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.
a₁ a²u absolutely convergent analytic analytic function b₁ boundary bounded C₁ C₂ coefficients components conformal mapping const constant continuous coordinates corresponding curl curve curvilinear coordinates defined differential equation diverges domain double integral dx dy dx¹ dx² dx³ dy dz Evaluate example following Section formula Fourier series function f(x given grad Green's theorem harmonic Hence Hint improper integral interval Jacobian Let f(x limit line integral linearly independent mapping matrix obtain one-to-one orthogonal P₁ partial derivatives path piecewise plane polynomials power series Problem proof Prove region rule satisfies scalar sequence series converges Show solution surface tangent tensor theorem u₁ uniformly convergent V₁ variables vector space x₁ xy-plane y₁ z₁ zero θυ ди ду