Advanced CalculusSeths and functions; Continuity; Defferentiation; Integration; Series; Uniform convergence; Diferentiation of transformations; Aplications to geometry and analysis; Differential geometry and vector calculus; Numerical methods. |
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3-space a₁ a₂ algebraic apply b₁ b₂ boundary bounded set Cauchy Cauchy sequence choose compact set compute continuous function coordinate Corollary curve definition differential forms divergent domain dx dy dz dz dx equation evaluate example Exercise exists f is continuous f₁ finite formula Fourier series function defined function f ƒ and g geometric given graph illustration improper integral interval inverse Jacobian Let f linear transformation mapping mathematical matrix mean value theorem neighborhood obtain open set P₁ P₂ partial derivatives plane polynomial power series proof prove q₁ real numbers rectangle region result sequence set function set of points space subset Suppose surface uniformly continuous uniformly convergent variables vector x₁ y₁ ди ду дх