Intermediate Mathematical Analysis aims at presenting advanced topics such as continuity, uniform continuity, tests of convergence of series, uniform convergence of series, power series, polynomial approximations and Fourier series in a more general setting. Metric and Normed Linear Spaces are introduced at an early stage and are used wherever found advantageous. The book places a consistent emphasis on showing the power of the classical analysis by applying it to the study of real valued functions and their applications. Requiring only a nodding acquaintance with ? – d type arguments and definition of Riemann integral, the book will provide sufficient background material for studies in Functional Analysis, Topology, Complex Analysis, Theory of Differential Equations and so on.

• • Theorems are proved in complete details and illustrated profusely using examples and counter examples • About hundred illustrations and four hundred exercises, most of which have hints or solutions at the end of the book • End of the chapter projects to challenge ambitious readers

Preface / Metric Spaces: Definition of a Metric Space / Some Examples / Euclidean Metric in Kn / Normed Spaces: Normed Spaces / The Sequence Space lp, p>1: / Topology of Metric Spaces: Topological Spaces / Topology of Metric Spaces / Equivalent Metrics / Subspaces / Sequences in Metric Spaces / Closure, Interior and Boundary / Complete Metric Spaces: The Cauchy Sequence / Subsequences / Contraction Mapping / Continuity: Continuity between Metric Spaces / Open Maps, Closed Maps / Uniform Continuity / Homeomorphism and Isometry / Discontinuities and All That / Connected Metric Spaces: Connected Metric Spaces / Application of Intermediate Value Theorem / Connected Components / Path Connected Spaces / Compact Metric Spaces: Compactness / Characterization of Compact Metric Spaces / Applications / Sequences and Series of Functions: Pointwise Convergence / Uniform Convergence / Power Series: Limit Superior and Limit Inferior / Power Series / The Circular Functions / The Exponential Function / Fourier Series: Orthogonal Functions / Fourier Sine and Cosine Series / Mean Square Convergence of Fourier Series / The Pointwise Convergence of Fourier Series / Appendixes / Bibliography / Index / Index of Symbols.

Undergraduate and Postgraduate Students