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dc.contributor.author Loomis, Lynn Harold
dc.contributor.author Sternberg, Shlomo Zvi
dc.date.accessioned 2023-06-29T20:53:55Z
dc.date.available 2023-06-29T20:53:55Z
dc.date.issued 1990
dc.identifier.isbn 0-86720-122-3
dc.identifier.uri ${sadil.baseUrl}/handle/123456789/3727
dc.description 592 p. (PDF) sm
dc.description.abstract Intro; CONTENTS; PREFACE; Chapter 0 Introduction; 1 Logic: quantifiers; 2 The logical connectives; 3 Negations of quantifiers; 4 Sets; 5 Restricted variables; 6 Ordered pairs and relations; 7 Functions and mappings; 8 Product sets; index notation; 9 Composition; 10 Duality; 11 The Boolean operations; 12 Partitions and equivalence relations; Chapter I Vector Spaces; 1 Fundamental notions; 2 Vector spaces and geometry; 3 Product spaces and Hom(V, W); 4 Affine subspaces and quotient spaces; 5 Direct sums; 6 Bilinearity; Chapter 2 Finite-Dimensional Vector Spaces; 1 Basps; 2 Dimension. 3 The dual space4 Matrices; 5 Trace and determinant; 6 Matrix computations; *7 The diagonalization of a quadratic form; Chapter 3 The Differential Calculus; 1 Review in R; 2 Norms; 3 Continuity; 4 Equivalent norms; 5 Infinitesimals; 6 The differential; 7 Directional derivatives; the mean-value theorem; 8 The differential and product spaces; 9 The differential and Rn; 10 Elementary applications; 11 The implicit-function theorem; 12 Submanifolds and Lagrange multipliers; *13 Functional dependence; *14 Uniform continuity and function-valued mappings; *15 The calculus of variations. *16 The second differential and the classification of critical points*17 The Taylor formula; Chapter 4 Compactness and Completeness; 1 Metric spaces; open and closed sets; *2 Topology; 3 Sequential convergence; 4 Sequential compactness; 5 Compactness and uniformity; 6 Equicontinuity; 7 Completeness; 8 A first look at Banach algebras; 9 The contraction mapping fixed-point theorem; 10 The integral of a parametrized arc; 11 The complex number system; *12 Weak methods; Chapter 5 Scalar Product Spaces; 1 Scalar products; 2 Orthogonal projection; 3 Self-adjoint transformations. 4 Orthogonal transformations5 Compact transformations; Chapter 6 Differential Equations; 1 The fundamental theorem; 2 Differentiable dependence on parameters; 3 The linear equation; 4 The nth-order linear equation; 5 Solving the inhomogeneous equation; 6 The boundary-value problem; 7 Fourier series; Chapter 7 Multilinear Functionals; 1 Bilinear functionals; 2 Multilinear functionals; 3 Permutations; 4 The sign of a permutation; 5 The subspace n of alternating tensors; 6 The determinant; 7 The exterior algebra; 8 Exterior powers of scalar product spaces; 9 The star operator. Chapter 8 Integration1 Introduction; 2 Axioms; 3 Rectangles and paved sets; 4 The minimal theory; 5 The minimal theory (continued); 6 Contented sets; 7 When is a set contented?; 8 Behavior under linear distortions; 9 Axioms for integration; 10 Integration of contented functions; 11 The change of variables formula; 12 Successive integration; 13 Absolutely integrable functions; 14 Problem set: The Fourier transform; Chapter 9 Differentiable Manifolds; 1 Atlases; 2 Functions, convergence; 3 Differentiable manifolds; 4 The tangent space; 5 Flows and vector fields; 6 Lie derivatives sm
dc.language.iso en sm
dc.publisher Jones and Bartlett Publishers International sm
dc.subject Calculus sm
dc.subject Vector spaces sm
dc.subject Finite-dimensional vector spaces sm
dc.subject Compactness and completeness sm
dc.subject Scalar product spaces sm
dc.subject Differential equations sm
dc.subject Multilinear functionals sm
dc.subject Intergration sm
dc.title Advanced calculus sm
dc.title.alternative Revised edition sm
dc.type Book sm


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