Examples of the Processes of the Differential and Integral Calculus |
From inside the book
Results 1-5 of 65
Page v
... corresponding one for differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem ...
... corresponding one for differentials , it is not applicable to all cases . Of this any one may satisfy himself by attempting to use it in transforming a multiple Integral from one system of independent variables to another , a problem ...
Page 52
... corresponding theorem in Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then du f ( x + h ) = u + h + + ...
... corresponding theorem in Finite Differences , and makes no application of it , or remark on its importance . The following is the statement of the theorem : If u = f ( x ) and a receive an increment h , then du f ( x + h ) = u + h + + ...
Page 76
... corresponding fore ( - ) " + 1 B2n - 1 1.2.3 ... ( 2n ) ' coefficient in 1 Ban - 1 is ( - ) " + 1 x 22 1.2.3 ... ( 2n ) 1 If therefore C2 , be the coefficient of " in the equation n x we have 2 B2n - 1 1.2.3 ( 2n ) ... = Can + 1 76 ...
... corresponding fore ( - ) " + 1 B2n - 1 1.2.3 ... ( 2n ) ' coefficient in 1 Ban - 1 is ( - ) " + 1 x 22 1.2.3 ... ( 2n ) 1 If therefore C2 , be the coefficient of " in the equation n x we have 2 B2n - 1 1.2.3 ( 2n ) ... = Can + 1 76 ...
Page 94
... correspond respectively to a maximum or minimum value of u if no such change of sign takes place the value a of a must be rejected . By applying this process to each of the : roots of the equations du dx du = 0 and = ∞ , we shall have ...
... correspond respectively to a maximum or minimum value of u if no such change of sign takes place the value a of a must be rejected . By applying this process to each of the : roots of the equations du dx du = 0 and = ∞ , we shall have ...
Page 103
... corresponding segment may be a maximum . Let a be the half - length of the arc , the radius of the α circle ; then is the half - angle of the segment . - 20 If u be the segment , a u = ax - x2 sin 00 Whence COS If cos a - = 0 , or 00 a ...
... corresponding segment may be a maximum . Let a be the half - length of the arc , the radius of the α circle ; then is the half - angle of the segment . - 20 If u be the segment , a u = ax - x2 sin 00 Whence COS If cos a - = 0 , or 00 a ...
Other editions - View all
Common terms and phrases
a² b2 a²x² angle arbitrary constant assume asymptote becomes branches C₁ Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular radius SECT singular points singular solution spiral Substituting subtangent surface tangent plane theorem triangle University of Cambridge vanish whence x²)³