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.
* 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.
Interesting and valuable historical account of ideas and methods in analysis with beautiful illustrationsRigorous exposition with full proofs motivated by numerous examplesExercises, comprehensive bibliography and index