Solving problems in mathematical analysis

by Radożycki, Tomasz

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Title Statements

Full title :Solving problems in mathematical analysis. / Tomasz Radożycki.

Summary

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 authors 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.

Edition Statements

Publication Date:2020.

Publication Statements

Publisher(s):Springer
Place of Publication:Cham
Language:eng
Publication Date:2020.

Notes

7.1 Some Common Tricks Useful for Calculating Limitsof Functions

Includes index.

The Physical Object

Description:1 online resource (375 pages)

Edition Identifiers

ISBN:9783030358440, 3030358445
oclc:on1142508405
LC Classification:QA300
Dewey Decimal:515

Intro -- Preface -- Contents -- Definitions and Notation -- 1 Examining Sets and Relations -- 1.1 Demonstrating Simple Identities -- Problem 1 -- Solution -- Problem 2 -- Solution -- Identity (a) -- Identity (b) -- Identity (c) -- Problem 3 -- Solution -- 1.2 Finding Sets on a Plane -- Problem 1 -- Solution -- Problem 2 -- Solution -- 1.3 Finding Lower and Upper Bounds of Numerical Sets -- Problem 1 -- Solution -- Problem 2 -- Solution -- 1.4 Verifying Whether R Is an Equivalence Relation, Looking for Equivalence Classes and Drawing a Graph of the Relation -- Problem 1 -- Solution

Problem 2 -- Solution -- Problem 3 -- Solution -- 1.5 Exercises for Independent Work -- 2 Investigating Basic Properties of Functions -- 2.1 Looking for Ranges (Images) and Level Sets -- Problem 1 -- Solution -- Problem 2 -- Solution -- 2.2 Verifying Whether a Function Is an Injection, Surjection, or Bijection and Looking for the Inverse Function -- Problem 1 -- Solution -- Problem 2 -- Solution -- Problem 3 -- Solution -- 2.3 Finding Images and Inverse Images of Sets -- Problem 1 -- Solution -- Problem 2 -- Solution -- 2.4 Exercises for Independent Work -- 3 Defining Distance in Sets

3.1 Examining Whe…