It is intended to serve as a textbook in Real Analysis at the "Advanced Calculus" level. Some of the welcome features of the book are motivation for the theory and abstraction through examples. Experience has convinced us that if Euclidean spaces are properly understood, it is a small jump to other spaces such as the space of continuous fundions and abstract metric spaces. Topics like Field of real numbers, Foundation of calculus, Metric spaces, Compactness, Connectedness, Riemann integration, Fourier series, Calculus of several variables and Multiple integrals are presented systematically with diagrams and illustrations. Graded examples are provided to enable the students to understand the basic concepts of Real Analysis. This book would also be useful for students doing Engineering and Physics.
D. Somasundaram.: Department of Mathematics (Retd.), Madras University P.G. Extn. Centre, Salem, Tamil Nadu, India B. Choudhary.: Department of Mathematics Indian Institute of Technology, New Delhi, India
Preface / Sets and Functions / Sequences of Real Numbers / Series of Real Numbers / Real Valued Functions / Metric Spaces / Completeness, Compactness and Correctedness / Differentiable Functions / The Riemann Integral / Elementary Functions and Taylor Series / Fourier Series/ Functions of Several Variable / Multiple Integrals / Bibliography / Index