A First Course in Higher AlbegraMacmillan, 1917 - 247 pàgines |
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a₁ b₁ algebraic Ax=0 Ax b₁ c₁ b₂ c₂ base binomial binomial theorem coefficients complex numbers constant continued fraction Corollary corresponding curve decimal places degree denominator derivative Descartes's rule determinant digits divided divisible divisor equa equal to zero evident Example exponent expression factor function geometric geometric progression geometric series given number graph greater Hence increasing infinite series infinitesimal integers irrational numbers less limit zero loga logarithms method modulus multiplied negative roots nth root number of decimal number of terms number of variations partial fractions positive integer positive number positive roots quotient r₂ rational numbers rational roots real numbers real roots represented result row or column second term series is convergent solution solved Sturm's theorem substituted subtraction synthetic division Theorem tion tive unity unknown quantities vanish WELLESLEY COLLEGE x-axis
Passatges populars
Pàgina 76 - The derivative of the product of two functions is equal to the first function times the derivative of the second plus the second times the derivative of the first. (4) The derivative of the quotient of two functions is equal to the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
Pàgina 17 - In the same way, since in action it frequently happens that no delay is permissible, it is very certain that, when it is not in our power to determine what is true, we ought to act according to what is most probable...
Pàgina 144 - Then by definition a1 = m, and a' = n. Multiplying these equations together we hare aI+» = mn. Whence x + y is the logarithm of mn. QED 122. Prop. 2. The logarithm of the quotient of two numbers is the logarithm of the dividend minus the logarithm of the divisor. DEM. — Let a be the base of the system, and m and n any two numbers whose logarithms are, respectively, x, and y. Then by definition wenave<tI=m, and a' = n. Dividing, we have a* — * = — . Whence x — y is the logarithm of — ....
Pàgina 75 - That is, the derivative of the product of a constant and a function is the product of the constant and the derivative of the function.
Pàgina v - ... and problems, which will serve to establish some connection between theory and practice. Logarithms are introduced in Chapter III, so as to make this method of computation available, early in the course, for the numerical valuation of unknowns from given data." . . . Professors Merrill and Smith say: "This book is an outgrowth of the conviction of the authors that Higher Algebra, to be worthy of the name, must employ advanced methods, and that the method which chiefly marks advanced work in analysis...
Pàgina 141 - ... and putteth other numbers in their place which perform as much as they can do, only by addition and subtraction, division by two or division by three. Which secret invention, being (as all other good things are) so much the better as it shall be the more common, I thought good heretofore to set forth in Latin for the public use of mathematicians. But now some of our countrymen in this Island, well affected to these studies and the more...
Pàgina 57 - The product of a constant and a variable 's also a variable, and the limit of the product of a constant and a variable is the product of the constant and the limit of the variable.
Pàgina 141 - Seeing there is nothing (right well beloved students in themathematickes) that is so troublesome to mathematicall practise, nor that doth more molest and hinder calculators, than the multiplications, divisions, square and cubical extractions of great numbers, which, besides the tedious expense of time, are for the most part subject to many slippery errors. I began, therefore, to consider in my minde, by what certaine and ready art I might remove those hindrances.
Pàgina 26 - It is an algebra upon algebra; a [* p. 136 above.] [t see p. 251 below.] calculus which enables us to combine and foretell the results of algebraical operations, in the same way as algebra itself enables us to dispense with the performance of the special operations of arithmetic.
Pàgina 19 - The general formula for the number of combinations of n things taken r at a time is C(n,r) = r\(nr)\ We have to find the number of combinations of 12 things taken 9 at a time.