For the student who masters just 30% of the problems in this volume, passing the actual oral exam becomes a realistic goal. For the student who masters 70%, they are likely ready to teach the course themselves.
Functions of several variables, differentiable maps, extremum problems, and partial differential equations (PDEs). Differential Equations: Linear and non-linear systems. Geometry: Curvature and properties of curves. Integration: Multiple integrals. Oraux X Ens Analyse 4 24.djvu
This looks simple, but the trap is that convergence of the integral does not imply the function tends to zero unless additional uniform continuity conditions (via the bounded derivative) are used. For the student who masters just 30% of