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Calculus Calculus of Several Variables by Lang

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  1. Jan 24, 2013 #1

    micromass

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    Table of Contents:
    Code (Text):

    [LIST]
    [*] Mappings from Numbers to Vectors and Vectors to Numbers
    [LIST]
    [*] Vectors
    [LIST]
    [*] Definition of points in n-space
    [*] Located vectors
    [*] Scalar product
    [*] The norm of a vector
    [*] Lines and planes
    [*] The cross product
    [/LIST]
    [*] Differentiation of Vectors
    [LIST]
    [*] Derivative
    [*] Length of curves
    [*] The chain rule and applications
    [/LIST]
    [*] Functions of Several Variables
    [LIST]
    [*] Graphs and level curves
    [*] Partial derivatives
    [*] Differentiability and gradient
    [/LIST]
    [*] The Chain Rule and the Gradient
    [LIST]
    [*] The chain rule
    [*] Tangent plane
    [*] Directional derivative
    [*] Conservation law
    [/LIST]
    [*] Potential Functions and Curve Integrals
    [LIST]
    [*] Potential functions
    [*] Differentiating under the integral
    [*] Local existence of potential functions
    [*] Curve integrals
    [*] Dependence of the integral on the path
    [/LIST]
    [*] Higher Derivatives
    [LIST]
    [*] Repeated partial derivatives
    [*] Partial differential operators
    [*] Taylor's formula
    [*] Integral expressions
    [/LIST]
    [*] Maximum and Minimum
    [LIST]
    [*] Critical points
    [*] The quadratic form
    [*] Boundary points
    [*] Lagrange multipliers
    [/LIST]
    [/LIST]
    [*] Matrices, Linear Maps, and Determinants
    [LIST]
    [*] Matrices
    [LIST]
    [*] Matrices
    [*] Multiplication of matrices
    [/LIST]
    [*] Linear Mappings
    [LIST]
    [*] Mappings
    [*] Linear mappings
    [*] Geometric applications
    [*] Composition and inverse of mappings
    [/LIST]
    [*] Determinants
    [LIST]
    [*] Determinants of order 2
    [*] Determinants of order 3
    [*] Additional properties of determinants
    [*] Independence of vectors
    [*] Determinant of a product
    [*] Inverse of a matrix
    [/LIST]
    [/LIST]
    [*] Mappings from Vectors to Vectors
    [LIST]
    [*] Applications to Functions of Several Variables
    [LIST]
    [*] The derivative as a linear map
    [*] The Jacobian matrix
    [*] The chain rule
    [*] Inverse mappings and implicit functions
    [/LIST]
    [/LIST]
    [*] Multiple Integration
    [LIST]
    [*] Multiple Integrals
    [LIST]
    [*] Double integrals
    [*] Repeated integrals
    [*] Polar coordinates
    [*] Triple integrals
    [*] Center of mass
    [/LIST]
    [*] The Change of Variables Formula
    [LIST]
    [*] Determinants as area and volume
    [*] Dilations
    [*] Change of variables formula in two dimensions
    [*] Change of variables formula in three dimensions
    [/LIST]
    [*] Green's Theorem
    [LIST]
    [*] Statement of the theorem
    [*] Application to the change of variables formula
    [/LIST]
    [*] Surface Integrals
    [LIST]
    [*] Parametrization, tangent plane, and normal vector
    [*] Surface area
    [*] Surface integrals
    [*] Curl and divergence of a vector field
    [*] Divergence theorem
    [*] Stokes' theorem
    [/LIST]
    [*] Appendix: Fourier Series
    [LIST]
    [*] General scalar products
    [*] Computation of Fourier series
    [/LIST]
    [/LIST]
    [*] Answers
    [*] Index
    [/LIST]
     
     
    Last edited by a moderator: May 6, 2017
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