PirateBay Download | hubbard j vector calculus linear algebra diff forms 5ed 2015

hubbard j vector calculus linear algebra diff forms 5ed 2015

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Textbook in PDF format Contents: Preliminaries Introduction Reading mathematics Quantifiers and negation Set theory Functions Real numbers Infinite sets Complex numbers Vectors, matrices and derivatives Introduction Introducing the actors: Points and vectors Introducing the actors: Matrices Matrix multiplication as a linear transformation The geometry of Rn Limits and continuity Five big theorems Derivatives in several variables as linear transformations Rules for computing derivatives The mean value theorem and criteria for differentiability Review exercises for Chapter Solving Equations Introduction The main algorithm: Row reduction manifolds, Taylor polynomials, quadratic forms and curvature Introduction Manifolds Tangent spaces Taylor polynomials in several variables Rules for computing Taylor polynomials Quadratic forms Classifying critical points of functions Constrained critical points and Lagrange multipliers Probability and the singular value decomposition Geometry of curves and surfaces Review exercises for Chapter Integration Introduction Defining the integral Probability and centers of gravity What functions can be integrated Measure zero Fubini's theorem and iterated integrals Numerical methods of integration Other pavings Determinants Volumes and determinants The change of variables formula Lebesgue integrals Review exercises for Chapter Volumes of manifolds Introduction Parallelograms and their volumes Parametrizations Computing volumes of manifolds Integration and curvature Fractals and fractional dimension Review exercises for Chapter Forms and vector calculus Introduction Forms on !Rn Integrating form fields over parametrized domains Orientation of manifolds vi Contents Integrating forms over oriented manifolds Forms in the language of vector calculus Boundary orientation The exterior derivative Grad, curl, div, and all that The pullback The generalized Stokes's theorem The integral theorems of vector calculus Electromagnetism Potentials Review exercises for Chapter Appendix: Analysis Introduction Arithmetic of real numbers Cubic and quartic equations Two results in topology: Nested compact sets and Heine-Borel Proof of the chain rule Proof of Kantorovich's theorem Proof of Lemma (superconvergence) Proof of differentiability of the inverse function Proof of the implicit function theorem Proving the equality of crossed partials Functions with many vanishing partial derivatives Proving rules for Taylor polynomials; big and little o Taylor's theorem with remainder Proving Theorem (completing squares) Classifying constrained critical points Geometry of curves and surfaces: Proofs Stirling's formula and proof of the central limit theorem Proving Fubini's theorem Justifying the use of other pavings Change of variables formula: A rigorous proof Volume and related results Lebesgue measure and proofs for Lebesgue integrals Computing the exterior derivative Proving Stokes's theorem Bibliography Photocredits Index

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hubbard j vector calculus linear algebra diff forms 5ed 2015

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