Advanced calculus : theory and practice /: theory and practice. (2013)

• Record Type: Book
• Further Information: Note: John Srdjan Petrovic.
• Other Names: Petrovic, John Srdjan
• Contents: Sequences and Their Limits; Computing the Limits; Definition of the Limit; Properties of Limits; Monotone Sequences; The Number e ; Cauchy Sequences; Limit Superior and Limit Inferior; Computing the Limits-Part II Real Numbers; The Axioms of the Set R; Consequences of the Completeness Axiom; Bolzano-Weierstrass Theorem; Some Thoughts about R Continuity; Computing Limits of Functions; A Review of Functions; Continuous Functions: A Geometric Viewpoint; Limits of Functions; Other Limits; Properties of Continuous Functions; The Continuity of Elementary Functions; Uniform Continuity; Two Properties of Continuous Functions The Derivative; Computing the Derivatives; The Derivative; Rules of Differentiation; Monotonicity. Local Extrema; Taylor’s Formula; L’Hôpital’s Rule The Indefinite Integral; Computing Indefinite Integrals; The Antiderivative The Definite Integral; Computing Definite Integrals; The Definite Integral; Integrable Functions; Riemann Sums; Properties of Definite Integrals; The Fundamental Theorem of Calculus; Infinite and Improper Integrals Infinite Series; A Review of Infinite Series; Definition of a Series; Series with Positive Terms; The Root and Ratio Tests; Series with Arbitrary Terms Sequences and Series of Functions; Convergence of a Sequence of Functions; Uniformly Convergent Sequences of Functions; Function Series; Power Series; Power Series Expansions of Elementary Functions Fourier Series; Introduction; Pointwise Convergence of Fourier Series; The Uniform Convergence of Fourier Series ; Cesàro Summability; Mean Square Convergence of Fourier Series; The Influence of Fourier Series Functions of Several Variables; Subsets of Rn ; Functions and Their Limits; Continuous Functions; Boundedness of Continuous Functions; Open Sets in Rn ; The Intermediate Value Theorem; Compact Sets Derivatives; Computing Derivatives; Derivatives and Differentiability; Properties of the Derivative; Functions from Rn to Rm ; Taylor’s Formula; Extreme Values Implicit Functions and Optimization; Implicit Functions; Derivative as a Linear Map; Open Mapping Theorem; Implicit Function Theorem; Constrained Optimization; The Second Derivative Test Integrals Depending on a Parameter; Uniform Convergence; The Integral as a Function; Uniform Convergence of Improper Integrals ; Integral as a Function; Some Important Integrals Integration in Rn ; Double Integrals over Rectangles; Double Integrals over Jordan Sets; Double Integrals as Iterated Integrals; Transformations of Jordan Sets in R2 ; Change of Variables in Double Integrals; Improper Integrals; Multiple Integrals Fundamental Theorems; Curves in Rn ; Line Integrals; Green’s Theorem; Surface Integrals; The Divergence Theorem; Stokes’ Theorem; Differential Forms on Rn ; Exact Differential Forms on Rn Solutions and Answers to Selected Problems Bibliography Subject Index; Author Index
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2013
• Extent: 1 online resource, illustrations
• Subjects: 515; Calculus -- Textbooks; MATHEMATICS / Applied; MATHEMATICS / Differential Equations; MATHEMATICS / Functional Analysis
• Languages: English
• ISBNs: 9781466565647; 1466565640
• 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.