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Precize ANALYSIS I (Pbi U)

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The present book is in accordance with the syllabus of Punjabi University Patiala in particular and other Universities in general. It provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved.

Description

Sequences : Definition of a sequence, Bounded and Monotonic sequences, Convergent sequence, Cauchy sequences, Cauchy’s Convergence Criterion, Theorems on limits of sequences. Subsequence, Sequential continuity.

Infinite Series : Definition of a series, Tests of convergence, Comparison tests. Cauchy’s integral test, Ratio tests, condensation test, Raabe’s, Logarithmic, Gauss Test, Cauchy’s root test,   Alternating series. Leibnitz’s test. Absolute and conditional convergence.

Weierstrass M-test for uniform convergence of sequences of functions and series of functions, simple applications. Determination of Radius of convergence of Power Series, (All tests without proof. Only applications)

Riemann Integration : Partitions, Upper and Lower integrals, Riemann integrability, Conditions of existence of Riemann integrability of continuous and monotonic functions. Algebra of Integrable functions.

Improper integrals : Definitions, statements of their conditions of existence, Tests of convergence of improper integrals, Beta and Gamma Functions and their convergence, Abel’s and Dirichlet’s tests

Additional information

ISBN

97893882295440

Language

English

Binding

Paperback

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