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**Book Description **Discovery Publishing House. Book Condition: New. pp. [viii] + 333. Bookseller Inventory # 7544611

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(2015)

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**Book Description **Discovery Publishing House Pvt.Ltd, New Delhi, 2015. Hardcover. Book Condition: New. Bookseller Inventory # 410751

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Published by
Discovery Publishing House Pvt. Ltd.
(2011)

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**Book Description **Discovery Publishing House Pvt. Ltd., 2011. Hardcover. Book Condition: New. Printed Pages:334. Bookseller Inventory # Discovery-9788183563406

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Published by
Discovery Publishing House Pvt. Ltd.
(2011)

ISBN 10: 8183563406
ISBN 13: 9788183563406

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Quantity Available: 20

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**Book Description **Discovery Publishing House Pvt. Ltd., 2011. Hardcover. Book Condition: New. Printed Pages:334. Bookseller Inventory # Discovery-9788183563406

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Discovery Publishing House Pvt. Ltd.
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ISBN 13: 9788183563406

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**Book Description **Discovery Publishing House Pvt. Ltd., 2011. Hardcover. Book Condition: New. This book "Real Analysis" is written according the latest syllabus prescribed by "UGC" for M.Sc. (first) students of all Indian Universities. It is also meant for these students who are appearing in various competitive examinations. Each topic of this book is treated in a systematic and logical manner. The scope and depth of coverage are strictly according to the prescribed syllabus. A large number of solved examples and graded exercise form an integral part of the text. We do not claim any originality of the results but we claim simplicity and lucidity of presentation coupled with comprehensiveness of the material. Contents, 1. THE RIEMANN-STIELTJES INTEGRAL : Introduction, Partition or Division of an Interval [a, b], Definition and Existence of the Integral, Some Deduction, (A Relation Between Riemann Integral and RS-Integral), Properties of RS-Integrals, Inequality for Intergrals, Refinement of Partitions, Darboux`s Theorem, Integral as a Limit of Sums, R-Integrability, Second Definition of Riemann Integral, Conditions of Integrability, Generalized First Mean Value Theorem, Bonnet`s Theorem, Second Mean Value Theorem, Mean Value Theorems of Integral Calculus, First Mean Value Theorem, Fundamental Theorem of Integral Calculus, Solved Examples, Exercises. 2. IMPROPER INTEGRALS : Introduction, Convergence of Improper Integral, Comparison Test, Alternative Form of the Above Comparison Test, Principal and General Values of Improper Integrals, Cauchy`s Test for Convergence at 8, Abel`s Test, The Improper Integral, Absolute Convergence, Dirichlet`s Test, Two Comparison Integrals, Solved Examples, 3. UNIFORM CONVERGENCE : Introduction, Uniform Convergence of an Infinite Series, Necessary and Sufficient Condition, Uniform Convergence of Sequences of Functions, Abel`s Test For the Convergence of Integral of A Product, Dirichlet`s Test for the Convergence of Integrate of A Product, The m-Test, Absolute Convergence, Cauchy`s Criteria for Uniform Convergence of Sequence of Functions, A Test for Uniform Convergence of Sequence, Uniform Convergence and Continuity, Uniform Convergence and Integrability, Uniform Convergence and Differentiation, Weierstrass`s Approximation Theorem, Uniform Convergence and Derivability, Solved Examples, Exercises 4. FOURIER, POWER, Double SERIES AND SERIES OF ARBITRARY TERMS : Introduction of Fourier Series, Periodic Function, Introduction to Power Series, Some Useful Tests for Convergence, Some Important Power Series, Absolute Convergence of Power Series S an zn, Radius of Convergent of Power Series, Solved Examples, Series of Arbitrary Terms, Rearrangement of Series, Double Sequence, Double Series, A Fundamental Theorem for Positive Term Double Series, Absolute Convergence of a Double Series, Multiplication of Series, Some Modes of Convergence, Miscellaneous Examples, Exercises Printed Pages: 334. Bookseller Inventory # 58999

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Published by
Discovery Publishing House Pvt. Ltd.
(2011)

ISBN 10: 8183563406
ISBN 13: 9788183563406

New
Hardcover
Quantity Available: > 20

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**Book Description **Discovery Publishing House Pvt. Ltd., 2011. Hardcover. Book Condition: New. This book "Real Analysis" is written according the latest syllabus prescribed by "UGC" for M.Sc. (first) students of all Indian Universities. It is also meant for these students who are appearing in various competitive examinations. Each topic of this book is treated in a systematic and logical manner. The scope and depth of coverage are strictly according to the prescribed syllabus. A large number of solved examples and graded exercise form an integral part of the text. We do not claim any originality of the results but we claim simplicity and lucidity of presentation coupled with comprehensiveness of the material. Contents, 1. THE RIEMANN-STIELTJES INTEGRAL : Introduction, Partition or Division of an Interval [a, b], Definition and Existence of the Integral, Some Deduction, (A Relation Between Riemann Integral and RS-Integral), Properties of RS-Integrals, Inequality for Intergrals, Refinement of Partitions, Darboux`s Theorem, Integral as a Limit of Sums, R-Integrability, Second Definition of Riemann Integral, Conditions of Integrability, Generalized First Mean Value Theorem, Bonnet`s Theorem, Second Mean Value Theorem, Mean Value Theorems of Integral Calculus, First Mean Value Theorem, Fundamental Theorem of Integral Calculus, Solved Examples, Exercises. 2. IMPROPER INTEGRALS : Introduction, Convergence of Improper Integral, Comparison Test, Alternative Form of the Above Comparison Test, Principal and General Values of Improper Integrals, Cauchy`s Test for Convergence at 8, Abel`s Test, The Improper Integral, Absolute Convergence, Dirichlet`s Test, Two Comparison Integrals, Solved Examples, 3. UNIFORM CONVERGENCE : Introduction, Uniform Convergence of an Infinite Series, Necessary and Sufficient Condition, Uniform Convergence of Sequences of Functions, Abel`s Test For the Convergence of Integral of A Product, Dirichlet`s Test for the Convergence of Integrate of A Product, The m-Test, Absolute Convergence, Cauchy`s Criteria for Uniform Convergence of Sequence of Functions, A Test for Uniform Convergence of Sequence, Uniform Convergence and Continuity, Uniform Convergence and Integrability, Uniform Convergence and Differentiation, Weierstrass`s Approximation Theorem, Uniform Convergence and Derivability, Solved Examples, Exercises 4. FOURIER, POWER, Double SERIES AND SERIES OF ARBITRARY TERMS : Introduction of Fourier Series, Periodic Function, Introduction to Power Series, Some Useful Tests for Convergence, Some Important Power Series, Absolute Convergence of Power Series S an zn, Radius of Convergent of Power Series, Solved Examples, Series of Arbitrary Terms, Rearrangement of Series, Double Sequence, Double Series, A Fundamental Theorem for Positive Term Double Series, Absolute Convergence of a Double Series, Multiplication of Series, Some Modes of Convergence, Miscellaneous Examples, Exercises Printed Pages: 334. Bookseller Inventory # 58999

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