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Now showing items 1-20 of 25

#### Convergence of infinite series

(University of Missouri, 1900)

We shall define an infinite series as a succession of series formed after sum definite law. Most generally the series are actual numbers or are at least regarded as constraints, and we are concerned with their sum. There ...

#### Solutions of differential equations not obtained by giving particular values to the constant of integration in the general solution

(University of Missouri, 1903)

In considering the solution of Differential Equations, let the equation be taken in the form f(x,y,p)=c, in which p denotes dy/dx, and f is a rational, integral, and algebraic function of x, y, and p of degree n in p. It ...

#### On integrals over sets of points

(University of Missouri, 1910)

The developments of the last twenty years in the theory of sets of points and in the applications of this theory to the theory of functions of real variables, besides leading to a tremendous extension of the ordinary theory ...

#### On the motion of a sphere on a rough horizontal plane

(University of Missouri, 1902)

The problem discussed in these pages is that of the motion of a billiard ball when struck by a horizontal cue. This is a special case of the motion of a sphere on a rough horizontal plane.

#### On some classes of non-analytic functions of a complex variable

(University of Missouri, 1909)

The fact, namely, that the analytic functions are a very limited and special class, with the additional fact that there seems to be no reason a priori why many of the theorems concerning analytic functions cannot be extended ...

#### On surfaces of constant negative curvature and their deformation

(University of Missouri, 1904)

We have shown that the pseudosphere is applicable to itself in an infinity of ways. Therefore these surfaces that are applicable to it can, after they are folded on the pseudosphere, be made to pass through the same ...

#### Pointwise discontinuous functions

(University of Missouri, 1912)

The concept of pointwise discontinuity is a fairly recent one in mathematics. Originally introduced as a convenient term in the study of integration, it has quite outgrown its former sphere of usefulness and has had an ...

#### Definition of improper groups by means of axioms : a dissertation

(University of Missouri, 1906)

Essentially, a group is an associative field, in which the inverse combinations are uniquely possible. This is a concise statement of the classical definition of a group. The conditions which it connotes will be used here ...

#### Convergence of an infinite series

(University of Missouri, 1902)

This thesis gives some of the more important tests for the convergence of an infinite series; also the conditions that must be fulfilled in order that certain operations and transformations may be applied to an infinite series.

#### Geometry of four dimensions

(University of Missouri, 1902)

In this thesis a brief outline of Four Dimensional Geometry, as far as the classification of quadrics, is attempted.

#### Foundations of geometry

(University of Missouri, 1901)

Geometry has been called the science of in-direct measurement, and as such is founded on certain definitions, postulates, and some assumptions or axioms which are said to be self-evident. It is a physical science idealized. ...

#### Singular solutions of differential equations of the first order

(University of Missouri, 1900)

A differential equation may be formed from all algebraic equations by the elimination of the arbitrary constants between the latter and its derivatives. The number of derivations being equal to the number of arbitrary ...

#### Errors in graphical methods

(University of Missouri, 1914)

The author suggests methods for determining errors in graphical computations and discusses errors in the graphical methods in the infinitesimal calculus.

#### A vector treatment of the projective properties of plane curves

(University of Missouri, 1916)

#### Lorentzian warped products and static space-times

(University of Missouri--Columbia, 1985)

#### Some new aspects of the Galois theory

(University of Missouri, 1913)

Realizing that the Galois theory of algebraic equations as commonly presented seems artificial, abstract, and intricate, we have been led in the following paper to attempt to present in a clear, tangible fashion the general, ...

#### A collection of graphs to accompany certain topics in the study of function theory of a real variable

(University of Missouri, 1913)

In Part I of this paper, I have dealt with only well-known properties of functions - treating them from the graphic standpoint entirely and referring the reader, to the best authorities I could find, for the Algebraic ...

#### Study of the convergence of series in certain orthogonal functions

(University of Missouri, 1914)

In this present paper we will develop some theorems concerning the degree of convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding ...

#### The treatment of irrational numbers in the secondary schools

(University of Missouri, 1908)

The subject matter of this paper was suggested by the belief that a treatment of irrational numbers, from the stand point of the "cut" number, has certain points of superiority over the common treatment from the standpoint ...

#### Vectors in four dimensions

(University of Missouri, 1909)

The interest attaching to n-dimensional geometry comes chiefly from two sources, first the light thrown upon analysis by a geometric interpretation of its results when more than three variables are involved, and second, ...