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Rapidsol ANALYSIS – II (G.N.D.U)

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The present book provides a comprehensive treatment of the concepts and topics by giving a vast variety of examples fully solved. The entire subject matter has been arranged in a systematic, graded, simple, lucid and exhaustive manner. Each chapter begins with some definitions followed by theorems with complete proofs and solved problems. A large number of notes and remarks have been added for a better understanding of the subject.

Description

Definition of a sequence. Theorems on limits of sequences. Bounded and monotonic sequences. Cauchy’s convergence criterion. Series of non-negative terms. Comparison tests. Cauchy’s integral tests. Ratio tests. Cauchy’s root test. Raabe’s test logarithmic test. De’morgan’s and Bertrand’s tests. Kummer’s test, Cauchy Condensation test, Gauss test, alternative series. Leibnitz’s test, absolute and conditional convergence.

Partitions, Upper and lower sums. Upper and lower integrals, Riemann integrability. Conditions of existence of Riemann integrability of continuous functions and of monotone functions. Algebra of integrable functions. Improper integrals and statements of their conditions of existence. Test of the convergence of improper integrals. Beta and Gamma functions.

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