Harmonic Analysis and Hypergroups [Paperback]

ContentsPreface1 Introduction1 The Set N of Natural Numbers2 The Set Q of Rational Numbers3 The Set R of Real Numbers4 The Completeness Axiom5 The Symbols + and -6 * A Development of R 2 Sequences7 Limits of Sequences8 A Discussion about Proofs9 Limit Theorems for Sequences10 Monotone Sequences and Cauchy Sequences11 Subsequences12 limsup's and liminf's13 * Some Topological Concepts in Metric Spaces14 Series15 Alternating Series and Integral Tests16 * Decimal Expansions of Real Numbers 3 Continuity17 Continuous Functions18 Properties of Continuous Functions19 Uniform Continuity20 Limits of Functions21 * More on Metric Spaces: Continuity22 * More on Metric Spaces: Connectedness 4 Sequences and Series of Functions23 Power Series24 Uniform Convergence25 More on Uniform Convergence26 Differentiation and Integration of Power Series27 * Weierstrass's Approximation Theorem 5 Differentiation28 Basic Properties of the Derivative29 The Mean Value Theorem30 * L'Hospital's Rule31 Taylor's Theorem 6 Integr ation32 The Riemann Integral33 Properties of the Riemann Integral34 Fundamental Theorem of Calculus35 * Riemann-Stieltjes Integrals36 * Improper Integrals37 * A Discussion of Exponents and Logarithms Appendix on Set NotationSelected Hints and AnswersReferencesIndexSpringer Book Archives