VECTOR ANALYSIS AND QUATERNIONS
AUTHOR'S PREFACE.
Since this introduction to "Vector Analysis and Quaternions" was first published in 1896, the study of the subject has become much more general; and whereas some reviewers then regarded the analysis as a luxury, it is now recognized as a necessity for the exact student of physics or engineering. In America, Professor Hathaway has published a "Primer of Quaternions" (New York, 1896), and Dr. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York, 1901). In Great Britain) Professor Henrici and Mr. Turner have published a manual for students entitled Vectors and Rotors (London, 1903); Dr. Knott has prepared a new edition of Kelland and Tait's "Introduction to Quaternions" (London, 1904); and Professor Joly has realized Hamilton's idea of a "Manual of Quaternions" (London, 1905). In Germany Dr. Bucherer has published "Elemente der Vektoranalysis" (Leipzig, 1903) which has now reached a second edition.
Also the writings of the great masters have been rendered more accessible. A new edition of Hamilton's classic, the "Elements of Quaternions," has been prepared by Professor Joly (London, 1899, 1901); Tait's Scientific Papers have been reprinted in collected form (Cambridge, 1898, 1900); and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig, 1894-). In the same interval many papers, pamphlets, and discussions have appeared. For those who desire information on the literature of the Subject a Bibliography has been published by the Association for the promotion of the study of "Quaternions and Allied Mathematics" (Dublin, 1904).
There is still much variety in the matter of notation, and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905).
****
An excerpt from the beginning:
1. Introduction.
By "Vector Analysis" is meant a space analysis in which the vector is the fundamental idea; by "Quaternions" is meant a space-analysis in which the quaternion is the fundamental idea. They are in truth complementary parts of one whole; and in this chapter they will be treated as such, and developed so as to harmonize with one another and with the Cartesian Analysis. The subject to be treated is the analysis of quantities in space, whether they are vector in nature, or quaternion in nature, or of a still different nature, or are of such a kind that they can be adequately represented by space quantities.
Every proposition about quantities in space ought to remain true when restricted to a plane; just as propositions about quantities in a plane remain true when restricted to a straight line. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. Arts. 2-4 treat of the more restricted analysis, while Arts. 5-10 treat of the general analysis.
This space analysis is a universal Cartesian analysis, in the same manner as algebra is a universal arithmetic. By providing an explicit notation for directed quantities, it enables their general properties to be investigated independently of any particular system of coordinates, whether rectangular, cylindrical, or polar. It also has this advantage that it can express the directed quantity by a linear function of the coordinates, instead of in a roundabout way by means of a quadratic function....
"1101048797"
Since this introduction to "Vector Analysis and Quaternions" was first published in 1896, the study of the subject has become much more general; and whereas some reviewers then regarded the analysis as a luxury, it is now recognized as a necessity for the exact student of physics or engineering. In America, Professor Hathaway has published a "Primer of Quaternions" (New York, 1896), and Dr. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York, 1901). In Great Britain) Professor Henrici and Mr. Turner have published a manual for students entitled Vectors and Rotors (London, 1903); Dr. Knott has prepared a new edition of Kelland and Tait's "Introduction to Quaternions" (London, 1904); and Professor Joly has realized Hamilton's idea of a "Manual of Quaternions" (London, 1905). In Germany Dr. Bucherer has published "Elemente der Vektoranalysis" (Leipzig, 1903) which has now reached a second edition.
Also the writings of the great masters have been rendered more accessible. A new edition of Hamilton's classic, the "Elements of Quaternions," has been prepared by Professor Joly (London, 1899, 1901); Tait's Scientific Papers have been reprinted in collected form (Cambridge, 1898, 1900); and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig, 1894-). In the same interval many papers, pamphlets, and discussions have appeared. For those who desire information on the literature of the Subject a Bibliography has been published by the Association for the promotion of the study of "Quaternions and Allied Mathematics" (Dublin, 1904).
There is still much variety in the matter of notation, and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905).
****
An excerpt from the beginning:
1. Introduction.
By "Vector Analysis" is meant a space analysis in which the vector is the fundamental idea; by "Quaternions" is meant a space-analysis in which the quaternion is the fundamental idea. They are in truth complementary parts of one whole; and in this chapter they will be treated as such, and developed so as to harmonize with one another and with the Cartesian Analysis. The subject to be treated is the analysis of quantities in space, whether they are vector in nature, or quaternion in nature, or of a still different nature, or are of such a kind that they can be adequately represented by space quantities.
Every proposition about quantities in space ought to remain true when restricted to a plane; just as propositions about quantities in a plane remain true when restricted to a straight line. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. Arts. 2-4 treat of the more restricted analysis, while Arts. 5-10 treat of the general analysis.
This space analysis is a universal Cartesian analysis, in the same manner as algebra is a universal arithmetic. By providing an explicit notation for directed quantities, it enables their general properties to be investigated independently of any particular system of coordinates, whether rectangular, cylindrical, or polar. It also has this advantage that it can express the directed quantity by a linear function of the coordinates, instead of in a roundabout way by means of a quadratic function....
VECTOR ANALYSIS AND QUATERNIONS
AUTHOR'S PREFACE.
Since this introduction to "Vector Analysis and Quaternions" was first published in 1896, the study of the subject has become much more general; and whereas some reviewers then regarded the analysis as a luxury, it is now recognized as a necessity for the exact student of physics or engineering. In America, Professor Hathaway has published a "Primer of Quaternions" (New York, 1896), and Dr. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York, 1901). In Great Britain) Professor Henrici and Mr. Turner have published a manual for students entitled Vectors and Rotors (London, 1903); Dr. Knott has prepared a new edition of Kelland and Tait's "Introduction to Quaternions" (London, 1904); and Professor Joly has realized Hamilton's idea of a "Manual of Quaternions" (London, 1905). In Germany Dr. Bucherer has published "Elemente der Vektoranalysis" (Leipzig, 1903) which has now reached a second edition.
Also the writings of the great masters have been rendered more accessible. A new edition of Hamilton's classic, the "Elements of Quaternions," has been prepared by Professor Joly (London, 1899, 1901); Tait's Scientific Papers have been reprinted in collected form (Cambridge, 1898, 1900); and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig, 1894-). In the same interval many papers, pamphlets, and discussions have appeared. For those who desire information on the literature of the Subject a Bibliography has been published by the Association for the promotion of the study of "Quaternions and Allied Mathematics" (Dublin, 1904).
There is still much variety in the matter of notation, and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905).
****
An excerpt from the beginning:
1. Introduction.
By "Vector Analysis" is meant a space analysis in which the vector is the fundamental idea; by "Quaternions" is meant a space-analysis in which the quaternion is the fundamental idea. They are in truth complementary parts of one whole; and in this chapter they will be treated as such, and developed so as to harmonize with one another and with the Cartesian Analysis. The subject to be treated is the analysis of quantities in space, whether they are vector in nature, or quaternion in nature, or of a still different nature, or are of such a kind that they can be adequately represented by space quantities.
Every proposition about quantities in space ought to remain true when restricted to a plane; just as propositions about quantities in a plane remain true when restricted to a straight line. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. Arts. 2-4 treat of the more restricted analysis, while Arts. 5-10 treat of the general analysis.
This space analysis is a universal Cartesian analysis, in the same manner as algebra is a universal arithmetic. By providing an explicit notation for directed quantities, it enables their general properties to be investigated independently of any particular system of coordinates, whether rectangular, cylindrical, or polar. It also has this advantage that it can express the directed quantity by a linear function of the coordinates, instead of in a roundabout way by means of a quadratic function....
Since this introduction to "Vector Analysis and Quaternions" was first published in 1896, the study of the subject has become much more general; and whereas some reviewers then regarded the analysis as a luxury, it is now recognized as a necessity for the exact student of physics or engineering. In America, Professor Hathaway has published a "Primer of Quaternions" (New York, 1896), and Dr. Wilson has amplified and extended Professor Gibbs' lectures on vector analysis into a text-book for the use of students of mathematics and physics (New York, 1901). In Great Britain) Professor Henrici and Mr. Turner have published a manual for students entitled Vectors and Rotors (London, 1903); Dr. Knott has prepared a new edition of Kelland and Tait's "Introduction to Quaternions" (London, 1904); and Professor Joly has realized Hamilton's idea of a "Manual of Quaternions" (London, 1905). In Germany Dr. Bucherer has published "Elemente der Vektoranalysis" (Leipzig, 1903) which has now reached a second edition.
Also the writings of the great masters have been rendered more accessible. A new edition of Hamilton's classic, the "Elements of Quaternions," has been prepared by Professor Joly (London, 1899, 1901); Tait's Scientific Papers have been reprinted in collected form (Cambridge, 1898, 1900); and a complete edition of Grassmann's mathematical and physical works has been edited by Friedrich Engel with the assistance of several of the eminent mathematicians of Germany (Leipzig, 1894-). In the same interval many papers, pamphlets, and discussions have appeared. For those who desire information on the literature of the Subject a Bibliography has been published by the Association for the promotion of the study of "Quaternions and Allied Mathematics" (Dublin, 1904).
There is still much variety in the matter of notation, and the relation of Vector Analysis to Quaternions is still the subject of discussion (see Journal of the Deutsche Mathematiker-Vereinigung for 1904 and 1905).
****
An excerpt from the beginning:
1. Introduction.
By "Vector Analysis" is meant a space analysis in which the vector is the fundamental idea; by "Quaternions" is meant a space-analysis in which the quaternion is the fundamental idea. They are in truth complementary parts of one whole; and in this chapter they will be treated as such, and developed so as to harmonize with one another and with the Cartesian Analysis. The subject to be treated is the analysis of quantities in space, whether they are vector in nature, or quaternion in nature, or of a still different nature, or are of such a kind that they can be adequately represented by space quantities.
Every proposition about quantities in space ought to remain true when restricted to a plane; just as propositions about quantities in a plane remain true when restricted to a straight line. Hence in the following articles the ascent to the algebra of space is made through the intermediate algebra of the plane. Arts. 2-4 treat of the more restricted analysis, while Arts. 5-10 treat of the general analysis.
This space analysis is a universal Cartesian analysis, in the same manner as algebra is a universal arithmetic. By providing an explicit notation for directed quantities, it enables their general properties to be investigated independently of any particular system of coordinates, whether rectangular, cylindrical, or polar. It also has this advantage that it can express the directed quantity by a linear function of the coordinates, instead of in a roundabout way by means of a quadratic function....
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VECTOR ANALYSIS AND QUATERNIONS
VECTOR ANALYSIS AND QUATERNIONS
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Product Details
| BN ID: | 2940016378657 |
|---|---|
| Publisher: | OGB |
| Publication date: | 03/03/2013 |
| Series: | Mathematical Monographs , #8 |
| Sold by: | Barnes & Noble |
| Format: | eBook |
| File size: | 3 MB |
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