Introduction to analysis in several variables : advanced calculus / Michael E. Taylor

By:

Taylor, Michael Eugene, 1946- [VerfasserIn]

Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Pure and applied undergraduate texts ; v.46Publisher: Providence, Rhode Island : American Mathematical Society, [2020]Description: 1 Online-Ressource (xii, 445 pages) : illustrationsISBN:

1470460165
9781470460167

Subject(s):

Genre/Form:

Lehrbuch

Additional physical formats: 9781470456696 | 1470456699 | Erscheint auch als: Introduction to analysis in several variables. Druck-Ausgabe Providence, Rhode Island : American Mathematical Society, 2020. xii, 445 SeitenMSC: MSC: 26B05 | 26B20 | 26B15 | 26B12 | 26B10RVK: RVK: SK 400LOC classification:

QA303.2

Online resources:

Zugang im Netz des KIT

Summary: 3.3. Partitions of unity -- 3.4. Sard's theorem -- 3.5. Morse functions -- 3.6. The tangent space to a manifold -- Chapter 4. Differential forms and the Gauss-Green-Stokes formula -- 4.1. Differential forms -- 4.2. Products and exterior derivatives of forms -- 4.3. The general Stokes formula -- 4.4. The classical Gauss, Green, and Stokes formulas -- 4.5. Differential forms and the change of variable formula -- Chapter 5. Applications of the Gauss-Green-Stokes formula -- 5.1. Holomorphic functions and harmonic functions -- 5.2. Differential forms, homotopy, and the Lie derivativeSummary: 5.3. Differential forms and degree theory -- Chapter 6. Differential geometry of surfaces -- 6.1. Geometry of surfaces I: geodesics -- 6.2. Geometry of surfaces II: curvature -- 6.3. Geometry of surfaces III: the Gauss-Bonnet theorem -- 6.4. Smooth matrix groups -- 6.5. The derivative of the exponential map -- 6.6. A spectral mapping theorem -- Chapter 7. Fourier analysis -- 7.1. Fourier series -- 7.2. The Fourier transform -- 7.3. Poisson summation formulas -- 7.4. Spherical harmonics -- 7.5. Fourier series on compact matrix groups -- 7.6. Isoperimetric inequalitySummary: Appendix A. Complementary material -- A.1. Metric spaces, convergence, and compactness -- A.2. Inner product spaces -- A.3. Eigenvalues and eigenvectors -- A.4. Complements on power series -- A.5. The Weierstrass theorem and the Stone-Weierstrass theorem -- A.6. Further results on harmonic functions -- A.7. Beyond degree theory-introduction to de Rham theory -- Bibliography -- Index -- Back CoverSummary: Cover -- Title page -- Copyright -- Contents -- Preface -- Some basic notation -- Chapter 1. Background -- 1.1. One-variable calculus -- 1.2. Euclidean spaces -- 1.3. Vector spaces and linear transformations -- 1.4. Determinants -- Chapter 2. Multivariable differential calculus -- 2.1. The derivative -- 2.2. Inverse function and implicit function theorems -- 2.3. Systems of differential equations and vector fields -- Chapter 3. Multivariable integral calculus and calculus on surfaces -- 3.1. The Riemann integral in variables -- 3.2. Surfaces and surface integralsSummary: This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential fPPN: PPN: 1755156308Package identifier: Produktsigel: BSZ-4-NLEBK-KAUB | ZDB-4-NLEBK

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