solving problems in mathematical analysis part ii pdf

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2020 | Buch

Solving Problems in Mathematical Analysis, Part II

Definite, improper and multidimensional integrals, functions of several variables and differential equations.

verfasst von: Prof. Dr. Tomasz Radożycki

Verlag: Springer International Publishing

Buchreihe : Problem Books in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

Über dieses Buch

This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

Inhaltsverzeichnis

Frontmatter, chapter 1. exploring the riemann and definite integral, chapter 2. examining improper integrals, chapter 3. applying one-dimensional integrals to geometry and physics, chapter 4. dealing with functions of several variables, chapter 5. investigating derivatives of multivariable functions, chapter 6. examining higher derivatives, differential expressions, and taylor’s formula, chapter 7. examining extremes and other important points, chapter 8. examining implicit and inverse functions, chapter 9. solving differential equations of the first order, chapter 10. solving differential equations of higher orders, chapter 11. solving systems of first-order differential equations, chapter 12. integrating in many dimensions, chapter 13. applying multidimensional integrals to geometry and physics, premium partner.

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Mathematical Analysis II

• © 2016
• Latest edition
• Vladimir A. Zorich 0

Dept. Mathematics & Mechanics, Moscow State University, Moskva, Russia

You can also search for this author in PubMed   Google Scholar

• Thoroughness of coverage, from elementary to very advanced
• Clarity of exposition
• Originality and variety of exercises and examples
• Complete logical rigor of discussion
• Various new appendices
• Useful not only to mathematicians, but also to physicists and engineers
• Includes supplementary material: sn.pub/extras

Part of the book series: Universitext (UTX)

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Table of contents (11 chapters)

Front matter, *continuous mappings (general theory).

Vladimir A. Zorich

*Differential Calculus from a More General Point of View

Multiple integrals, surfaces and differential forms in \(\mathbb{r}^{n}\), line and surface integrals, elements of vector analysis and field theory, *integration of differential forms on manifolds, uniform convergence and the basic operations of analysis on series and families of functions, integrals depending on a parameter, fourier series and the fourier transform, asymptotic expansions, back matter.

• differential equations
• integral calculus
• real numbers

About this book

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Especially notable in this course are the clearly expressed orientation toward the natural sciences and the informal exploration of the essence and the roots of the basic concepts and theorems of calculus. Clarity of exposition is matched by a wealth of instructive exercises, problems, and fresh applications to areas seldom touched on in textbooks on real analysis.

This second volume presents classical analysis in its current form as part of a unified mathematics. It shows how analysis interacts with other modern fields of mathematics such as algebra, differential geometry, differential equations, complex analysis, and functional analysis. This book provides a firm foundation for advanced work in any of these directions.

Authors and Affiliations

Dept. mathematics & mechanics, moscow state university, moskva, russia, about the author, bibliographic information.

Book Title : Mathematical Analysis II

Authors : Vladimir A. Zorich

Translated by : Roger Cooke, Octavio Paniagua

Series Title : Universitext

DOI : https://doi.org/10.1007/978-3-662-48993-2

Publisher : Springer Berlin, Heidelberg

eBook Packages : Mathematics and Statistics , Mathematics and Statistics (R0)

Copyright Information : Springer-Verlag Berlin Heidelberg 2016

Hardcover ISBN : 978-3-662-48991-8 Published: 22 February 2016

Softcover ISBN : 978-3-662-56966-5 Published: 13 March 2019

eBook ISBN : 978-3-662-48993-2 Published: 12 February 2016

Series ISSN : 0172-5939

Series E-ISSN : 2191-6675

Edition Number : 2

Number of Pages : XX, 720

Number of Illustrations : 42 illustrations in colour

Additional Information : Original Russian edition (6th edition) published by MCCME, Moscow, Russia, 2012

Topics : Analysis , Theoretical, Mathematical and Computational Physics

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Solving Problems in Mathematical Analysis, Part II

Definite, improper and multidimensional integrals, functions of several variables and differential equations, publisher description.

This textbook offers an extensive list of completely solved problems in mathematical analysis. This second of three volumes covers definite, improper and multidimensional integrals, functions of several variables, differential equations, and more. The series contains the material corresponding to the first three or four semesters of a course in Mathematical Analysis. Based on the author’s years of teaching experience, this work stands out by providing detailed solutions (often several pages long) to the problems. The basic premise of the book is that no topic should be left unexplained, and no question that could realistically arise while studying the solutions should remain unanswered. The style and format are straightforward and accessible. In addition, each chapter includes exercises for students to work on independently. Answers are provided to all problems, allowing students to check their work. Though chiefly intended for early undergraduate students of Mathematics, Physics and Engineering, the book will also appeal to students from other areas with an interest in Mathematical Analysis, either as supplementary reading or for independent study.

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Solving problems in mathematical analysis. Part II, Definite, improper and multidimensional integrals, functions of several variables and differential equations

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Publication Details

• Cham : Springer, 2020
• Problem books in mathematics
• 1 online resource (389 pages)
• Includes index.
• Description based upon print version of record.
• Mathematical analysis.

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• Prof. Victor Guillemin

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• Mathematics

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• Mathematical Analysis
• Topology and Geometry

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Analysis ii, lecture notes.

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Solving Problems in Mathematical Analysis, Part III Curves and Surfaces, Conditional Extremes, Curvilinear Integrals, Complex Functions, ... Fourier Series by Tomasz Rad

2023, Solving Problems in Mathematical Analysis, Part III Curves and Surfaces, Conditional Extremes, Curvilinear Integrals, Complex Functions, ... Fourier Series by Tomasz Rad

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