** ** this article makes use of the language and notation of vectors and matrices to explain matters in multivariable calculus. obtainable to a person with a great heritage in single-variable calculus, it provides extra linear algebra than frequently present in a multivariable calculus publication. Colley balances this with very transparent and expansive exposition, many figures, and diverse, wide-ranging routines. teachers will savor Colley’s writing type, mathematical precision, point of rigor, and entire collection of themes treated.

** ** **Vectors: **Vectors in and 3 Dimensions. extra approximately Vectors. The Dot Product. The move Product. Equations for Planes; Distance difficulties. a few *n*-Dimensional Geometry. New Coordinate structures. **Differentiation in different Variables: **Functions of a number of Variables; Graphing Surfaces. Limits. The spinoff. houses; Higher-Order Partial Derivatives; Newton’s procedure. The Chain Rule. Directional Derivatives and the Gradient.** Vector-Valued capabilities: **Parametrized Curves and Kepler's legislation. Arclength and Differential Geometry. Vector Fields: An creation. Gradient, Divergence, Curl, and the Del Operator.** Maxima and Minima in different Variables: **Differentials and Taylor's Theorem. Extrema of capabilities. Lagrange Multipliers. a few purposes of Extrema.** a number of Integration: **Introduction: parts and Volumes. Double Integrals. altering the Order of Integration. Triple Integrals. swap of Variables. functions of Integration.** Line Integrals: **Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields.** floor Integrals and Vector research: **Parametrized Surfaces. floor Integrals. Stokes's and Gauss's Theorems. extra Vector research; Maxwell's Equations.** Vector research in larger Dimensions: **An creation to Differential types. Manifolds and Integrals of *k*-forms. The Generalized Stokes's Theorem.

** ** For all readers attracted to multivariable calculus.

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