Scalar field ( Definition, examples). Directional derivative of the scalar field (Definition, physical meaning, calculation )....

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Scalar field ( Definition, examples). Directional derivative of the scalar field (Definition, physical meaning, calculation ). Task: Find a directional derivative of the scalar field 2y -2 x +y' at the point M(1, 2, -1) along the u=xz+ direction of the vector 5 2i -j+ 3k . 2. Given a complex number z=- a) Represent the number graphically in the complex plane; b) Find its principle value of argument and modulus; c) Express the number in trigonometric and exponential form; 3-i. d) Calculate z and 2+3i 3. Evaluate the surface integral f x+y+2 d$ , if 4. Find the original of Laplace transform: F(p)=- (p-1)(p+8p+ 5. Check out if the Cauchy-Riemann equations are satisfied for the f f(z) = ze-2i . Calculate f'(z) if it exists. 6. Find a work of the vector field a=4yi +8xj+ zyk along a triangle contour ABC, if A(1, 0, 0), B(0, 3, 0), C(0, 0, 1). Scalar field ( Definition, examples). Directional derivative of the scalar field (Definition, physical meaning, calculation ). Task: Find a directional derivative of the scalar field 2y -2 x +y' at the point M(1, 2, -1) along the u=xz+ direction of the vector 5 2i -j+ 3k . 2. Given a complex number z=- a) Represent the number graphically in the complex plane; b) Find its principle value of argument and modulus; c) Express the number in trigonometric and exponential form; 3-i. d) Calculate z and 2+3i 3. Evaluate the surface integral f x+y+2 d$ , if 4. Find the original of Laplace transform: F(p)=- (p-1)(p+8p+ 5. Check out if the Cauchy-Riemann equations are satisfied for the f f(z) = ze-2i . Calculate f'(z) if it exists. 6. Find a work of the vector field a=4yi +8xj+ zyk along a triangle contour ABC, if A(1, 0, 0), B(0, 3, 0), C(0, 0, 1).