Practical Session 2: Surface Integrals and Advanced Theorems

This practical session focuses on applying surface integral concepts through hands-on problem-solving. Students work through seven problems covering scalar surface integrals, surface area calculation, flux integrals, Stokes' Theorem, and the Divergence Theorem. Each problem includes complete step-by-step solutions. Key skills developed include parameterizing surfaces in cylindrical and spherical coordinates, computing normal vectors and surface area elements, evaluating scalar surface integrals for mass and area calculations, computing flux through cylinders, spheres, and planar surfaces, applying Stokes' Theorem to convert line integrals to surface integrals, using the Divergence Theorem to simplify flux calculations through closed surfaces, and verifying these theorems through explicit computation. The session concludes with homework problems and a summary of key formulas for reference.