Practical Class 6: Functions of Several Variables

This practical class is a comprehensive review session consolidating all topics on functions of several variables from previous classes. The material is designed for students completing their study of multivariable differential calculus.

The session systematically revisits key concepts: domain determination, limit computation and path dependence, continuity, partial derivatives and differentiability, the chain rule and implicit differentiation, gradient and directional derivatives, and local extrema classification. Each topic is reinforced through carefully selected problems with detailed solutions.

The class includes group work on domain sketching, limit analysis along different paths, investigation of differentiability, and classification of critical points. A quick self-test section helps students verify understanding, while the homework assignment provides additional practice. Common mistakes and key takeaways are highlighted throughout.