A basic course in real analysis. ([2014])

• Record Type: Book
• Further Information: Note: Ajit Kumar, S. Kumaresan.
• Other Names: Kumar, Ajit, 1972-; Kumaresan, S
• Contents: Real Number System; Algebra of the Real Number System; Upper and Lower Bounds; LUB Property and Its Applications; Absolute Value and Triangle Inequality; ; Sequences and Their Convergence; Sequences and Their Convergence; Cauchy Sequences; Monotone Sequences; Sandwich Lemma; Some Important Limits; Sequences Diverging to ; Subsequences; Sequences Defined Recursively; ; Continuity; Continuous Functions; Definition of Continuity; Intermediate Value Theorem; Extreme Value Theorem; Monotone Functions; Limits; Uniform Continuity; Continuous Extensions; ; Differentiation; Differentiability of Functions; Mean Value Theorems; L'Hospital's Rules; Higher-order Derivatives; Taylor's Theorem; Convex Functions; Cauchy's Form of the Remainder; ; Infinite Series; Convergence of an Infinite Series; Abel's Summation by Parts; Rearrangements of an Infinite Series; Cauchy Product of Two Infinite Series; ; Riemann Integration; Darboux Integrability; Properties of the Integral; Fundamental Theorems of Calculus; Mean Value Theorems for Integrals; Integral Form of the Remainder; Riemann's Original Definition; Sum of an Infinite Series as an Integral; Logarithmic and Exponential Functions; Improper Riemann Integrals; ; Sequences and Series of Functions; Pointwise Convergence; Uniform Convergence; Consequences of Uniform Convergence; Series of Functions; Power Series; Taylor Series of a Smooth Function; Binomial Series; Weierstrass Approximation Theorem; ; A Quantifiers; B Limit Inferior and Limit Superior; C Topics for Student Seminars; D Hints for Selected Exercises; Bibliography; Index
• Publisher Details: Boca Raton : Taylor & Francis
• Publication Date: 2014
• Extent: 1 online resource
• Subjects: 515.8; Functions of real variables -- Textbooks; Mathematical analysis -- Textbooks; Numbers, Real -- Textbooks; Functions of real variables; Mathematical analysis; Numbers, Real; Electronic books; Textbooks
• Languages: English
• ISBNs: 9781482216387; 1482216388
• Notes: Note: Includes bibliographical references (page 297) and index.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.