Abstract
We wrote this book as a supplement for the third semester of a physical science or engineering calculus sequence. It can equally well be used in a postcalculus course or problem seminar on mathematical methods for scientists and engineers. The subject is traditionally called Calculus of Several Variables, Vector Calculus, or Multivariable Calculus. The usual content is:
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Preliminary Theory of Vectors: Dot and Cross Products; Vectors, Lines, and Planes in R3.
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Vector-Valued Functions: Derivatives and Integrals of Vector-Valued Functions of One Variable; Space Curves; Tangents and Normals; Arclength and Curvature.
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Partial Derivatives: Directional Derivatives; Gradients; Surfaces; Tangent Planes; Multivariable Max/Min Problems; Lagrange Multipliers.
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Multiple Integrals: Double and Triple Integrals; Cylindrical and Spherical Coordinates; Change of Variables.
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Calculus of Vector Fields: Line and Surface Integrals; Fundamental Theorem of Line Integrals; Green’s, Stokes’, and Divergence Theorems.
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© 1998 Springer Science+Business Media New York
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Coombes, K.R., Lipsman, R.L., Rosenberg, J.M. (1998). Introduction. In: Multivariable Calculus and Mathematica®. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1698-8_1
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DOI: https://doi.org/10.1007/978-1-4612-1698-8_1
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98360-8
Online ISBN: 978-1-4612-1698-8
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