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Copeland A.H. — Geometry, algebra, and trigonometry by vector methods
Copeland A.H. — Geometry, algebra, and trigonometry by vector methods



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Название: Geometry, algebra, and trigonometry by vector methods

Автор: Copeland A.H.

Аннотация:

The radically different elementary texts appearing recently mark a reaction against the failure of earlier books to take advantage of the modern developments in mathematics. In many of the new texts the novelty is in the subject matter, whereas in the present one modern methods are used to develop conventional subject matter. A cursory reading of this text may give the impression that the employment of these modern techniques presupposes a high degree of sophistication on the part of the student. This is not the case. The reader is carefully prepared for the modern techniques and they should cause no more difficulty than the older methods. Often a modern method has a much broader range of applicability than the older one, although the two methods can be applied with comparable difficulty to the development of a given subject. In such cases modern methods are used in this text.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1962

Количество страниц: 298

Добавлена в каталог: 25.01.2011

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$n$-dimensional space      31 147
Abelian group      29 221
Absolute value      12 71
Addition of vectors      6
Altitude      274
angle      215 225
Angle sum      231
Angular velocity vector      7
Area of parallelogram      45
Area of triangle      45
Associative law      6
Asymptote      84
Azimuth      274
Barycentric coordinates      87
Base of logarithm      251
Bisector of an angle      74
Cartesian coordinates      87
Characteristic equation      187 201
Characteristic of logarithm      246
circle      55
Circle, center and radius of      177
Colatitude      273
Commutative group      29
Commutative law      6 21
Completing the square      177 178
complex numbers      277 278
Component of a vector      15
Cone      144 211 273
Conic section      77 211
Conjugate complex      278
Consistency of postulates      149
Constant term      168
Coordinate plane      128
coordinates      12 18 27 34 35
Coordinates, barycentric      89
Coordinates, Cartesian      87
Coordinates, cylindrical      272
Coordinates, polar      265
Coordinates, spherical      272
Cosecant      233
Cosine      216
Cosine, inverse      262
Cosines, Law of      230 231
Cotangent      233
Cross product      113
Cross product term      185
Cubic equation      207
Cyclic order      119
Cylinder      144 272
Cylindrical coordinates      272
De Moivre’s Theorem      283
Degree      168
Determinant, higher order      153
Determinant, second order      50
Determinant, third order      91
Diagonal, principle      52
Diagonal, secondary      52
Direction      1
Direction perpendicular to given direction      41
Directrix      77
Discriminant      178
Displacement      17
Distance between two points      30 35 88
Distance formula      35 88
Distance from point to line      42 47 108
Distance from point to plane      109 122
Distributive law      21 118
Dividing a segment in a given ratio      39 91
Dividing a segment in a given ratio, problem      7
Dot product      21
Eccentricity      77
Eigen-value      187 201
Eigen-vector      187 201
ellipse      75 77 79
Ellipsoid      136 137
Elliptic paraboloid      140
Empty set      61
Equation of a line      47 88 164
Equation of locus      73
Equations, linear      54 99
Equations, simultaneous      160
Equilibrium of forces      10
Equivalent vectors      2
Expansion of determinant      52 93 154 156
Exponents      248
Extrapolation      241
Focus      77
force      7
Function, inverse trigonometric      261
Function, linear vector      47
Function, scalar      216
Function, trigonometric      216 233
Graphs of trigonometric functions      238 239 240
Group      29 221
Group, additive      221
Group, multiplicative      221
Higher degree equation      207
Hyperbola      77 82
Hyperbola, conjugate hyperbolas      85
Hyperbolic paraboloid      141
Hyperboloid      137 138 139
Identity      256
imaginary numbers      277
Inconsistent      149
Inequality, Schwarz      108
Inequality, triangle      109
intercept      67
Intercept formula      68
Interpolation      240
Intersection of lines      59
Intersection of planes      126 130
Intersection of sets      61
Inverse      221
Isometric projection      26
Latitude      273
Latus rectum      77
Law of Cosines      230 231
Law of Sines      230
Left handed      71 106
Line      36 88 150
Line parallel to a given line      66
Line perpendicular to a given line      66
Linear dependence      62 119
Linear equations      54 65 122 160
Linear equations, geometric properties of      65
Linear independence      62 110
Linear vector function      183 186
Locus, equation of      73 136
Logarithm      244
Logarithm, base of      244 251
longitude      273
Magnitude of a vector      1 22 30
Mantissa      246
Matrix      183 186 189 199 204
Minor of a determinant      52 93 94 95 154
Models of postulates      147
Multiplication of a vector by a number      11
Negative of a vector      9
Normal vector to a line      47
Normal vector to a plane      123
Obvious solution      63
Opposite sense      2
Orientation      71 106
Oriented angle      215 227
Origin      34
Origin of a ray      214
Origin of a vector      3
Orthonormal system      18 25 31
Orthonormal system, left handed      71 106
Orthonormal system, orientation of      71 106
Orthonormal system, right handed      71 106
parabola      77
Parabolic cylinder      143
Paraboloid      136 140 141
Parallelepiped, volume of      111
Parallelogram, area of      45
PARAMETER      37 88
Parametric equations      37 88
Perpendicular      16 22
Perpendicular, to a line      47
Perpendicular, to a plane      123
Plane      90
Plane analytic geometry      18 34
Point-slope formula      68
Point-slope formula, two-point formula      68
Polar coordinates      265
Postulates      5 29
Product of two determinants      69 104
Product, scalar (or dot)      21
Product, scalar triple      116
Product, vector (or cross)      113
Product, Vector triple      121
Projection      15
Pure imaginary      277
Pythagorean Theorem      23 28
Quadratic equation      169 173 199
Quadratic formula      177 178
Quadric surface      137
Radian measure      235
Ray      214
REAL      277
Reduction formula      223
Right handed      71 106
Rotation      169 180 182 194 280
Rotation, through an angle      218
Ruled surface      142
Ruler and compass constructions      210 287 288 289
Ruling      144
scalar      22
Scalar product      21
Scalar triple product      116
Schwarz inequality      108
Secant      233
Sense      1
Set      31 35
Set, empty      61
Sets, intersection of      61
Sets, union of      74
Signed minor      51 92 153
Sine      216
Sine, inverse      262
Sines, law of      230
Slide rule      242
slope      67
Slope-intercept formula      68
Space      31 147
Sphere      88 273
Spherical coordinates      272
Standard form of conic section      85
Sum of vectors      6
Surface, quadric      137
Surface, ruled      142
Symmetric determinant      176
Symmetric matrix      190 204
Symmetry      77 80 83
Tangent      233
Terminal point      3
Tetrahedron, volume of      111
Three dimensional space      25 31 147
TIP      3
Translation      169 193
Transpose of a determinant      53 97 156
Transpose of a matrix      190 204
Triangle inequality      109
Triangle, area of      45
Triangle, solution of      232 254
Trigonometry      214
Two-point formula      68
Union of sets      74
Unit vector      3
Unoriented angle      215 226 227
Vector      2
Vector function      183
Vector product      113
Vector space      31
Velocity      2
Velocity vector      2
Vertex of a cone      144
Work      17 20
Zero vector      9
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