Wolstenholme / Langford / Maxwell Elementary Vectors

The Commonwealth and International Library: Mathematics Division
1. Auflage 2014
ISBN: 978-1-4831-8192-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 116 Seiten, Web PDF

Elementary Vectors is an introductory course in vector analysis which is both rigorous and elementary, and demonstrates the elegance of vector methods in geometry and mechanics. Topics covered range from scalar and vector products of two vectors to differentiation and integration of vectors, as well as central forces and orbits. Comprised of seven chapters, this book begins with an introduction to relevant definitions; addition and subtraction of vectors; multiplication of a vector by a real number; position vectors and distance between two points; and direction cosines and direction ratios. The discussion then turns to scalar and vector products of two vectors; application of vector methods to simple kinematical and dynamical problems concerning the motion of a particle; and differentiation and integration of vectors. Central forces and orbits are also considered, along with the equation of a straight line and that of a plane. A parametric treatment of certain three-dimensional curves and curved surfaces, including the helix, is presented. This monograph will be of value to students, teachers, and practitioners of mathematics.

Autoren/Hrsg.

Wolstenholme, E. Oe.

Langford, W. J.

Maxwell, E. A.

Inhaltsverzeichnis

1;Front Cover;1
2;Elementary Vectors;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;7
6;CHAPTER I. Definitions; addition and subtraction of vectors; multiplication of a vector by a real number; applications to statistical problems; position vectors; distance between two points; direction cosines and direction ratios; applications to geometrical problems;8
6.1;1.1. Real Numbers and Scalar Quantities;8
6.2;1.2. Vector Quantities;8
6.3;1.3. Notation;8
6.4;1.4. Nomenclature;9
6.5;1.5. Equivalence of Two Vectors;9
6.6;1.6. Sum of Two Vectors;10
6.7;1.7. Difference of Two Vectors;11
6.8;1.8. Multiplication of a Vector by a Real Number;11
6.9;1.9. Sum of a Number of Vectors;12
6.10;1.10;13
6.11;1.11. Unit Vector;17
6.12;1.12. Components of a Vector;17
6.13;1.13. The Components of the Sum of Two Vectors;20
6.14;1.14;21
6.15;1.15. Modulus of a Vector in Terms of its Components in Three Mutually Perpendicular Directions;21
6.16;1.16. Oblique Axes;22
6.17;1.17. Direction Cosines and Direction Ratios;22
6.18;1.18. Geometrical AppUcation;24
6.19;1.19. Centroid of a Triangle;25
7;CHAPTER II. Scalar and vector products of two vectors; vector area; scalar and vector triple products;30
7.1;2.1;30
7.2;2.2;30
7.3;2.3;31
7.4;2.4;33
7.5;2.5. Scalar Product of Two Vectors;33
7.6;2.6. Vector Product of Two Vectors;34
7.7;2.7. Distributive Law—Scalar Product;35
7.8;2.8;37
7.9;2.9. Distributive Law—Vector Product;38
7.10;2.10;40
7.11;2.11;41
7.12;2.12;41
7.13;2.13;42
7.14;2.14. Vector Area;46
7.15;2.15. Triple Products of Three Vectors;47
7.16;2.16. Scalar Triple Product;47
7.17;2.17;49
7.18;2.18. Vector Triple Product;49
8;CHAPTER III. Differentiation and integration of vectors;52
8.1;3.1;52
8.2;3.2. Derivative of a Sum of Two Vectors;53
8.3;3.3. Derivative of a Product;54
8.4;3.4. Derivative of a Triple Product of Three Vectors;55
8.5;3.5. Integration;58
8.6;3.6;58
9;CHAPTER IV. Application of vector methods to simple kinematical and dynamical problems concerning the motion of a particle;61
9.1;4.1;61
9.2;4.2;62
9.3;4.3;63
9.4;4.4;64
9.5;4.5. Momentum;67
9.6;4.6. Newton's Laws of Motion Applied to a Particle;67
9.7;4.7;68
10;CHAPTER V. Central forces and orbits;73
10.1;5.1;73
10.2;5.2;73
10.3;5.3;74
10.4;5.4. The Inverse Square Law;75
10.5;5.5. The Inverse Square Law;80
10.6;5.6. Laws of Force Other than the Inverse Square Law;82
11;CHAPTER VI. Equation of a straight line; equation of a plane; geometrical problems;88
11.1;6.1;88
11.2;6.2. Equation of a Straight Line Through a Given Point in a Given Direction;88
11.3;6.3. Equation of a Straight Line through Two Given Points;89
11.4;6·4. Equation of a Plane Through a Given Point and Parallel to Two Given Vectors;90
11.5;6.5. Equation of a Plane Containing Three Given Points;91
11.6;6.6. Equation of a Plane Containing a Given Point and Normal to a Given Direction;92
11.7;6.7. Alternative Forms of the Equation of a Plane and of its Distance from the Origin;92
11.8;6.8. Vector Area and Condition for Collinearity;94
12;CHAPTER VII. Parametric equations of curves and curved surfaces;101
12.1;7.1. Parametric Equations;101
12.2;7.2. Tangent to a Curve;102
12.3;7.3. Tangent Plane to a Surface;103
12.4;7.4. Some Special Cases;106
13;ANSWERS;111
14;Index;116