The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1 (Classic Reprint) - Softcover

Inhaltsangabe

Explore the foundations of real-variable theory and how Fourier’s series fit in. This edition presents Hobson’s approach to rigor, definitions, and the conditions that justify the limiting processes used in mathematical analysis.

The text introduces the arithmetic continuum, the nature of limits, and the precise formulation of when limiting techniques are valid. It surveys the theory of sets of points, aggregates, and the representation of functions by series or sequences, with a focus on functions of one variable and, to a lesser extent, two.

• Clear definitions of continuity, discontinuity, and related function classes.


• Discussion of point-wise discontinuous functions and the structure of their discontinuities.


• Explanations of monotone functions, saltus (jumps), oscillation, and the behavior of limits.


• Connections between the theory of sets, aggregates, and the representation of functions by trigonometrical series.

Ideal for readers of real analysis and the history of the subject, this edition helps students grasp the core ideas behind modern function theory and its applications to mathematical physics.

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