Laplace transform ( Definition), its original (Definition). Using definition and Lisint]= prove that Usin ar)= 2...

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Laplace transform ( Definition), its original (Definition). Using definition and Lisint]= prove that Usin ar)= 2 +1 4+3p Task: Find the original of the Laplace transform: F(p)=- p-8p+7 2 Evaluate the contour integral where C: C:-2, (2-z-3) using the Cauchy's integral formula. 3. Represent the complex number :=5-i graphically in the complex plane, find its principle value of argument, modulus, trigonometric and exponential forms. Calculate 1-2 Find a flux of the vector field a=yi-3x7+(x-:k through a part of the surface S: 8r+y+4z-8=0, created as a result of intersection of the plane S with coordinate planes. 5. Find a directional derivative of the scalar field u(x, y,)= +3: at the point M(1, 2, 2) along the direction of a normalvector to the surface S7-y-+1=0, that makes an acute angle with Oz axis. Find a work of the vector field F= (r+4y)i +(ry-5)/ on shifting a unit mass along a broken line ABC, where A(0, 0), B(2, 4), C(2, 5). Laplace transform ( Definition), its original (Definition). Using definition and Lisint]= prove that Usin ar)= 2 +1 4+3p Task: Find the original of the Laplace transform: F(p)=- p-8p+7 2 Evaluate the contour integral where C: C:-2, (2-z-3) using the Cauchy's integral formula. 3. Represent the complex number :=5-i graphically in the complex plane, find its principle value of argument, modulus, trigonometric and exponential forms. Calculate 1-2 Find a flux of the vector field a=yi-3x7+(x-:k through a part of the surface S: 8r+y+4z-8=0, created as a result of intersection of the plane S with coordinate planes. 5. Find a directional derivative of the scalar field u(x, y,)= +3: at the point M(1, 2, 2) along the direction of a normalvector to the surface S7-y-+1=0, that makes an acute angle with Oz axis. Find a work of the vector field F= (r+4y)i +(ry-5)/ on shifting a unit mass along a broken line ABC, where A(0, 0), B(2, 4), C(2, 5).