Multivariable MathematicsThis book explores the standard problem-solving techniques of multivariable mathematics -- integrating vector algebra ideas with multivariable calculus and differential equations. Provides many routine, computational exercises illuminating both theory and practice. Offers flexibility in coverage -- topics can be covered in a variety of orders, and subsections (which are presented in order of decreasing importance) can be omitted if desired. Provides proofs and includes the definitions and statements of theorems" to show how the subject matter can be organized around a few central ideas. Includes new sections on: flow lines and flows; centroids and moments; arc-length and curvature; improper integrals; quadratic surfaces; infinite series--with application to differential equations; and numerical methods. Presents refined method for solving linear systems using exponential matrices. |
Contents
VECTORS | 1 |
DOT PRODUCTS AND CROSS PRODUCTS | 28 |
EQUATIONS AND MATRICES | 49 |
Copyright | |
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Common terms and phrases
approximation arrow c₁ c₁e c₂ c₂e chain rule Chapter coefficients column compute constant continuously differentiable converges coordinate functions curl F curve defined differential equation direction div F domain dot product dx dy dx/dt dy/dt entries Example Exercise field F field F(x Figure Find flow lines formula function f geometric given graph Green's theorem Hence Hint homogeneous initial conditions interval inverse iterated integral Laplace transform line integral linear combination linearly independent matrix multiple particular solution path perpendicular plane positive radius real numbers real-valued function rectangle region satisfies scalar Section Show shown in Fig sketch solve Suppose surface tangent vector Theorem u₁ variable vector field velocity Vf(x x₁ xy-plane y₁ zero ου ди ду