## Advanced Calculus The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, because of their practical value and the insights they give about theory. KEY TOPICS: Vectors and Matrices; Differential Calculus of Functions of Several Variables; Vector Differential Calculus; Integral Calculus of Functions of Several Variables; Vector Integral Calculus; Two-Dimensional Theory; Three-Dimensional Theory and Applications; Infinite Series; Fourier Series and Orthogonal Functions; Functions of a Complex Variable; Ordinary Differential Equations; Partial Differential Equations MARKET: For all readers interested in advanced calculus. |

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Accordingly analytic apply assume basis becomes boundary bounded called chapter chosen circle closed complex components consider const constant continuous converges coordinates corresponding curl curve defined definition dependent derivatives determine differential equation direction diverges domain dx dy equal equation Evaluate example exists expression Figure following Section formula function given gives grad Hence holds independent infinite integral interval limit linear linearly mapping matrix multiple normal obtain orthogonal partial particular path plane positive Problem proof Prove region Remark replaced represented respect result rule satisfies scalar sequence Show shown simply solution space surface tensor theorem transformation uniformly unit variables vector verify write zero ду