Essential Mathematics for Applied Fields

1. Purpose The purpose of this work is to provide, in one volume, a wide spectrum of essential (non-measure theoretic) Mathematics for use by workers in the variety of applied fields. To obtain the background developed here in one volume would require studying a prohibitive number of separate Mathematics courses (assuming they were available). Before, much of the material now covered was (a) unavailable, (b) too widely scattered, or © too advanced as presented, to be of use to those who need it. Here, we present a sound basis requiring only Calculus through however, Differential Equations. It provides the needed flexibility to cope, in a rigorous manner, with the every-day, non-standard and new situations that present themselves. There is no substitute for this. 2. Arrangement The volume consists of twenty Sections, falling into several natural units: Basic Real Analysis 1. Sets, Sequences, Series, and Functions 2. Doubly Infinite Sequences and Series 3. Sequences and Series of Functions 4. Real Power Series 5. Behavior of a Function Near a Point: Various Types of Limits 6. Orders of Magnitude: the D, 0, ~ Notation 7. Some Abelian and Tauberian Theorems v Riemann-Stieltjes Integration 8. I-Dimensional Cumulative Distribution Functions and Bounded Variation Functions 9. I-Dimensional Riemann-Stieltjes Integral 10. n-Dimensional Cumulative Distribution Functions and Bounded Variation Functions 11. n-Dimensional Riemann-Stieltjes Integral The Finite Calculus 12. Finite Differences and Difference Equations Basic Complex Analysis 13. Complex Variables Applied Linear Algebra 14. Matrices and Determinants 15.