 3 dimensions A.E. Hirst |
| title_short | Vectors in 2 or 3 dimensions |
| title_sort | vectors in 2 or 3 dimensions |
| topic | Vector algebra Vector analysis MATHEMATICS / Vector Analysis bisacsh Vector algebra fast Vector analysis fast Vektorrechnung (DE-588)4062471-7 gnd |
| topic_facet | Vector algebra Vector analysis MATHEMATICS / Vector Analysis Vektorrechnung |
| work_keys_str_mv | AT hirstae vectorsin2or3dimensions AT hirstae vectorsintwoorthreedimensions |