Advanced Calculus

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The evolution of advanced calculus in undergraduate mathematics reveals a significant shift in curriculum focus over the past fifty years. Initially a core subject, it gradually gave way to real analysis as educators prioritized rigorous foundations. This led to a bifurcation in calculus courses, with one path exploring complex topics like calculus on n-manifolds and another simplifying to two- and three-dimensional calculus. However, the traditional depth of advanced calculus is often lost, particularly in addressing the complexities of several functions of several variables within limited course time.