Real analysis by Robert G bartle
Download Real analysis by Robert G bartle.pdf
Real analysis by Robert G bartle.pdf
Real analysis by Robert G bartle pdf
Real analysis is the area of mathematics dealing with real numbers and the analytic properties of real-valued functions and sequences. In this course we shall develop concepts such as convergence, continuity, completeness, compactness and convexity in the settings of real numbers, Euclidean spaces, and more general metric spaces.
Real analysis is part of the foundation for further study in mathematics as well as graduate studies in economics. A considerable part of economic theory is difficult to follow without a strong background in real analysis. For example, the concepts of compactness and convexity play an important role in optimisation theory and thus in microeconomics.
The theorems of real analysis rely on the properties of the real number system, which must be established. The real number system consists of an uncountable set R together with two binary operations denoted + and ⋅, and an order denoted <. The operations make the real numbers a field, and, along with the order, an ordered field. The real number system is the unique complete ordered field, in the sense that any other complete ordered field is isomorphic to it. Intuitively, completeness means that there are no 'gaps' in the real numbers. This property distinguishes the real numbers from other ordered fields (e.g., the rational numbers Q) and is critical to the proof of several key properties of functions of the real numbers
| CLICK HERE TO SEE OUR WEBSITE COMPLETE CATALOGUE |
|---|
| DIPS ACADEMY BOOKLETS |
| RISING STAR BOOKLETS |
| BALWAN MUDGAL SIR BOOKLETS |
| PIAM ACADEMY TEST SERIES |
| BALWAN SIR TEST SERIES |
| DIPS ACADEMY TEST SERIES |
| CLICK HERE TO SEE OUR WEBSITE COMPLETE CATALOGUE |
|---|
| LINEAR ALGEBRA BOOKS |
| REAL ANALYSIS BOOKS |
| COMPLEX ANALYSIS BOOKS |
| ABSTRACT ALGEBRA BOOKS |
| DIFFERENTIAL EQUATION BOOKS |
| PDE BOOKS |