Description

Book Synopsis
This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.

Table of Contents
How We will Do Mathematics; Concepts with Which We will Do Mathematics; Construction of the Basic Number Systems; Limits of Functions; Continuity; Differentiation; Integration; Sequences; Infinite Series and Power Series; Exponential and Trigonometric Functions; Appendix A: Advice on Writing Mathematics; Appendix B: What One Should Never Forget;

Introduction To Analysis With Complex Numbers

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    A Paperback / softback by Irena Swanson

    £58.50

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 25 March 2021
      ISBN-13 9789811227691
      978-9811227691
      ISBN-10 9811227691
      Also in:
      Mathematics Real analysis, real variables

      Description

      Book Synopsis
      This is a self-contained book that covers the standard topics in introductory analysis and that in addition constructs the natural, rational, real and complex numbers, and also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.

      Table of Contents
      How We will Do Mathematics; Concepts with Which We will Do Mathematics; Construction of the Basic Number Systems; Limits of Functions; Continuity; Differentiation; Integration; Sequences; Infinite Series and Power Series; Exponential and Trigonometric Functions; Appendix A: Advice on Writing Mathematics; Appendix B: What One Should Never Forget;

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