Solving problems in mathematical analysis
著者
書誌事項
Solving problems in mathematical analysis
（Problem books in mathematics / edited by K. Bencsáth and P.R. Halmos）
Springer, 2020
- pt. 1
- pt. 2
- pt. 3
- タイトル別名
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Rozwiązujemy zadania z analizy matematycznej
大学図書館所蔵 件 / 全12件
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pt. 1FU:Radożycki:T.8010765694,
pt. 2FU:Radożycki:T.8010765942, pt. 3FU:Radożycki:T.8010765959 -
pt. 1413||R 11||12123000685,
pt. 2413||R 11||22123000652, pt. 3413||R 11||32123000663 -
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
pt.1: Sets, functions, limits, derivatives, integrals, sequences and series
pt.2: Definite, improper and multidimensional integrals, functions of several variables and differential equations
pt.3: Curves and surfaces, conditional extremes, curvilinear integrals, complex functions, singularities and Fourier series
Based on a translation from the Polish language ed.: Rozwiązujemy zadania z analizy matematycznej, (Rzeszów : Wydawnictwo Oświatowe FOSZE)
内容説明・目次
- 巻冊次
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pt. 1 ISBN 9783030358433
内容説明
This textbook offers an extensive list of completely solved problems in mathematical analysis. This first of three volumes covers sets, functions, limits, derivatives, integrals, sequences and series, to name a few. 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.
目次
Examining Sets and Relations.- Investigating Basic Properties of Functions.- Defining Distance in Sets.- Using Mathematical Induction.- Investigating Convergence of Sequences and Looking for Their Limits.- Dealing with Open, Closed and Compact Sets.- Finding Limits of Functions.- Examining Continuity and Uniform Continuity of Functions.- Finding Derivatives of Functions.- Using Derivatives to Study Certain Properties of Functions.- Dealing with Higher Derivatives and Taylor's Formula.- Looking for Extremes and Examine Functions.- Investigating the Convergence of Series.- Finding Indefinite Integrals.- Investigating the Convergence of Sequences and Series of Functions.
- 巻冊次
-
pt. 2 ISBN 9783030368470
内容説明
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.
目次
Exploring the Riemann and Definite Integral.- Examining Improper Integrals.- Applying One-Dimensional Integrals to Geometry and Physics.- Dealing with Functions of Several Variables.- Investigating Derivatives of Multivariable Functions.- Examining Higher Derivatives, Differential Expressions and the Taylor's Formula.- Examining Extremes and Other Important Points.- Examining Implicit and Inverse Functions.- Solving Differential Equations of the First Order.- Solving Differential Equations of Higher Orders.- Solving Systems of First-Order Differential Equations.- Integrating in Many Dimensions.- Applying Multidimensional Integrals to Geometry and Physics.
- 巻冊次
-
pt. 3 ISBN 9783030385958
内容説明
This textbook offers an extensive list of completely solved problems in mathematical analysis. This third of three volumes covers curves and surfaces, conditional extremes, curvilinear integrals, complex functions, singularities and Fourier series. 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.
目次
Examining Curves and Surfaces.- Investigating Conditional Extremes.- Investigating Integrals with Parameters.- Examining Unoriented Curvilinear Integrals.- Examining Differential Forms.- Examining Oriented Curvilinear Integrals.- Studying Functions of Complex Variable.- Investigating Singularities of Complex Functions.- Dealing with Multi-Valued Functions.- Studying Fourier Series.
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