Real analysis and foundations. (2013)

• Record Type: Book
• Further Information: Note: Steven G. Krantz.
• Other Names: Krantz, Steven G (Steven George), 1951-
• Contents: Number Systems; The Real Numbers; The Complex Numbers Sequences; Convergence of Sequences; Subsequences; Limsup and Liminf; Some Special Sequences Series of Numbers; Convergence of Series; Elementary Convergence Tests; Advanced Convergence Tests; Some Special Series; Operations on Series Basic Topology; Open and Closed Sets; Further Properties of Open and Closed Sets; Compact Sets; The Cantor Set; Connected and Disconnected Sets; Perfect Sets Limits and Continuity of Functions; Basic Properties of the Limit of a Function; Continuous Functions; Topological Properties and Continuity; Classifying Discontinuities and Monotonicity Differentiation of Functions; The Concept of Derivative; The Mean Value Theorem and Applications; More on the Theory of Differentiation The Integral; Partitions and the Concept of Integral; Properties of the Riemann Integral; Another Look at the Integral; Advanced Results on Integration Theory Sequences and Series of Functions; Partial Sums and Pointwise Convergence; More on Uniform Convergence; Series of Functions; The Weierstrass Approximation Theorem Elementary Transcendental Functions; Power Series; More on Power Series: Convergence Issues; The Exponential and Trigonometric Functions; Logarithms and Powers of Real Numbers Differential Equations; Picard’s Existence and Uniqueness Theorem; Power Series Methods Introduction to Harmonic Analysis; The Idea of Harmonic Analysis; The Elements of Fourier Series; An Introduction to the Fourier Transform; Fourier Methods and Differential Equations Functions of Several Variables; A New Look at the Basic Concepts of Analysis; Properties of the Derivative; The Inverse and Implicit Function Theorems Advanced Topics; Metric Spaces; Topology in a Metric Space; The Baire Category Theorem; The Ascoli-Arzela Theorem Normed Linear Spaces; What Is This Subject About?; What Is a Normed Linear Space?; Finite-Dimensional Spaces; Linear Operators; The Three Big Results; Applications of the Big Three Appendix I: Elementary Number Systems; Appendix II: Logic and Set Theory; Appendix III: Review of Linear Algebra Table of Notation Glossary Bibliography Index Exercises are included at the end of each section.
• Publisher Details: Boca Raton : CRC Press/Taylor & Francis Group
• Publication Date: 2013
• Extent: 1 online resource
• Subjects: 515.8; Functions of real variables; Mathematical analysis; Functions of real variables; Mathematical analysis; Electronic books
• Languages: English
• ISBNs: 9781466587328; 1466587326; 9781498777698; 1498777694
• Related ISBNs: 9781466587311; 1466587318
• Notes: Note: Includes bibliographical references (pages 403-405) 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.