A. K. Sharma Text Book of Analysis-II

ISBN 13: 9788171418299

Text Book of Analysis-II

 
9788171418299: Text Book of Analysis-II
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Sharma A.K.
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A.K. Sharma
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Book Description Discovery Publishing House Pvt. Ltd., 2004. Hardcover. Condition: New. Printed Pages: 520. Seller Inventory # Discovery-9788171418299

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A.K. Sharma
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Book Description Discovery Publishing House Pvt. Ltd., 2004. Softcover. Condition: New. This book Analysis-II (for graduate students) is an out come of author`s long Teaching experience of the subject. The book present a thorough treatment of what is required for the students of B.A./B.Sc., of all Indian Universities. It include fundamental concepts illustrative examples and applications to various problems. These illustrative examples have been selected carefully on each topic and sufficient number of unsolved questions are provided which aims at sharpening the skill of the students. Almost every aspect of the subject. The Riemann Integral, The Function of Single Variable, The Function of Complex Variable, Improper Integral, Uniform Convergence, Metric Spaces, Beta and Gamma Functions, Differential Under Integral Sign, Integration on R2, is covered and illustrated by large number of examples. It is believed that the publication will serve as useful guide not only to the under graduate and post graduate students of several universities but also for the students of appearing at various competitive examinations. Contents, Relations1. THE RIEMANN INTEGRAL : Introduction, Partition or Division of an Interval [a, b], Inequality for Integrals, Refinement of Partitions, Darboux`s Theorem, Integral as a Limit of Sums, R-Integrability, Second Definition of Reimann Integral, Condition of Integrability, Fundamental Theorem of Integral Calculus, Mean Value Theorems of Integral Calculus, First Mean Value Theorem, Generalized First Mean Value Theorem, Bonnet`s Theorem, Second Mean Value Theorem 2. FUNCTIONS OF A SINGLE VARIABLE : Limit and Continuity, Introduction, Neighbourhood (nbd) of a Point, Limits, Left Hand and Right Hand Limits, Existence of Limit, The Algebra of Limits, `s Criterion for Finite Limits, Continuous Functions, Continuity of a Function on an Internal, Derivability at a Point, Increasing and Decreasing Function, Darboux`s Theorem, Rolle`s Theorem, Interpretation of Rolle`s Theorem 3. FUNCTIONS OF A COMPLEX VARIABLE : Complex Number, Addition of Complex Number, Multiplication Inverse, Difference of Two Complex Number, Division Inc., Modulus of A Complex Number, Conjugate of A Complex Number, Modulus-Argument Form or Rolar Standard Form, Geometrical Applications of Complex Number, Equation of a Straight Line in the Complex Plane, Exponential, Trigonometric and Hyperbolic Functions of a Complex Variable (Separation into Real and Imaginary Parts), Trigonometrical Functions or Circular Functions of a Complex Variable, Periodicity of Functions, De-Moivre`s Theorem for Complex Argument, Some Standard Trigonometrical Results for Complex Arguments, Hyperbolic Functions, Relations Between Hyperbolic and Circular Functions, Properties of Hyperbolic Functions, Expansions in series for sinh x and cosh x, Periods of Hyperbolic Functions, Separation into Real and Imaginary Parts, Curves in the Argand Plane, Functions of a Complex Variable, Neighbourhood of Point, Limits and Continuity, Differentiability, Analytic Function, The Necessary and Sufficient Conditions for f(z) to be Analytic, Polar Form of Cauchy-Riemann Equations, Derivative of W = f(z) in Polar Form, Orthogonal System, Harmonic Function, Determination of the Conjugate Function, Methods of Constructing A Regular Function 4. IMPROPER INTEGRALS : Introduction, Principal and General Values of Improper Integrals, Convergence of Improper Integral, Comparison Test, Two Comparison Integrals, Cauchy`s Test for Convergence at 8, Abel`s Test, The Improper Integral, Absolute Convergence, Dirichlet`s Test 5. UNIFORM CONVERGENCE : Convergence of a Sequence of Real Numbers, Point-wise Convergence of Sequences of Functions, Uniform Convergence of Sequences of Functions, Let us Consider Few Examples, Cauchy`s Criteria for Uniform Convergence of Sequence of Functions, Uniform Convergence of an Infinite Series, Necessary and Sufficient Printed Pages: 520. Seller Inventory # 58884

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A. K. Sharma
Published by Discovery Publishing Pvt.Ltd (2004)
ISBN 10: 8171418295 ISBN 13: 9788171418299
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