01060nam 2200325Ia 450 99639640490331620221107205518.0(CKB)4940000000057321(EEBO)2248561754(OCoLC)12381245(EXLCZ)99494000000005732119850813d1686 uy |laturbn||||a|bb|M. Tullii Ciceronis Orationum selectarum liber[electronic resource] editus in usum scholarum Hollandiæ & West Frisiæ ..Londini Typis T. Hodgkin, pro R. Scot [and 4 others]1686[4], 236, [1] pReproduction of original in the University of Illinois (Urbana-Champaign Campus). Library.Table of contents: p. [1] at end.eebo-0167Cicero Marcus Tullius82411EAAEAAm/cEAAWaOLNBOOK996396404903316M. Tullii Ciceronis Orationum selectarum liber2328775UNISA05377nam 22006733u 450 991100680830332120230802010927.00-486-13500-41-62198-656-X(CKB)2550000001186499(EBL)1894769(SSID)ssj0001002717(PQKBManifestationID)12489498(PQKBTitleCode)TC0001002717(PQKBWorkID)10997567(PQKB)11361317(MiAaPQ)EBC1894769(Au-PeEL)EBL1894769(CaONFJC)MIL565870(OCoLC)868269914(EXLCZ)99255000000118649920141222d2012|||| u|| |engur|n|---|||||txtccrElementary Real and Complex Analysis1st ed.Newburyport Dover Publications20121 online resource (943 p.)Dover Books on MathematicsDescription based upon print version of record.0-486-68922-0 1-306-34619-3 Cover; Title Page; Copyright Page; Contents; Preface; 1 Real Numbers; 1.1. Set-Theoretic Preliminaries; 1.2. Axioms for the Real Number System; 1.3. Consequences of the Addition Axioms; 1.4. Consequences of the Multiplication Axioms; 1.5. Consequences of the Order Axioms; 1.6. Consequences of the Least Upper Bound Axiom; 1.7. The Principle of Archimedes and Its Consequences; 1.8. The Principle of Nested Intervals; 1.9. The Extended Real Number System; Problems; 2 Sets; 2.1. Operations on Sets; 2.2. Equivalence of Sets; 2.3. Countable Sets; 2.4. Uncountable Sets; 2.5. Mathematical Structures2.6. n-Dimensional Space2.7. Complex Numbers; 2.8. Functions and Graphs; Problems; 3 Metric Spaces; 3.1. Definitions and Examples; 3.2. Open Sets; 3.3. Convergent Sequences and Homeomorphisms; 3.4. Limit Points; 3.5. Closed Sets; 3.6. Dense Sets and Closures; 3.7. Complete Metric Spaces; 3.8. Completion of a Metric Space; 3.9. Compactness; Problems; 4 Limits; 4.1. Basic Concepts; 4.2. Some General Theorems; 4.3. Limits of Numerical Functions; 4.4. Upper and Lower Limits; 4.5. Nondecreasing and Nonincreasing Functions; 4.6. Limits of Numerical Sequences; 4.7. Limits of Vector FunctionsProblems5 Continuous Functions; 5.1. Continuous Functions on a Metric Space; 5.2. Continuous Numerical Functions on the Real Line; 5.3. Monotonie Functions; 5.4. The Logarithm; 5.5. The Exponential; 5.6. Trigonometric Functions; 5.7. Applications of Trigonometric Functions; 5.8. Continuous Vector Functions of a Vector Variable; 5.9. Sequences of Functions; Problems; 6 Series; 6.1. Numerical Series; 6.2. Absolute and Conditional Convergence; 6.3. Operations on Series; 6.4. Series of Vectors; 6.5. Series of Functions; 6.6. Power Series; Problems; 7 The Derivative; 7.1. Definitions and Examples7.2. Properties of Differentiable Functions7.3. The Differential; 7.4. Mean Value Theorems; 7.5. Concavity and Inflection Points; 7.6. L'Hospital's Rules; Problems; 8 Higher Derivatives; 8.1. Definitions and Examples; 8.2. Taylor's Formula; 8.3. More on Concavity and Inflection Points; 8.4. Another Version of Taylor's Formula; 8.5. Taylor Series; 8.6. Complex Exponentials and Trigonometric Functions; 8.7. Hyperbolic Functions; Problems; 9 The Integral; 9.1. Definitions and Basic Properties; 9.2. Area and Arc Length; 9.3. Antiderivatives and Indefinite Integrals9.4. Technique of Indefinite Integration9.5. Evaluation of Definite Integrals; 9.6. More on Area; 9.7. More on Arc Length; 9.8. Area of a Surface of Revolution; 9.9. Further Applications of Integration; 9.10. Integration of Sequences of Functions; 9.11. Parameter-Dependent Integrals; 9.12. Line Integrals; Problems; 10 Analytic Functions; 10.1. Basic Concepts; 10.2. Line Integrals of Complex Functions; 10.3. Cauchy's Theorem and Its Consequences; 10.4. Residues and Isolated Singular Points; 10.5. Mappings and Elementary Functions; Problems; 11 Improper Integrals11.1. Improper Integrals of the First Kind In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required.The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2,Dover Books on MathematicsMathematical analysisEngineering & Applied SciencesHILCCApplied MathematicsHILCCMathematical analysis.Engineering & Applied SciencesApplied Mathematics515Shilov Georgi E349442Silverman Richard AAU-PeELAU-PeELAU-PeELBOOK9911006808303321Elementary Real and Complex Analysis4391176UNINA