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Woods F. S, Bailey F.H. — A course in mathematics. Volume I
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Название: A course in mathematics. Volume IАвторы: Woods F. S, Bailey F.H. Аннотация: This is an EXACT reproduction of a book published before 1923. This IS NOT an OCR'd book with strange characters, introduced typographical errors, and jumbled words. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 1907Количество страниц: 397Добавлена в каталог: 28.10.2012Операции: Положить на полку |
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Abscissa 36 Acceleration 202 Addition of segments of a straight line 32 Algebraic functions 43 121 Algebraic functions, differentiation of 178 Algebraic functions, implicit 188 Angle between two curves 211 Angle between two lines 57 Angle, eccentric 304 Angle, vectorial 329 angles 55 Arc, derivatives with respect to 197 347 Arc, length of 195 Arc, limit of ratio to chord 195 Archimedes, spiral of 332 Area 204 Area in polar coordinates 348 Area of an ellipse 304 Asymptote 128 Asymptote of an hyperbola 145 Auxiliary circle of ellipse 304 Axes of an ellipse 141 Axes of an hyperbola 145 Axis of a parabola 147 Axis, of symmetry 121 Axis, radical 175 Bisection of a line 39 Cardioid 337 Cassini, ovals of 338 Catenary 281 Center of a conic 238 Change from rectangular to oblique axes without change of origin 224 Change from rectangular to polar coordinates 341 Change of direction of axes without change of origin 221 Change of origin without change of direction of axes 217 Chord of contact 248 circle 134 Circle of curvature 354 Circle with center on known line 137 Circle, involute of 311 Circle, parametric equation of 303 Circle, polar equation of 342 Circle, tangent to a known line 136 Circle, through a known point 136 Circle, through three known points 138 Cissoid 151 Classes of functions 43 Coefficient of an element of a determinant 8 Collinear points 38 complex numbers 31 Complex numbers, roots of an equation 82 Components of velocity 200 Concavity of a curve 112 Conchoid 334 conic 148 229 Conic, classification 237 Conic, polar equation 343 Conic, through five points 241 Conjugate axis of an hyperbola 145 Conjugate complex numbers 32 Conjugate diameters 258 Conjugate hyperbolas 262 Constant 40 Constant of integration 206 Constant, chord of 248 Contact, point of 105 Continuity 101 Cooerdinate axes 35 Cooerdinate axes, change of 217 Coordinates, Cartesian 224 Coordinates, oblique 223 Coordinates, polar 329 Coordinates, rectangular 35 Coordinates, relation between rectangular and polar 341 Coordinates, transformation of 217 Curvature 353 Curvature, center of 356 Curvature, circle of 354 Curvature, radius of 354 300 301 Curve, Cartesian equation of 44 Curve, degree of 166 Curve, parametric equations of 302 Curve, polar equation of 330 Curve, slope of 99 Curves of second degree 229 Curves, intersection of 161 Cycloid 305 Degree of a curve 166 Depressed equation 79 Derivative 102 Derivative of 185 Derivative of a polynomial 97 103 Derivative with respect to an arc 196 347 Derivative, higher 111 187 Derivative, illustrations of 203 Derivative, second 110 Derivative, sign of 106 111 Derivative, theorems on 179 Descartes’ Rule of Signs 87 Descartes’ rule of signs, folium of 132 Determinants 1 Determinants, elements of 4 Determinants, expansion of 8 Determinants, minors of 4 Determinants, properties of 6 Diameters, conjugate 258 Diameters, of a conic 252 Diameters, of a parabola 254 Diameters, of an ellipse 256 Diameters, of an hyperbola 257 Differentiation 102 Differentiation of a polynomial 103 Differentiation of algebraic functions 178 Differentiation of implicit functions 188 Differentiation, formulas of, for 185 Differentiation, formulas of, for a polynomial 103 Differentiation, formulas of, for exponential functions 284 Differentiation, formulas of, for hyperbolic functions 290 Differentiation, formulas of, for inverse hyperbolic functions 291 Differentiation, formulas of, for inverse trigonometric functions 276 Differentiation, formulas of, for logarithmic functions 284 Differentiation, formulas of, for trigonometric functions 272 Differentiation, formulas of, general 184 Differentiation, successive 187 Direction of a curve 197 Direction of a curve in polar coordinates 345 Directrix of a conic 148 Directrix of a parabola 146 Directrix of an ellipse 149 Directrix of an hyperbola 149 Discontinuity 101 Discontinuity, examples of 41 128 268 282 Discriminant 117 Discriminant of a cubic equation 114 117 Discriminant of a quadratic equation 73 117 Discriminant of the general equation of the second degree 236 Distance between two points 36 Distance of a point from a straight line 63 e, the number 280 Eccentric angle of ellipse 304 Eccentricity of a conic 148 Elasticity 204 Elements of a determinant 4 Eliminants 23 Elimination 1 ellipse 139 Ellipse, parametric representation of 303 Ellipse, referred to conjugate diameters as axes 260 Energy, kinetic 203 Epicycloid 307 Epitrochoid 309 Equation in one variable with given roots 79 Equation in one variable, complex roots of 82 Equation in one variable, depressed 79 Equation in one variable, multiple roots of 116 Equation in one variable, Newton’s method of solution of 114 Equation in one variable, number of roots of 80 Equation in one variable, resultant 161 Equation in one variable, solution by factoring 77 Equation in one variable, solution of 89 Equation in one variable, sum and product of roots of 82 Equation of a curve 44 Equations in several variables, homogeneous 21 Equations in several variables, linear 1 Equations in several variables, systems of 12 Equations in two variables of first degree 52 Equations in two variables of second degree 229 Equations, transcendental 293 Evolute 357 Expansion of a determinant 8 Expansion of a determinant, coefficient of 204 Explicit algebraic function 188 Exponential functions 279 Exponential functions, differentiation of 284 Factoring of quadratic expressions 79 Factoring, solution of equations by 77 Factors and roots of a polynomial 81 83 Factors and roots of an equation 78 Foci of an ellipse 139 Foci of an hyperbola 142 Focus of a conic 148 Focus of a parabola 146 Folium of Descartes 132 force 202 Function 40 Functional notation 44 Functions, algebraic 43 121 Functions, classes of 43 Functions, defined by equations of the second degree 127 Functions, exponential 279 Functions, hyperbolic 288 Functions, inverse hyperbolic 291 Functions, inverse trigonometric 269 Functions, involving fractions 128 Functions, irrational 44 131 Functions, logarithmic 279 Functions, transcendental 44 266 Functions, trigonometric 266 Graph 40 Graphical representation 28 Harmonic division of a line 250 Harmonic motion 275 Harmonic property of polars 249 Homogeneous equations 21 Horner’s method 92 Hyperbola 142 Hyperbola, conjugate 262 Hyperbola, equilateral 146 Hyperbola, referred to asymptotes as axes 224 Hyperbola, referred to conjugate diameters as axes 259 Hyperbolic functions 288 Hyperbolic functions, differentiation of 290 292 Hyperbolic functions, inverse 291 Hyperbolic spiral 332 Hypocycloid 309 Hypocycloid, four-cusped 132 Hypotrochoid 309 imaginary numbers see "Number Complex" Implicit algebraic function 188 Increment 100 infinity 29 128 Inflection, points of 112 194 Initial line 329 Integration 205 Intercepts 53 Interchange of axes 223 Intersection of curves 161 Intersection of curves, number of points of 109 Involute 357 Involute of circle 311 Irrational number 28 Irrational number, algebraic functions 44 131 Irrational number, roots of an equation 92 114 Isolated point 120 kinetic energy 203 Latus rectum 211 Lemniscate 340 Limacon 336 Limit of 283 Limit of 270 Limit of ratio of arc to chord 195 Limiting cases of a conic 234 Limits 97 Limits, theorems on 178 Locus 45 Locus problems 316 Logarithm, Napierian 280 Logarithmic function 279 Logarithmic function, differentiation of 284 Logarithmic function, spiral 333 Maxima and minima 108 112 192 Minors of a determinant 4 Momentum 203 Motion, harmonic 275 Motion, uniform 199 Multiple roots of an equation 116 Napierian logarithm 280 Newton’s method of solving numerical equations 114 normal 64 191 Normal equation of straight line 64 Number, complex 31 Number, real 28 Oblique cooerdinates 223 Ordinate 36 Ovals of Cassini 338 parabola 146 Parabola, cubical 74 Parabola, referred to a diameter and a tangent as axes 255 Parabola, referred to tangent at ends of latus rectum 132 Parabola, semi-cubical 131 Parallel lines 56 59 Parametric representation of curves 302 Pedal curves 319 Perpendicular lines 57 59 plotting 36 329 Point of division 38 Polar cooerdinates 329 Polar of a point 247 Polars, reciprocal 251 Pole of a straight line 247 Pole of a system of polar coordinates 329 Polynomial 43 Polynomial of 74 Polynomial of first degree 50 Polynomial of second degree 70 Polynomial, derivative of 97 Polynomial, factors of 81 83 Polynomial, square root of 121 Problems on straight lines 58 Products, graphs of 83 Projection 34 Radical axis 175 Radius vector 329 Radius vector of curvature 354 360 361 Rate of change 203 Rational algebraic function 43 Rational number 28 Rational roots 89 Reciprocal polars 251 Resultant 23
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