1.12.14 Vector analysis
Condition: The scalar field is defined by the function \( \varphi=\tan ^{-1} \frac{2 x+z^{2}}{x^{2}+y^{2}} \). Find its gradient at point \( M(0,1,1) \) and construct level surfaces for: \( \varphi= \pm \frac{\pi}{4}, \varphi= \pm \frac{\pi}{6} \).
Vector analysis. Scalar and vector fields, level surfaces, calculation of gradient, divergence and field curl.