Solving problems in mathematical analysis. Sets, functions, limits, derivatives, integrals, sequences and series / Part I, (2020)

• Record Type: Book
• Other Titles: Sets, functions, limits, derivatives, integrals, sequences and series
• Uniform Title: Rozwiązujemy zadania z analizy matematycznej.
• Further Information: Note: Tomasz Radożycki.
• Other Names: Radożycki, Tomasz
• Contents: 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 Whether a Given Function Is a Metric -- Problem 1 -- Solution -- Problem 2 -- Solution -- 3.2 Drawing Balls and Segments -- Problem 1 -- Solution -- Problem 2 -- Solution -- 3.3 Exercises for Independent Work -- 4 Using Mathematical Induction -- 4.1 Proving Divisibility of Numbers and Polynomials -- Problem 1 -- Solution -- Problem 2 -- Solution -- 4.2 Proving Equalities and Inequalities -- Problem 1 -- Solution -- Problem 2 -- Solution -- Problem 3 -- Solution -- Problem 4 -- Solution -- Problem 5 -- Solution -- 4.3 Demonstrating Some Important Formulas -- Problem 1 -- Solution Problem 2 -- Solution -- Problem 3 -- Solution -- Problem 4 -- Solution -- 4.4 Exercises for Independent Work -- 5 Investigating Convergence of Sequences and Looking for Their Limits -- 5.1 Some Common Tricks Useful for Calculating Limitsof Sequences -- Problem 1 -- Solution -- Problem 2 -- Solution -- Problem 3 -- Solution -- Problem 4 -- Solution -- Problem 5 -- Solution -- 5.2 Using Various Criteria -- Problem 1 -- Solution -- Problem 2 -- Solution -- Problem 3 -- Solution -- Problem 4 -- Solution -- Problem 5 -- Solution -- 5.3 Examining Recursive Sequences -- Problem 1 -- Solution Problem 2 -- Solution -- 5.4 When a Sequence Oscillates -- Problem 1 -- Solution -- Problem 2 -- Solution -- 5.5 Demonstrating Divergence of Sequences -- Problem 1 -- Solution -- Problem 2 -- Solution -- 5.6 Exercises for Independent Work -- 6 Dealing with Open, Closed, and Compact Sets -- 6.1 Examining Openness and Closeness of Sets -- Problem 1 -- Solution -- Problem 2 -- Solution -- Problem 3 -- Solution -- 6.2 Examining Compactness -- Problem 1 -- Solution -- Problem 2 -- Solution -- 6.3 Exercises for Independent Work -- 7 Finding Limits of Functions
• Publisher Details: Cham : Springer
• Publication Date: 2020
• Extent: 1 online resource (375 pages)
• Subjects: 515; Mathematical analysis; Mathematical analysis; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783030358440; 3030358445
• Related ISBNs: 9783030358433; 3030358437
• Notes: Note: Print version record.
• 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.