University of Virginia Library

For Graduates.

Mathematics D1: Differential Geometry: Mathematics C1 prerequisite.—In
this course the year will be devoted to 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.

Mathematics D2: Differential Equations: Mathematics C1 prerequisite.—In
this course there will be presented a study of 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.

[Only one of the Courses D1 and D2 will be offered in 1915-1916.]

Mathematics D3: Theory of Functions: Mathematics C1 prerequisite.—In
this course is offered to advanced students a study of 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.
Monday, Wednesday, Friday, 11-12. Professor Echols.

The work in Mathematics D1, D2, and D3 is carried on by means of
lectures, notes, and the systematic reading of the standard authors in
texts and in journals.