| Autore |
Fusco Nicola <1956->
|
| Pubbl/distr/stampa |
Cham, Switzerland : , : Springer, , [2022]
|
| Descrizione fisica |
1 online resource (678 pages)
|
| Disciplina |
519.4
|
| Collana |
Unitext - Matematica per il 3 + 2
|
| Soggetto topico |
Numerical analysis
Anàlisi numèrica
|
| Soggetto genere / forma |
Llibres electrònics
|
| ISBN |
3-031-04151-8
|
| Formato |
Materiale a stampa  |
| Livello bibliografico |
Monografia |
| Lingua di pubblicazione |
eng
|
| Nota di contenuto |
Intro -- Preface -- Contents -- 1 Sequences and Series of Functions -- 1.1 Sequences of Functions: Pointwise and Uniform Convergence -- 1.2 First Theorems on Uniform Convergence -- 1.3 Theorems on Interchanging Limits and Integrals or Derivatives -- 1.4 Uniform Convergence and Monotonicity -- 1.5 Series of Functions -- 1.6 Power Series -- 1.7 Taylor Series -- 1.8 Fourier Series -- 1.9 The Convergence of Fourier Series -- Appendix to Chap.1 -- 1.10 The Ascoli-Arzelà Theorem -- 1.11 The Weierstrass Approximation Theorem -- 1.12 Abel's Theorem on Power Series -- 2 Metric Spaces and Banach Spaces -- 2.1 Introduction -- 2.2 Metric Spaces -- 2.3 Sequences in a Metric Space: Continuous Functions -- 2.4 Vector Spaces: Linear Maps -- 2.5 The Vector Space ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and Its Dual -- 2.6 Normed Vector Spaces -- 2.7 The Normed Vector Space ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 2.8 Complete Metric Spaces: Banach Spaces -- 2.9 Lipschitz Functions: The Contraction Theorem -- 2.10 Compact Sets: Continuous Functions on Compact Sets -- 2.11 Connected Open Subsets of ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- Appendix to Chap. 2 -- 2.12 Further Compactness Theorems: Generalised Weierstrass Theorem -- 3 Functions of Several Variables.
3.1 Round-Up of Topology in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 3.2 Limits and Continuity -- 3.3 Partial Derivatives -- 3.4 Higher Derivatives. Schwarz's Theorem -- 3.5 Gradient. Differentiability -- 3.6 Composite Functions -- 3.7 Directional Derivatives -- 3.8 Functions with Vanishing Gradient on Connected Sets -- 3.9 Homogeneous Functions -- 3.10 Functions Defined by Integrals -- 3.11 Taylor Formula and Higher-Order Differentials -- 3.12 Quadratic Forms. Definite, Semi-definite and Indefinite Matrices -- 3.13 Local Maxima and Minima -- 3.14 Vector-Valued Functions -- Appendix to Chap.3 -- 3.15 Convex Functions -- 3.16 Complements on Quadratic Forms -- 3.17 The Maximum Principle for Harmonic Functions -- 4 Ordinary Differential Equations -- 4.1 Introduction: The Initial Value Problem -- 4.2 Cauchy's Local Existence and Uniqueness Theorem -- 4.3 First Consequences of Cauchy's Theorem -- 4.4 The Global Existence and Uniqueness Theorem: Extension of Solutions -- 4.5 Solving First-Order ODEs in Normal Form -- 4.6 Solving First-Order ODEs Not in Normal Form -- 4.7 Solving Higher-Order Equations -- 4.8 Qualitative Study of Solutions -- Appendix to Chap. 4 -- 4.9 Peano's Theorem -- 5 Linear Differential Equations -- 5.1 General Properties -- 5.2 General Integral of Linear ODEs -- 5.3 The Method of Variation of Parameters -- 5.4 Bernoulli Equations -- 5.5 Homogeneous Equations with Constant Coefficients -- 5.6 Equations with Constant Coefficients and Special Right-Hand Side -- 5.7 Linear Euler Equations -- Appendix to Chap.5 -- 5.8 Boundary Value Problems -- 5.9 Linear Systems -- 6 Curves and Integrals Along Curves -- 6.1 Regular Curves -- 6.2 Oriented Curves -- 6.3 The Length of a Curve.
6.4 The Integral of a Function Along a Curve -- 6.5 The Curvature of a Plane Curve -- 6.6 The Cross Product in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R cubed) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 6.7 Biregular Curves in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R cubed) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark: Curvature -- Appendix to Chap.6 -- 6.8 Curves in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R cubed) /StPNE pdfmark [/StBMC pdfmarkR3ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark: Torsion, Frenet Frame -- 7 Differential One-Forms -- 7.1 Vector Fields. Work. Conservative Fields -- 7.2 Differential 1-Forms. Line Integrals -- 7.3 Exact 1-Forms -- 7.4 Exact 1-Forms on the Plane. Simply Connected Open Sets in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R squared) /StPNE pdfmark [/StBMC pdfmarkR2ps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 7.5 One-Forms in Space. Irrotational Vector Fields -- Appendix to Chap.7 -- 7.6 Simply Connected Open Sets in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark and Exact 1-Forms -- 8 Multiple Integrals -- 8.1 Double Integrals on Normal Domains -- 8.2 Reduction Formulas for Double Integrals -- 8.3 Gauss-Green Formulas. The Divergence Theorem. Stokes's Formula -- 8.4 Variable Change in Double Integrals -- 8.5 Triple Integrals -- 8.6 Peano-Jordan Measurable Subsets of ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark.
8.7 The Riemann Integral in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 8.8 Properties of Riemann Integrals -- 8.9 Summable Functions -- Appendix to Chap.8 -- 8.10 Jensen's Inequality -- 8.11 The Gamma Function. The Measure of the Unit Ball in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript bold italic n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 9 The Lebesgue Integral -- 9.1 Introduction -- 9.2 Pluri-Intervals. Open Sets. Compact Sets -- 9.3 Bounded Measurable Sets -- 9.4 Unbounded Measurable Sets -- 9.5 Measurable Functions -- 9.6 The Lebesgue Integral. Interchanging Limits and Integrals -- 9.7 Measure and Integration on Product Spaces -- 9.8 Changing Variables in Multiple Integrals -- Appendix to Chap.9 -- 9.9 Lp Spaces -- 9.10 Differentiability of Monotone Functions -- 9.11 Functions with Bounded Variation -- 9.12 Absolutely Continuous Functions -- 9.13 The Indefinite Integral in Lebesgue's Theory -- 10 Surfaces and Surface Integrals -- 10.1 Regular Surfaces -- 10.2 Local Coordinates and Change of Parameters -- 10.3 The Tangent Plane and the Unit Normal -- 10.4 The Area of a Surface -- 10.5 Orientable Surfaces: Surfaces with Boundary -- 10.6 Surface Integrals -- 10.7 Stokes's Formula and the Divergence Theorem -- 11 Implicit Functions -- 11.1 The Implicit Function Theorem for Equations -- 11.2 The Implicit Function Theorem for Systems -- 11.3 Local and Global Invertibility -- 11.4 Constrained Maxima and Minima. Lagrange Multipliers -- Appendix to Chap.11 -- 11.5 Singular Points of a Plane Curve -- 12 Manifolds in Rn and k-Forms.
12.1 k-Dimensional Manifolds in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 12.2 The Tangent Space and the Normal Space of a Manifold -- 12.3 Measure and Integration on k-Submanifolds in ps: [/EMC pdfmark [/Subtype /Span /ActualText (double struck upper R Superscript n) /StPNE pdfmark [/StBMC pdfmarkRnps: [/EMC pdfmark [/StPop pdfmark [/StBMC pdfmark -- 12.4 The Divergence Theorem -- 12.5 Alternating Forms -- 12.6 Differential k-Forms -- 12.7 Orientable Manifolds. Integration of k-Forms on Manifolds -- 12.8 Manifolds with Boundary. Stokes's Formula -- Appendix to Chap.12 -- 12.9 Exact and Closed Differential Forms -- Index.
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| Record Nr. | UNISA-996503549503316 |
Info
Mathematical analysis : functions of several real variables and applications / / Nicola Fusco, Paolo Marcellini, Carlo Sbordone
