PDF (1941) - CaltechCampusPubs

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CALIFORNIA INSTITUTE OF TECHNOLOGY
for dealing with integral equations. Laplace's type of equation and the Heaviside
calculus, calculus of variations, matrices and bilinear forms. Partial differential
equations and the related simple solutions. Expansions in series of orthogonal
functions.
(Not given in 1940-41.)
Instructor: Bateman or Ward.
Ma. 256 a, b, c. Modern Differential Geometry. 9 units; first, second and
third terms.
Prerequisite: Graduate standing.
Riemannian and Non-Riemannian geometries. Theory of parallel displacement
of tensors. Affine differential geometry. Projective differential geometry. Continuous
groups and their applications to geometry. Contemporary researches in differential
geometry.
Instructor: Michal.
Ma. 257 a, b, c. Seminar in Abstract Spaces. 6 units; first, second and
third terrns.
Prerequisite: Graduate standing.
Metric 'paces, linear vector spaces; topological spaces; abstract polynomials;
general function theories; analysis and geometry in abstract spaces; connectiotll
with abstract algebra and the theory of functionals; analysis of selected papers of
Frechet, Riesz and Banach; contemporary researches; applications to mathematical
problems in modern theoretical physics.
In charge: Michal.
Ma. 258 a, b, c. Partial Differential Equation. of Mathematical Physic',
12 units; first, second and third terms.
Prerequisites: Ma. 8, 10.
Illustration of general methods by consideration of ordinary linear equations.
The simple wave-equation, the potential equation. Applications of the integral
theorems of Stokes and Green. Reduction to variation problems and the solution of
such problems by direct methods. Use of difference equations to obtain approximate
solutions. Use of simple solutions expressed as products. Properties of the special
functions introduced in this way. Solution of initial and boundary problems by
various methods.
Instructor: Bateman.
Ma. 260. Reading.
Occasionally advanced work is given by a reading course under the direction of
an instructor. Hours and units by arrangement.
Ma. 261. Research.
By arrangement with members of the staff, properly qualified graduate students
are directed in research. Hours and units by arrangement.