دانلود کتاب Non-standard Analysis

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LIST OF CONTENTS\nCHAPTER I GENERAL INTRODUCTION\n 1.1. Purpose of this book\n 1.2. Summary of contents\nCHAPTER II TOOLS FROM LOGIC\n 2.1. The Lower Predicate Calculus\n 2.2. Interpretation\n 2.3. Ultraproducts\n 2.4. Prenex normal form\n 2.5. The finiteness principle\n 2.6. Higher order structures and corresponding languages\n 2.7. Type symbols\n 2.8. Finiteness principle for higher order theories\n 2.9. Enlargements\n 2.10. Examples of enlargements\n 2.11. General properties of enlargements\n 2.12. Remarks and references\nCHAPTER III DIFFERENTIAL AND INTEGRAL CALCULUS\n 3.1. Non-standard Arithmetic\n 3.2. Non-standard Analysis\n 3.3. Convergence\n 3.4. Continuity and differentiation\n 3.5. Integration\n 3.6. Differentials\n 3.7. Total differentials\n 3.8. Elementary Differential Geometry\n 3.9. Remarks and references\nCHAPTER IV GENERAL TOPOLOGY\n 4.1. Topological spaces\n 4.2. Sequences, nets, mappings\n 4.3. Metric spaces\n 4.4. Topologies in *T\n 4.5. Functions, limits, continuity, in metric spaces\n 4.6. Sequences of functions. Compact mappings\n 4.7. Euclidean space\n 4.8. Remarks and references\nCHAPTER V FUNCTIONS OF A REAL VARIABLE\n 5.1. Measure and integration\n 5.2. Sequences of functions\n 5.3. Distributions\n 5.4. Remarks and references\nCHAPTER VI FUNCTIONS OF A COMPLEX VARIABLE\n 6.1. Analytic theory of polynomials\n 6.2. Analytic functions\n 6.3. Picard’s theorems and Julia’s directions\n 6.4. Compactness arguments in classical Function Theory\n 6.5. Remarks and references\nCHAPTER VII LINEAR SPACES\n 7.1. Normed spaces\n 7.2. Hilbert space\n 7.3. Spectral theory of compact operators\n 7.4. An invariant subspace problem\n 7.5. Remarks and references\nCHAPTER VIII TOPOLOGICAL GROUPS AND LIE GROUPS\n 8.1. Topological groups\n 8.2. Metric groups\n 8.3. One-parametric subgroups\n 8.4. The Lie algebra of a group\n 8.5. Remarks and references\nCHAPTER IX SELECTED TOPICS\n 9.1. Variations\n 9.2. Riemann’s mapping theorem\n 9.3. Dirichlet’s principle\n 9.4. Sources and doublets\n 9.5. Local perturbations\n 9.6. Boundary layer theory\n 9.7. Saint-Venant’s principle\n 9.8. Remarks and references\nCHAPTER X CONCERNING THE HISTORY OF THE CALCULUS\n 10.1. Introduction\n 10.2. Leibniz\n 10.3. De l’Hospital\n 10.4. Lagrange and d’Alembert\n 10.5. Cauchy\n 10.6. Bolzano, Weierstrass, and after\n 10.7. Infinitely small and large numbers and the infinite\nBIBLIOGRAPHY\nINDEX OF AUTHORS\nSUBJECT INDEX