This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
Logic and Proof Techniques. Sets and Functions. Real Numbers. Open and Closed Sets. Cardinality. Real-valued Functions. Real Sequences. Real Sequences (Contd.). Infinite Series. Infinite Series (Contd.). Limits of Functions. Continuous Functions. Discontinuous Functions. Uniform and Absolute Continuities and Functions of Bounded Variation. Differentiable Functions. Higher Order Differentiable Functions. Convex Functions. Indeterminate Forms. Riemann Integration. Properties of the Riemann Integral. Improper Integrals. Riemann-Lebesgue Theorem. Riemann-Stieltjes Integral. Sequences of Functions. Sequences of Functions (Contd.). Series of Functions. Power and Taylor Series. Power and Taylor Series (Contd.). Metric Spaces. Metric Spaces (Contd.). Bibliography. Index.