Pedagogical Study on the Relationship between Continuity and Existence of Directional Derivatives of a Multivariate Function
Continuity of a function at one point and existence of directional derivatives at that point are important parts in multivariate differential calculus.In the mathematical analysis exercise class,students are guided to explore the relationship between these two notions,and through continuous attempts,reverse thinking and seeking counter-examples,they can eventu-ally find that each one cannot be implied by the other.Inquiry-based teaching can strengthen students'ability of divergent thinking,mobilize students'initiative to explore and study,cultivate students'quality of perseverance and not fearing set-backs,and let them establish a rigorous thinking habit and a scientific attitude of seeking truth from facts.
inquiry teachingcontinuity of multivariate functiondirectional derivativeconical surface
万方数据
维普
