Mathematics for economists. 1: Foundations of analysis, functions of a variable (Q2754892)

See Zbl 0685.90001 for the review of the 3rd ed. (1989). NEWLINENEWLINENEWLINEThis textbook is the result of the author's rich experience of holding mathematical courses to the students in Economics at the University of Regensburg. This is the first volume (on mathematical analysis and one-variable functions) from a series of three volumes devoted to the students in Economy and Social Sciences. Volume 2 exposes linear algebra and functions of several variables, while Volume 3 contains a large number of exercises and practical applications based on the theory in the first two volumes.NEWLINENEWLINENEWLINEThe main purpose of the book is to provide to the students a gentle introduction to the necessary notions of mathematical analysis. Each mathematical concept is explained in detail, with numerous examples and figures, such that the student to properly understand not only the formal concepts but, very important, the intuitive aspects behind the defined mathematical objects and results. This latest edition contains two new sections (Difference Equations and Differential Equations), removes some previous printing errors, and provides for university and professional high school students both a theoretical course and an individual studying guide in specialized mathematics for economy and social sciences.NEWLINENEWLINENEWLINEThis volume 1 of the textbook series contains two chapters with the following sections: Chapter 1 (The Basics of Analysis): (1.1) Basic aspects of mathematical Logic; (1.2) Sets; (1.3) Graphical representations; (1.4) Computation rules in \(\mathbb{R}\); (1.5) Inequalities and bounded sets; (1.6) Sequences and series; (1.7) Difference equations and financial mathematics; (1.8) Combinatorics; (1.9) Program scheme description. Chapter 2 (Functions of one-variable): (2.1) Basic notions: (2.2) Various functions used in economics; (2.3) Extremum points and function continuity; (2.4) The derivative of a function; (2.5) Calculus of derivatives; (2.6) Exponential and logarithmic functions; (2.7) Increase rate and elasticities; (2.8) Curve analysis; (2.9) Definite integral; (2.10) Indefinite integral; (2.11) Differential equations and applications of integral calculus.