By David A. Sprecher
This vintage textual content in introductory research delineates and explores the intermediate steps among the fundamentals of calculus and the final word level of arithmetic: abstraction and generalization.
Since many abstractions and generalizations originate with the genuine line, the writer has made it the unifying subject of the textual content, developing the genuine quantity procedure from the perspective of a Cauchy series (a step which Dr. Sprecher feels is vital to profit what the true quantity process is).
The fabric lined in Elements of genuine research should be available to those that have accomplished a direction in calculus. to assist in giving scholars a valid footing, half one of many textual content studies the elemental innovations of units and features and the rational numbers. half explores the true line when it comes to the true quantity procedure, sequences and sequence of quantity and the constitution of element units. half 3 examines the features of a true variable when it comes to continuity, differentiability, areas of constant services, degree and integration, and the Fourier series.
An specially useful characteristic of the booklet is the routines which stick with each one part. There are over , starting from the easy to the hugely tricky, each one targeting an idea formerly introduced.
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Extra resources for Elements of Real Analysis (Dover Books on Mathematics)