 | University of Virginia record February, 1911 |  |
Primarily for Graduates.
Course 6D: A Course in Geometry: Course 3C prerequisite.—An
advanced course in analytical geometry, in homogeneous, tangential and
radial coördinates, with applications to kinematics and the theory of
homogeneous displacement. Hours by appointment. Professor Echols.
Course 7D: A Course in Differential Geometry: Course 3C prerequisite.—In
this the year will be devoted to a course in the applications
of the Differential and Integral Calculus to Geometry, with special
reference to the theory of the General Space Curve, the Surface, and the
Surface Curve. Hours by appointment. Professor Page.
Course 8D: A Course in the Theory of Continuous Groups: Course
3C prerequisite.—In this will be presented an outline of the General Theory
of Continuous Groups of point and contact transformations. Numerous
applications to Geometry and Differential Equations will be adduced.
Hours by appointment. Professor Page.
Course 9D: A Course in Differential Equations: Course 3C prerequisite.—In
this there will be presented a course in Ordinary and Partial
Differential Equations. In the discussion of the Ordinary Differential
Equation particular attention is paid to the theory of integration of such
equations as admit of a known Transformation Group, and the classic
methods of integration are compared with those which flow from the
Theory of Continuous Groups. A similar method is adopted in the study
of the Linear Partial Differential Equation of the First Order. As far
as the time admits, the theories of integration of the Complete System,
as well as those of the General Partial Differential Equation of the First
and Second Orders, will be discussed. Hours by appointment. Professor
Page.
[Not more than two of the Courses 7D, 8D, 9D, are offered in one
session.]
Course 10D: A Course in the Theory of Functions: Course 3C prerequisite.—In
this class is offered to advanced students a course in Mathematical
Analysis. The treatment of the subject is arranged under three
heads, as follows:
The design of the numbers of analysis and the laws of the operations
to which they are subject are studied after the methods of Dedekind and
Tannery, Cantor and Weierstrass, as introductory to the study of functions.
The study of the Theory of Functions of a Real Variable, including
series, products, and continued fractions.
The General Theory of Functions of a Complex Variable is studied
after the methods of Cauchy, Riemann, and Weierstrass.
A special study is made of the series of Taylor and of Fourier. Tuesday,
Thursday, Saturday, 11-12. Professor Echols.
The work in Courses 6D, 7D, 8D, 9D, and 10D is carried on by means
of lectures, notes, and the systematic reading of the standard authors in
texts and in journals.
| University of Virginia record February, 1911 | |