A First Course in Mathematical Analysis（ISBN=9780521684248） 下载 mobi 免费 pdf 百度网盘 epub 2025 在线 电子书

　　Mathematical Analysis (often called Advanced Calculus) is

generally found by students to be one of their hardest courses in

Mathematics. This text uses the so-called sequential approach to

continuity, differentiability and integration to make it easier to

understand the subject.Topics that are generally glossed over in

the standard Calculus courses are given careful study here. For

example, what exactly is a 'continuous' function? And how exactly

can one give a careful definition of 'integral'? The latter

question is often one of the mysterious points in a Calculus course

- and it is quite difficult to give a rigorous treatment of

integration! The text has a large number of diagrams and helpful

margin notes; and uses many graded examples and exercises, often

with complete solutions, to guide students through the tricky

points. It is suitable for self-study or use in parallel with a

standard university course on the subject.

Preface

Introduction: calculus and analysis

1. Numbers

2. Sequences

3. Series

4. Continuity

5. Limits and continuity

6. Differentiation

7. Integration

8. Power series

Appendix 1. Sets, functions and proofs

Appendix 2. Standard derivatives and primitives

Appendix 3. The first 1,000 decimal places of the square root of 2,

e and pi

Appendix 4. Solutions to the problems

Index.

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书籍介绍

Mathematical Analysis (often called Advanced Calculus) is generally found by students to be one of their hardest courses in Mathematics. This text uses the so-called sequential approach to continuity, differentiability and integration to make it easier to understand the subject.Topics that are generally glossed over in the standard Calculus courses are given careful study here. For example, what exactly is a 'continuous' function? And how exactly can one give a careful definition of 'integral'? The latter question is often one of the mysterious points in a Calculus course - and it is quite difficult to give a rigorous treatment of integration! The text has a large number of diagrams and helpful margin notes; and uses many graded examples and exercises, often with complete solutions, to guide students through the tricky points. It is suitable for self-study or use in parallel with a standard university course on the subject.