theory and practice in SearchWorks catalog (2024)

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Author/Creator

Petrovic, John Srdjan, author.

Bibliography

Includes bibliographical references (pages 543-550) and indexes.

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'Hopital'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 Cesaro 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.
• (source: Nielsen Book Data)

Publisher's summary

Suitable for a one- or two-semester course, Advanced Calculus: Theory and Practice expands on the material covered in elementary calculus and presents this material in a rigorous manner. The text improves students' problem-solving and proof-writing skills, familiarizes them with the historical development of calculus concepts, and helps them understand the connections among different topics. The book takes a motivating approach that makes ideas less abstract to students. It explains how various topics in calculus may seem unrelated but in reality have common roots. Emphasizing historical perspectives, the text gives students a glimpse into the development of calculus and its ideas from the age of Newton and Leibniz to the twentieth century. Nearly 300 examples lead to important theorems as well as help students develop the necessary skills to closely examine the theorems. Proofs are also presented in an accessible way to students. By strengthening skills gained through elementary calculus, this textbook leads students toward mastering calculus techniques. It will help them succeed in their future mathematical or engineering studies.
(source: Nielsen Book Data)

Subjects

Calculus > Textbooks.

Publication date

2014

Series

Textbooks in mathematics

ISBN

9781466565630 (hardback)

1466565632 (hardback)