LEADER 05377nam 22006733u 450 001 9911006808303321 005 20230802010927.0 010 $a0-486-13500-4 010 $a1-62198-656-X 035 $a(CKB)2550000001186499 035 $a(EBL)1894769 035 $a(SSID)ssj0001002717 035 $a(PQKBManifestationID)12489498 035 $a(PQKBTitleCode)TC0001002717 035 $a(PQKBWorkID)10997567 035 $a(PQKB)11361317 035 $a(MiAaPQ)EBC1894769 035 $a(Au-PeEL)EBL1894769 035 $a(CaONFJC)MIL565870 035 $a(OCoLC)868269914 035 $a(EXLCZ)992550000001186499 100 $a20141222d2012|||| u|| | 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aElementary Real and Complex Analysis 205 $a1st ed. 210 $aNewburyport $cDover Publications$d2012 215 $a1 online resource (943 p.) 225 1 $aDover Books on Mathematics 300 $aDescription based upon print version of record. 311 08$a0-486-68922-0 311 08$a1-306-34619-3 327 $aCover; 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 Structures 327 $a2.6. 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 Functions 327 $aProblems5 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 Examples 327 $a7.2. 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 Integrals 327 $a9.4. 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 Integrals 327 $a11.1. Improper Integrals of the First Kind 330 $a In this book the renowned Russian mathematician Georgi E. Shilov brings his unique perspective to real and complex analysis, an area of perennial interest in mathematics. Although there are many books available on the topic, the present work is specially designed for undergraduates in mathematics, science and engineering. A high level of mathematical sophistication is not required.The book begins with a systematic study of real numbers, understood to be a set of objects satisfying certain definite axioms. The concepts of a mathematical structure and an isomorphism are introduced in Chapter 2, 410 0$aDover Books on Mathematics 606 $aMathematical analysis 606 $aEngineering & Applied Sciences$2HILCC 606 $aApplied Mathematics$2HILCC 615 0$aMathematical analysis. 615 7$aEngineering & Applied Sciences 615 7$aApplied Mathematics 676 $a515 700 $aShilov$b Georgi E$0349442 702 $aSilverman$b Richard A 801 0$bAU-PeEL 801 1$bAU-PeEL 801 2$bAU-PeEL 906 $aBOOK 912 $a9911006808303321 996 $aElementary Real and Complex Analysis$94391176 997 $aUNINA