MAT 301 Analysis 1 Exam 2023

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MAT 301: University of Buea, End-of-Semester Examination (11-01-2023, 2hrs): definitions; full analysis of a scaled xy/sqrt(x^2+y^2)*sin(1/sqrt(x^2+y^2))-type function including an explicit proof that its partial derivatives are unbounded (hence discontinuous) near the origin, on top of the usual non-differentiability argument; the recurring Lagrange/level-set problems from Papers 7/9/10; a vector-field-Curl identity (Curl(f(r)r) = grad(f) x r) proven via the product rule for curl; the Newtonian-potential Laplacian computation (div(grad(1/rho))=0); statements of the Divergence/Green's/Stokes' Theorems; a cylindrical-to-rectangular coordinate conversion and an astroid-region double integral evaluated via a cubic trigonometric substitution.