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linear algebra by covering Sections 1 through 7 of Chapter 1 and then either
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3-dimensional affine function approximation arbitrary axis basis boundary called chain rule coefficients column Compute Consider constant continuously differentiable converges coordinate functions curl F denote differentiable vector field dimension direction dx dy entries equal equation Example Exercise exists field F Find finite formula Fourier function defined given gradient field graph Green's theorem Hence implicitly defined inequality inner product interval inverse function theorem iterated integral Jacobian determinant Jacobian matrix line integral linear combination linear function multiplication one-one open set orthonormal partial derivatives perpendicular piecewise smooth point x0 proof Prove quadratic polynomial real number real-valued function rectangle respect Riemann satisfies Section Show shown in Figure smooth curve smooth surface solution Stokes's theorem subset subspace Suppose symmetric tangent plane tangent vector Taylor expansion tends to zero tion variable vector field vector function vector space