{"product_id":"multivariable-mathematics-linear-algebra-multivariable-calculus-and-manifolds-international-edition-9780471631606","title":"Multivariable Mathematics Linear Algebra","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003eMultivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface. \u003cp\u003eChapter 1. Vectors and Matrices.\u003c\/p\u003e \u003cp\u003e1.1 Vectors in R\u003csup\u003e.\u003c\/sup\u003e.\u003c\/p\u003e \u003cp\u003e1.2 Dot Product.\u003c\/p\u003e \u003cp\u003e1.3 Subspaces of R\u003csup\u003e.\u003c\/sup\u003e\u003c\/p\u003e \u003cp\u003e1.4 Linear Transformations and Matrix Algebra.\u003c\/p\u003e \u003cp\u003e1.5 Introduction to Determinates and the Cross Product.\u003c\/p\u003e \u003cp\u003eChapter 2. Functions, Limits, and Continuity.\u003c\/p\u003e \u003cp\u003e2.1. Scalar- and Vector-Valued Functions.\u003c\/p\u003e \u003cp\u003e2.2. A Bit of Topology in R\u003csup\u003e.\u003c\/sup\u003e\u003c\/p\u003e \u003cp\u003e2.3. Limits and Continuity.\u003c\/p\u003e \u003cp\u003eChapter 3. The Derivative.\u003c\/p\u003e \u003cp\u003e3.1. Partial Derivatives and Directional Derivatives.\u003c\/p\u003e \u003cp\u003e3.2. Differentiability.\u003c\/p\u003e \u003cp\u003e3.3. Differentiation Rules.\u003c\/p\u003e \u003cp\u003e3.4. The Gradient.\u003c\/p\u003e \u003cp\u003e3.5. Curves.\u003c\/p\u003e \u003cp\u003e3.6. Higher-Order Partial Derivatives.\u003c\/p\u003e \u003cp\u003eChapter  4. Implicit and Explicit Solutions of Linear Systems.\u003c\/p\u003e \u003cp\u003e4.1. Gaussian Elimination and the Theory of Linear Systems.\u003c\/p\u003e \u003cp\u003e4.2. Elementary Matrices and Calculating Inverse Matrices.\u003c\/p\u003e \u003cp\u003e4.3. Linear Independence, Basis, and Dimension.\u003c\/p\u003e \u003cp\u003e4.4. The Four Fundamental Subspaces.\u003c\/p\u003e \u003cp\u003e4.5. The Nonlinear Case: Introduction to Manifolds.\u003c\/p\u003e \u003cp\u003eChapter 5. Extremum Problems.\u003c\/p\u003e \u003cp\u003e5.1. Compactness and the Maximum Value Theorem.\u003c\/p\u003e \u003cp\u003e5.2. Maximum\/Minimum Problems.\u003c\/p\u003e \u003cp\u003e5.3. Quadratic Forms and the Second Derivative Test.\u003c\/p\u003e \u003cp\u003e5.4. Lagrange Multipliers.\u003c\/p\u003e \u003cp\u003e5.5. Projections, Least Squares, and Inner Product Spaces. \u003c\/p\u003e \u003cp\u003eChapter 6. Solving Nonlinear Problems.\u003c\/p\u003e \u003cp\u003e6.1. The Contraction Mapping Principle.\u003c\/p\u003e \u003cp\u003e6.2. The Inverse and Implicit Function Theorems.\u003c\/p\u003e \u003cp\u003e6.3. Manifolds Revisited.\u003c\/p\u003e \u003cp\u003eChapter 7. Integration.\u003c\/p\u003e \u003cp\u003e7.1. Multiple Integrals.\u003c\/p\u003e \u003cp\u003e7.2. Iterated Integrals and Fubini’s Theorem.\u003c\/p\u003e \u003cp\u003e7.3. Polar, Cylindrical, and Spherical Coordinates.\u003c\/p\u003e \u003cp\u003e7.4. Physical Applications.\u003c\/p\u003e \u003cp\u003e7.5. Determinants and \u003ci\u003en\u003c\/i\u003e-Dimensional Volume.\u003c\/p\u003e \u003cp\u003e7.6. Change of Variables Theorem.\u003c\/p\u003e \u003cp\u003eChapter 8. Differential Forms and Integration on Manifolds.\u003c\/p\u003e \u003cp\u003e8.1. Motivation.\u003c\/p\u003e \u003cp\u003e8.2. Differential Forms.\u003c\/p\u003e \u003cp\u003e8.3. Line Integrals and Green’s Theorem.\u003c\/p\u003e \u003cp\u003e8.4. Surface Integrals and Flux.\u003c\/p\u003e \u003cp\u003e8.5. Stokes’s Theorem.\u003c\/p\u003e \u003cp\u003e8.6. Applications to Physics.\u003c\/p\u003e \u003cp\u003e8.7. Applications to Topology.\u003c\/p\u003e \u003cp\u003e9.  Eigenvalues, Eigenvectors, and Applications.\u003c\/p\u003e \u003cp\u003e9.1. Linear Transformations and Change of Basis.\u003c\/p\u003e \u003cp\u003e9.2. Eigenvalues, Eigenvectors, and Diagonalizability.\u003c\/p\u003e \u003cp\u003e9.3. Difference Equations and Ordinary Differential Equations.\u003c\/p\u003e \u003cp\u003e9.4. The Spectral Theorem.\u003c\/p\u003e \u003cp\u003eGlossary of Notations and Results from Single-Variable Calculus.\u003c\/p\u003e \u003cp\u003eFor Further Reading.\u003c\/p\u003e \u003cp\u003eAnswers to Selected Exercises.\u003c\/p\u003e \u003cp\u003eIndex.\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":51037070426455,"sku":"9780471631606","price":171.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780471631606.jpg?v=1750934255","url":"https:\/\/bookcurl.com\/products\/multivariable-mathematics-linear-algebra-multivariable-calculus-and-manifolds-international-edition-9780471631606","provider":"Book Curl","version":"1.0","type":"link"}