Mathematical Analysis: Functions of One Variable: v. 1 Book

This self-contained work in mathematical analysis introduces the main ideas and fundamental methods of the subject, focusing on a simple and direct exposition of differential and integral calculus for functions of one variable with some of its applications.

Key features:

* Interesting and valuable historical account of ideas and methods in analysis with beautiful illustrations

* Topics: functions of one variable, differential and integral calculus, asymptotic expansion and inequalities, basic ordinary differential equations (including 1-dimensional motions, central motions, Kepler's laws and free and forced vibrations), and a discussion of elementary minimum principles in physics and geometry (such as refraction laws, Steiner's problem, isoperimetric problems, Dijkstra's algorithm for minimal connections in graphs); the preliminaries treat the real numbers, trigonometric functions and some elementary Cartesian geometry

* Rigorous exposition with full proofs motivated by numerous examples

* Exercises, comprehensive bibliography and index

This work is a first step toward developing connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. An excellent resource for self-study or for classroom use at the advanced undergraduate or graduate level.