LEADER 04091nam 2200505 450 001 996495171103316 005 20230417104023.0 010 $a981-19-4793-7 035 $a(MiAaPQ)EBC7105506 035 $a(Au-PeEL)EBL7105506 035 $a(CKB)24978817500041 035 $a(PPN)265862345 035 $a(EXLCZ)9924978817500041 100 $a20230304d2022 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aIntegral calculus for engineers /$fGavril Pa?ltineanu, Ileana Bucur, Mariana Zamfir 210 1$aGateway East, Singapore :$cSpringer,$d[2022] 210 4$d©2022 215 $a1 online resource (263 pages) 311 08$aPrint version: Paltineanu, Gavriil Integral Calculus for Engineers Singapore : Springer,c2022 9789811947926 320 $aIncludes bibliographical references and index. 327 $aIntro -- Preface -- Contents -- 1 Indefinite Integrals -- 1.1 The Notion of Primitive Function (Antiderivative) of a Function -- 1.2 Basic Properties of Indefinite Integrals -- 1.3 Primitives of Rational Functions -- 1.4 Primitives of Trigonometric Functions -- 1.5 Primitives of Irrational Functions. Binomial Integrals -- 2 Definite Integrals -- 2.1 Area of a Curvilinear Trapezoid -- 2.2 Darboux Sums. Definition of Definite Integral -- 2.3 Integrability of Continuous and Monotonic Functions -- 2.4 Riemann Sums. Riemann Criterion for Integrability -- 2.5 Lebesgue Criterion for Integrability -- 2.6 Properties of Integrable Functions -- 2.7 Area of a Plane Figure -- 2.8 Approximating Definite Integral -- 3 Improper Integrals -- 3.1 Convergence and Divergence of Improper Integrals -- 3.2 Convergence Criteria for Improper Integrals -- 4 Integrals Depending on Parameter -- 4.1 Proper Integrals Depending on a Parameter -- 4.2 Improper Integrals Depending on a Parameter -- 4.3 Euler Integrals -- 5 Line Integrals -- 5.1 Parameterized Paths. Definition of a Curve -- 5.2 Rectifiable Paths and Curves -- 5.3 Natural Parameterization of a Curve -- 5.4 Line Integrals of the First Kind -- 5.5 Line Integrals of the Second Kind -- 5.6 Independence on the Path of Line Integral of the Second Kind -- 6 Double and Triple Integrals -- 6.1 Double Integral. Definition and Properties -- 6.2 Basic Properties of the Double Integral -- 6.3 Reducing a Double Integral to an Iterated Single Integral -- 6.4 Change of Variables in Double Integral -- 6.5 Applications of the Double Integral in Geometry and Mechanics -- 6.5.1 Mass of a Lamina -- 6.5.2 Coordinates of the Center of Mass of a Lamina -- 6.5.3 Moments of Inertia of a Lamina -- 6.6 Riemann-Green Formula -- 6.7 Improper Double Integrals -- 6.8 Volume of a Space Figure. 327 $a6.9 Triple Integrals. Definition and Basic Properties -- 6.10 Computing Triple Integral. Change of Variables in Triple Integral -- 6.11 Applications of the Triple Integral in Geometry and Mechanics -- 6.11.1 Volume of a Space Domain -- 6.11.2 Mass of a Solid -- 6.11.3 Coordinates of the Center of Mass of a Solid -- 6.11.4 Moment of Inertia of a Solid -- 7 Surface Integrals -- 7.1 Parameterized Surface Canvases. Definition of a Surface -- 7.2 The Area of a Smooth Surface -- 7.3 Surface Integral of the First Kind -- 7.4 Surface Integral of the Second Kind -- 7.5 Integral Formulas -- References -- Index. 606 $aCalculus, Integral 606 $aEngineering mathematics 606 $aCàlcul integral$2thub 606 $aMatemàtica per a enginyers$2thub 608 $aLlibres electrònics$2thub 615 0$aCalculus, Integral. 615 0$aEngineering mathematics. 615 7$aCàlcul integral 615 7$aMatemàtica per a enginyers 676 $a515.43 700 $aPa?ltineanu$b Gavril$01252227 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996495171103316 996 $aIntegral calculus for engineers$93041719 997 $aUNISA