MA 366 Functions of a Real Variable
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Calculus of functions of a single variable.
A more careful development of the basic concepts of analysis, including sequences,
limits, continuity, differentiability, integration, infinite series, power series,
Taylor's Theorem, and uniform convergence.
Mandelbrot set - links to
Fractals from Wikipedia,
the free encyclopedia.
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This is a rigorous course in the study of
one-variable calculus. The emphasis in the course is on understanding
exactly what is a limit and what does it mean for a limit
to exist really. The understanding of the existence of a limit
is then applied to give a rigorous foundation to calculus
of one variable. This understanding is fundamental to provide
deeper insight to such mathematical topics as fractals, dynamical
systems, partial differential equations, differential geometry,
numerical analysis, calculus of variations and applied topics
such as fluid mechanics, signal processing, image analysis,
computer graphics (geometric modelling), et cetera. Without an understanding of this, most advanced topics in mathematics are inaccessible. |
A Mobius Type Minimal Surface
from GANG at UMass - picture links to an interactive view
of this surface |
Image Analysis - Inpainting
Inpainting Image Example from Guilermo Sapiro - University
of Minnesota - picture links to his inpainting site |
Evaluation will be by
homework sets (40%), quizzes (20%),
midterm exam (20%), final exam (20%) and class participation
(+/- 5%). |
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