MATH 332(a) Real Variables
- Faculty
- Mathematics
- Last listed
- 1974–75
No longer offered. It’s in Waterloo’s scanned calendars from 1974–75 to 1974–75 (before that, 1963–64 to 1973–74 used the number for Theory of Functions and (b) An Introduction to Complex Variable Theory); the 1995–96 to 2023–24 calendars are on ucalendar.
Description of real numbers by means of a few fundamental properties (l.u.b. axiom, principle of Archimedes, etc.); proof of some theorems on continuous functions using l.u.b. axiom. _ functions of bounded variation and the Riemann Stieltjes integral. Cesaro summability of series; derivation, discussion and applications of Cauchy-Schwartz and Minkowski inequalities for series and integrals; inner product spaces and normed linear spaces with examples; orthonormal systems with examples including Legendre, Tschebyscheff, and trigonometric systems; Fourier series; ordinary differential equations and Picard existence Theorem (by means of fixed point theorem). 3 hours lectures.
As printed in the 1974–75 calendar, read by OCR; the scanned page is the original.
Check it elsewhere
In the scanned calendars
How it read in each calendar from 1963–64 to 1974–75, newest first. The text is OCR of the scanned pages; years whose wording matches are shown once, from the clearest scan. Each year links to its page on uwloo and to that page of the scanned PDF.
1974–75 1 calendar
Description of real numbers by means of a few fundamental properties (l.u.b. axiom, principle of Archimedes, etc.); proof of some theorems on continuous functions using l.u.b. axiom.
_ functions of bounded variation and the Riemann Stieltjes integral.
Cesaro summability of series; derivation, discussion and applications of Cauchy-Schwartz and Minkowski inequalities for series and integrals; inner product spaces and normed linear spaces with examples; orthonormal systems with examples including Legendre, Tschebyscheff, and trigonometric systems; Fourier series; ordinary differential equations and Picard existence Theorem (by means of fixed point theorem). 3 hours lectures.
1971–72 to 1973–74 3 calendars
Another title: (b) An Introduction to Complex Variable Theory, probably a different course under the same number (or a misread scan).
Complex numbers; continuity, differentiability, analyticity of functions; the Cauchy Riemann equations: solutions of Laplace’s equation; conformal mapping by elementary functions, and applications; the Cauchy and allied theorems; Taylor and Laurent expansions; uniform convergence and power series; the residue calculus, and applications. 3 hours lectures.
Faculty of Mathematics
1963–64 to 1970–71 8 calendars
Another title: Theory of Functions, probably a different course under the same number (or a misread scan).
The real number system. Uniform convergence. Theory of Fourier series. The complex number system. Analytic functions. The Cauchy theorems. Contour integration. Singularities. Conformal mapping. 3 lectures.