A course in real analysis. (2015)

• Record Type: Book
• Further Information: Note: Hugo D. Junghenn.
• Authors: Junghenn, Hugo D (Hugo Dietrich), 1939-
• Contents: Functions of One Variable; The Real Number System; From Natural Numbers to Real Numbers; Algebraic Properties of R; Order Structure of R; Completeness Property of R; Mathematical Induction; Euclidean Space Numerical Sequences; Limits of Sequences; Monotone Sequences; Subsequences. Cauchy Sequences; Limit Inferior and Limit Superior Limits and Continuity on R ; Limit of a Function; Limits Inferior and Superior; Continuous Functions; Some Properties of Continuous Functions; Uniform Continuity Differentiation on R ; Definition of Derivative. Examples; The Mean Value Theorem; Convex Functions; Inverse Functions; L’Hospital’s Rule; Taylor’s Theorem on R; Newton’s Method Riemann Integration on R ; The Riemann-Darboux Integral; Properties of the Integral; Evaluation of the Integral; Stirling’s Formula; Integral Mean Value Theorems; Estimation of the Integral; Improper Integrals; A Deeper Look at Riemann Integrability; Functions of Bounded Variation; The Riemann-Stieltjes Integral Numerical Infinite Series; Definition and Examples; Series with Nonnegative Terms; More Refined Convergence Tests; Absolute and Conditional Convergence; Double Sequences and Series Sequences and Series of Functions; Convergence of Sequences of Functions; Properties of the Limit Function; Convergence of Series of Functions; Power Series Functions of Several Variables ; Metric Spaces; Definitions and Examples; Open and Closed Sets; Closure, Interior, and Boundary; Limits and Continuity; Compact Sets; The Arzelà-Ascoli Theorem; Connected Sets; The Stone-Weierstrass Theorem; Baire’s Theorem Differentiation on Rn ; Definition of the Derivative; Properties of the Differential; Further Properties of the Derivative; The Inverse Function Theorem; The Implicit Function Theorem; Higher Order Partial Derivatives; Higher Order Differentials. Taylor’s Theorem on Rn ; Optimization Lebesgue Measure on Rn ; Some General Measure Theory; Lebesgue Outer Measure; Lebesgue Measure; Borel Sets; Measurable Functions Lebesgue Integration on Rn ; Riemann Integration on Rn ; The Lebesgue Integral; Convergence Theorems; Connections with Riemann Integration; Iterated Integrals; Change of Variables Curves and Surfaces in Rn ; Parameterized Curves; Integration on Curves; Parameterized Surfaces; m -Dimensional Surfaces Integration on Surfaces; Differential Forms; Integrals on Parameterized Surfaces; Partitions of Unity; Integration on m -Surfaces; The Fundamental Theorems of Calculus; Closed Forms in Rn Appendices; A Set Theory; B Summary of Linear Algebra; C Solutions to Selected Problems Bibliography Index
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource, illustrations (black and white)
• Subjects: 515.8; Functions of real variables; Functional analysis; Mathematical analysis
• Languages: English
• ISBNs: 9781482219371; 9781482219289; 9781482219357
• Related ISBNs: 9781482219272
• Notes: Note: Description based on CIP data; item not viewed.
• 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.