Multivariable Calculus with Linear Algebra and Series

PrefaceAcknowledgmentsChapter 1. Linear Equations and Matrices 1.1 Linear Systems and Matrices 1.2 Solution of Equations 1.3 The Inverse of a Matrix 1.4 DeterminantsChapter 2. Vector Spaces and Linear Transformations 2.1 Vector Spaces 2.2 Linear Independence and Bases 2.3 Linear Transformations 2.4 Rank of a Matrix 2.5 More About Rn 2.6 Eigenvalues and EigenvectorsChapter 3. Vectors and Analytic Geometry 3.1 Lines and Planes 3.2 Vectors in R3 3.3 Motion in R3 3.4 Parametrically Defined Curves 3.5 Coordinate Systems in R3 3.6 Surfaces in R3Chapter 4. Differential Calculus of Real-Valued Functions 4.1 Functions, Limits, and Continuity 4.2 Directional and Partial Derivatives 4.3 Differentiable Functions 4.4 The Mean-Value Theorem 4.5 Graphs and Tangent Planes 4.6 Implicit Functions 4.7 The Gradient 4.8 Taylor's Theorem 4.9 Maxima and Minima 4.10 The Method of Lagrange MultipliersChapter 5. Differential Calculus of Vector-Valued Functions 5.1 Functions, Limits, and Continuity 5.2 Differentiable Functions 5.3 The Chain Rule 5.4 Vector and Scalar Fields 5.5 Implicit Functions 5.6 Inverse Functions and Coordinate TransformationsChapter 6. Integration 6.1 Multiple Integrals 6.2 Iterated Integrals 6.3 Change of Variables 6.4 Physical Applications 6.5 Line Integrals 6.6 Surface Integrals of Scalar Fields 6.7 Surface Integrals of Vector Fields 6.8 The Divergence Theorem; Green's and Stokes's TheoremsChapter 7. Series 7.1 Infinite Sequences 7.2 Infinite Series 7.3 Power SeriesAnswers to Selected ProblemsIndex