Columbia University Press, 1912 - Algebra - 148 pages

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Page 150 - Price, \$1.50 net. THE PRINCIPLES OF POLITICS FROM THE VIEWPOINT OF THE AMERICAN CITIZEN. By JEREMIAH W. JENKS, LL.D., Professor of Government and Public Administration in New York University.
Page 35 - F sin pt, and let us multiply the second equation by i and add it to the first. We then have The movement of the point Z representing the complex number z then serves as well to show the movement corresponding to x. We need only consider the projection of Z on the axis of x. A solution of the differential equation may be obtained by writing z = z0ep".
Page 150 - BLUMENTHAL LECTURES POLITICAL PROBLEMS OF AMERICAN DEVELOPMENT. By ALBERT SHAW, LL.D., Editor of the Review of Reviews.
Page 76 - Now we have shown above that a positive value of the functional determinant <pu\f/v — <pv^u means that Z2 is on the positive side of Zi, so that in this case Z moves in the positive sense (that is, in the direction from the positive axis of x to the positive axis of y) with increasing values of a. With a negative value Z moves in the opposite direction. Let us now suppose that the curves x = const. and y — const. in the uv plane intersect except on a certain curve where their direcu FIG.
Page 150 - Price, §1.50 net. WORLD ORGANIZATION AS AFFECTED BY THE NATURE OF THE MODERN STATE. By HON. DAVID JAYNE HILL, sometime American Ambassador to Germany.
Page 115 - We begin the integral curve over the upper part at the vertical x = a at a point E, the ordinate of which is arbitrary, and draw the broken line as far as F on the vertical x = b (Fig. 82). Then we integrate back again over the lower part, continuing the broken line from F to G. The line EG measured in the unit of length set down for the ordinates is equal to the area measured in units of area, this unit being a rectangle formed by PO and the unit of ordinates. That is to say, the area is equal to...
Page 150 - THE NATURE AND SOURCES OF THE LAW. By JOHN CHIPMAN GRAY, LL.D., Royall Professor of Law in Harvard University.
Page 51 - On the back side of the movable part of an ordinary slide rule there generally is a scale y = 2 + log sin t. When this part is turned round and the scale is brought into contact with the scale y = log x, we obtain for any position of the instrument log x — log sin t — log x...
Page 65 - When the functions <p(u, v) and ^(M, v) are defined for the values u, v of a certain region, they will furnish for every point u, v of this region a point in the xy plane. Let us call this a depiction of the uv plane on the xy plane. Similarly a function of one variable x = <p(u) might be said to depict the u line on the x line.
Page 98 - ... the pencil coincides with the scale division 5. As long as the celestial body does not materially alter its declination the diagram in this position will enable us to find any of the three values <p, h, a from the other two. As a second example let us consider the relation between the declination...

References from web pages

Carl Runge: <i>Graphical Methods</i>
Carl Runge gave a course of lectures on Graphical Methods at Columbia University in New York which were published by Columbia University Press in 1912. ...
www-history.mcs.st-andrews.ac.uk/ Extras/ Runge_Graphical_Methods.html

JSTOR: Graphical Methods
Graphical methods are no doubt a most valuable means of giving to the student a clear idea in concrete form of the symbolism which, without their aid, ...

Internet Archive: Details: Graphical methods; a course of lectures ...
Graphical methods; a course of lectures delivered in Columbia university, New York, October, 1909, to January, 1910 (1912). Graphical methods; a course of ...
www.archive.org/ details/ graphmethods00rungrich

Phys. Rev. 91, 1122 (1953): Quimby and Sutton - Computation of ...
6 C. Runge, Graphical Methods (Columbia University Press, New York, 1912), p. 59. /B M FIG. 3. Detail of Fig. 2 (schematic). the respective double roots ...