Woods F. S, Bailey F.H. — A course in mathematics. Volume I
Обсудите книгу на
Нашли опечатку? Выделите ее мышкой и нажмите Ctrl+Enter
Название: A course in mathematics. Volume I
Авторы: 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.
Abscissa36 Acceleration202 Addition of segments of a straight line32 Algebraic functions43121 Algebraic functions, differentiation of178 Algebraic functions, implicit188 Angle between two curves211 Angle between two lines57 Angle, eccentric304 Angle, vectorial329 angles55 Arc, derivatives with respect to197347 Arc, length of195 Arc, limit of ratio to chord195 Archimedes, spiral of332 Area204 Area in polar coordinates348 Area of an ellipse304 Asymptote128 Asymptote of an hyperbola145 Auxiliary circle of ellipse304 Axes of an ellipse141 Axes of an hyperbola145 Axis of a parabola147 Axis, of symmetry121 Axis, radical175 Bisection of a line39 Cardioid337 Cassini, ovals of338 Catenary281 Center of a conic238 Change from rectangular to oblique axes without change of origin224 Change from rectangular to polar coordinates341 Change of direction of axes without change of origin221 Change of origin without change of direction of axes217 Chord of contact248 circle134 Circle of curvature354 Circle with center on known line137 Circle, involute of311 Circle, parametric equation of303 Circle, polar equation of342 Circle, tangent to a known line136 Circle, through a known point136 Circle, through three known points138 Cissoid151 Classes of functions43 Coefficient of an element of a determinant8 Collinear points38 complex numbers31 Complex numbers, roots of an equation82 Components of velocity200 Concavity of a curve112 Conchoid334 conic148229 Conic, classification237 Conic, polar equation343 Conic, through five points241 Conjugate axis of an hyperbola145 Conjugate complex numbers32 Conjugate diameters258 Conjugate hyperbolas262 Constant40 Constant of integration206 Constant, chord of248 Contact, point of105 Continuity101 Cooerdinate axes35 Cooerdinate axes, change of217 Coordinates, Cartesian224 Coordinates, oblique223 Coordinates, polar329 Coordinates, rectangular35 Coordinates, relation between rectangular and polar341 Coordinates, transformation of217 Curvature353 Curvature, center of356 Curvature, circle of354 Curvature, radius of354300301 Curve, Cartesian equation of44 Curve, degree of166 Curve, parametric equations of302 Curve, polar equation of330 Curve, slope of99 Curves of second degree229 Curves, intersection of161 Cycloid305 Degree of a curve166 Depressed equation79 Derivative102 Derivative of 185 Derivative of a polynomial97103 Derivative with respect to an arc196347 Derivative, higher111187 Derivative, illustrations of203 Derivative, second110 Derivative, sign of106111 Derivative, theorems on179 Descartes’ Rule of Signs87 Descartes’ rule of signs, folium of132 Determinants1 Determinants, elements of4 Determinants, expansion of8 Determinants, minors of4 Determinants, properties of6 Diameters, conjugate258 Diameters, of a conic252 Diameters, of a parabola254 Diameters, of an ellipse256 Diameters, of an hyperbola257 Differentiation102 Differentiation of a polynomial103 Differentiation of algebraic functions178 Differentiation of implicit functions188 Differentiation, formulas of, for 185 Differentiation, formulas of, for a polynomial103 Differentiation, formulas of, for exponential functions284 Differentiation, formulas of, for hyperbolic functions290 Differentiation, formulas of, for inverse hyperbolic functions291 Differentiation, formulas of, for inverse trigonometric functions276 Differentiation, formulas of, for logarithmic functions284 Differentiation, formulas of, for trigonometric functions272 Differentiation, formulas of, general184 Differentiation, successive187 Direction of a curve197 Direction of a curve in polar coordinates345 Directrix of a conic148 Directrix of a parabola146 Directrix of an ellipse149 Directrix of an hyperbola149 Discontinuity101 Discontinuity, examples of41128268282 Discriminant117 Discriminant of a cubic equation114117 Discriminant of a quadratic equation73117 Discriminant of the general equation of the second degree236 Distance between two points36 Distance of a point from a straight line63 e, the number280 Eccentric angle of ellipse304 Eccentricity of a conic148 Elasticity204 Elements of a determinant4 Eliminants23 Elimination1 ellipse139 Ellipse, parametric representation of303 Ellipse, referred to conjugate diameters as axes260 Energy, kinetic203 Epicycloid307
Epitrochoid309 Equation in one variable with given roots79 Equation in one variable, complex roots of82 Equation in one variable, depressed79 Equation in one variable, multiple roots of116 Equation in one variable, Newton’s method of solution of114 Equation in one variable, number of roots of80 Equation in one variable, resultant161 Equation in one variable, solution by factoring77 Equation in one variable, solution of89 Equation in one variable, sum and product of roots of82 Equation of a curve44 Equations in several variables, homogeneous21 Equations in several variables, linear1 Equations in several variables, systems of12 Equations in two variables of first degree52 Equations in two variables of second degree229 Equations, transcendental293 Evolute357 Expansion of a determinant8 Expansion of a determinant, coefficient of204 Explicit algebraic function188 Exponential functions279 Exponential functions, differentiation of284 Factoring of quadratic expressions79 Factoring, solution of equations by77 Factors and roots of a polynomial8183 Factors and roots of an equation78 Foci of an ellipse139 Foci of an hyperbola142 Focus of a conic148 Focus of a parabola146 Folium of Descartes132 force202 Function40 Functional notation44 Functions, algebraic43121 Functions, classes of43 Functions, defined by equations of the second degree127 Functions, exponential279 Functions, hyperbolic288 Functions, inverse hyperbolic291 Functions, inverse trigonometric269 Functions, involving fractions128 Functions, irrational44131 Functions, logarithmic279 Functions, transcendental44266 Functions, trigonometric266 Graph40 Graphical representation28 Harmonic division of a line250 Harmonic motion275 Harmonic property of polars249 Homogeneous equations21 Horner’s method92 Hyperbola142 Hyperbola, conjugate262 Hyperbola, equilateral146 Hyperbola, referred to asymptotes as axes224 Hyperbola, referred to conjugate diameters as axes259 Hyperbolic functions288 Hyperbolic functions, differentiation of290292 Hyperbolic functions, inverse291 Hyperbolic spiral332 Hypocycloid309 Hypocycloid, four-cusped132 Hypotrochoid309 imaginary numberssee "NumberComplex" Implicit algebraic function188 Increment100 infinity29128 Inflection, points of112194 Initial line329 Integration205 Intercepts53 Interchange of axes223 Intersection of curves161 Intersection of curves, number of points of109 Involute357 Involute of circle311 Irrational number28 Irrational number, algebraic functions44131 Irrational number, roots of an equation92114 Isolated point120 kinetic energy203 Latus rectum211 Lemniscate340 Limacon336 Limit of and 283 Limit of and 270 Limit of ratio of arc to chord195 Limiting cases of a conic234 Limits97 Limits, theorems on178 Locus45 Locus problems316 Logarithm, Napierian280 Logarithmic function279 Logarithmic function, differentiation of284 Logarithmic function, spiral333 Maxima and minima108112192 Minors of a determinant4 Momentum203 Motion, harmonic275 Motion, uniform199 Multiple roots of an equation116 Napierian logarithm280 Newton’s method of solving numerical equations114 normal64191 Normal equation of straight line64 Number, complex31 Number, real28 Oblique cooerdinates223 Ordinate36 Ovals of Cassini338 parabola146 Parabola, cubical74 Parabola, referred to a diameter and a tangent as axes255 Parabola, referred to tangent at ends of latus rectum132 Parabola, semi-cubical131 Parallel lines5659 Parametric representation of curves302 Pedal curves319 Perpendicular lines5759 plotting36329 Point of division38 Polar cooerdinates329 Polar of a point247 Polars, reciprocal251 Pole of a straight line247 Pole of a system of polar coordinates329 Polynomial43 Polynomial of degree74 Polynomial of first degree50 Polynomial of second degree70 Polynomial, derivative of97 Polynomial, factors of8183 Polynomial, square root of121 Problems on straight lines58 Products, graphs of83 Projection34 Radical axis175 Radius vector329 Radius vector of curvature354360361 Rate of change203 Rational algebraic function43 Rational number28 Rational roots89 Reciprocal polars251 Resultant23
and 
and 
degree 
|
|
О проекте