Elementary Analysis through Examples and Exercises

✍ Scribed by John Schmeelk, Djurdjica Takači, Arpad Takači (auth.)

• Publisher: Springer Netherlands
• Year: 1995
• Tongue: English
• Leaves: 328
• Series: Kluwer Texts in the Mathematical Sciences 10
• Edition: 1
• Category: Library

✦ Synopsis

It is hard to imagine that another elementary analysis book would contain ma­ terial that in some vision could qualify as being new and needed for a discipline already abundantly endowed with literature. However, to understand analysis, be­ ginning with the undergraduate calculus student through the sophisticated math­ ematically maturing graduate student, the need for examples and exercises seems to be a constant ingredient to foster deeper mathematical understanding. To a talented mathematical student, many elementary concepts seem clear on their first encounter. However, it is the belief of the authors, this understanding can be deepened with a guided set of exercises leading from the so called "elementary" to the somewhat more "advanced" form. Insight is instilled into the material which can be drawn upon and implemented in later development. The first year graduate student attempting to enter into a research environment begins to search for some original unsolved area within the mathematical literature. It is hard for the student to imagine that in many circumstances the advanced mathematical formulations of sophisticated problems require attacks that draw upon, what might be termed elementary techniques. However, if a student has been guided through a serious repertoire of examples and exercises, he/she should certainly see connections whenever they are encountered.

✦ Table of Contents

Front Matter....Pages i-ix
Real numbers....Pages 1-44
Functions....Pages 45-81
Sequences....Pages 83-140
Limits of functions....Pages 141-180
Continuity....Pages 181-212
Derivatives....Pages 213-284
Graphs of functions....Pages 285-312
Back Matter....Pages 313-321

✦ Subjects

Analysis; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences