LEADER 05024nam 22008895 450 001 9910768190003321 005 20200703051340.0 010 $a9783034806367 010 $a3034806361 024 7 $a10.1007/978-3-0348-0636-7 035 $a(CKB)3710000000002550 035 $a(EBL)1398255 035 $a(SSID)ssj0000962855 035 $a(PQKBManifestationID)11544094 035 $a(PQKBTitleCode)TC0000962855 035 $a(PQKBWorkID)10979930 035 $a(PQKB)11319422 035 $a(DE-He213)978-3-0348-0636-7 035 $a(MiAaPQ)EBC6314131 035 $a(MiAaPQ)EBC1398255 035 $a(Au-PeEL)EBL1398255 035 $a(CaPaEBR)ebr10969130 035 $a(OCoLC)922907164 035 $a(PPN)172421888 035 $a(EXLCZ)993710000000002550 100 $a20130725d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aIntroduction to Mathematical Analysis /$fby Igor Kriz, Ale? Pultr 205 $a1st ed. 2013. 210 1$aBasel :$cSpringer Basel :$cImprint: Birkhäuser,$d2013. 215 $a1 online resource (517 p.) 300 $aDescription based upon print version of record. 311 08$a9783034806350 311 08$a3034806353 320 $aIncludes bibliographical references (pages 501) and indexes. 327 $aPreface -- Introduction -- Part 1. A Rigorous Approach to Advanced Calculus -- 1. Preliminaries -- 2. Metric and Topological Spaces I -- 3. Multivariable Differential Calculus -- 4. Integration I: Multivariable Riemann Integral and Basic Ideas toward the Lebesgue Integral -- 5. Integration II: Measurable Functions, Measure and the Techniques of Lebesgue Integration -- 6. Systems of Ordinary Differential Equations -- 7. System of Linear Differential Equations -- 8. Line Integrals and Green's Theorem -- Part 2. Analysis and Geometry -- 9. An Introduction to Complex Analysis -- 10. Metric and Topological Spaces II -- 11. Multilinear Algebra -- 12. Smooth Manifolds, Differential Forms and Stokes' Theorem -- 13. Calculus of Variations and the Geodesic Equation -- 14. Tensor Calculus and Riemannian Geometry -- 15. Hilbert Spaces I: Definitions and Basic Properties -- 16. Hilbert Spaces II: Examples and Applications -- Appendix A. Linear Algebra I: Vector Spaces -- Appendix B. Linear Algebra II: More about Matrices -- Bibliography -- Index of Symbols -- Index.  . 330 $aThe book begins at an undergraduate student level, assuming only basic knowledge of calculus in one variable. It rigorously treats topics such as multivariable differential calculus, the Lebesgue integral, vector calculus and differential equations. After having created a solid foundation of topology and linear algebra, the text later expands into more advanced topics such as complex analysis, differential forms, calculus of variations, differential geometry and even functional analysis. Overall, this text provides a unique and well-rounded introduction to the highly developed and multi-faceted subject of mathematical analysis as understood by mathematicians today. 606 $aFunctions of real variables 606 $aMatrix theory 606 $aAlgebra 606 $aMeasure theory 606 $aFunctions of complex variables 606 $aDifferential equations 606 $aSequences (Mathematics) 606 $aReal Functions$3https://scigraph.springernature.com/ontologies/product-market-codes/M12171 606 $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094 606 $aMeasure and Integration$3https://scigraph.springernature.com/ontologies/product-market-codes/M12120 606 $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074 606 $aOrdinary Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12147 606 $aSequences, Series, Summability$3https://scigraph.springernature.com/ontologies/product-market-codes/M1218X 615 0$aFunctions of real variables. 615 0$aMatrix theory. 615 0$aAlgebra. 615 0$aMeasure theory. 615 0$aFunctions of complex variables. 615 0$aDifferential equations. 615 0$aSequences (Mathematics) 615 14$aReal Functions. 615 24$aLinear and Multilinear Algebras, Matrix Theory. 615 24$aMeasure and Integration. 615 24$aFunctions of a Complex Variable. 615 24$aOrdinary Differential Equations. 615 24$aSequences, Series, Summability. 676 $a515 700 $aKriz$b Igor$4aut$4http://id.loc.gov/vocabulary/relators/aut$01453471 702 $aPultr$b Ale?$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910768190003321 996 $aIntroduction to Mathematical Analysis$93656108 997 $aUNINA