Transcription of Multivariable Calculus - Duke University
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Multivariable CalculusJerry ShurmanReed CollegeContentsPreface..ix1 Results from One-Variable Calculus .. The Real Number System .. Foundational and Basic Theorems .. Taylor s Theorem .. 6 Part I Multivariable Differential Calculus2 Euclidean Space.. Algebra: Vectors .. Geometry: Length and Angle .. Analysis: Continuous Mappings .. Topology: Compact Sets and Continuity .. Review of the One-Variable Derivative .. Summary .. 603 Linear Mappings and Their Matrices.. Linear Mappings .. Operations on Matrices .. The Inverse of a Linear Mapping .. Inhomogeneous Linear Equations .. The Determinant: Characterizing Properties and TheirConsequences.
By way of a warm-up, chapter 1 reviews some ideas from one-variable calculus, and then covers the one-variable Taylor’s Theorem in detail. Chapters 2 and 3 coverwhat might be called multivariable pre-calculus, in-
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