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Line Integral and Vector Calculus




 
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A series of free Engineering Mathematics video lessons.

Path integral (scalar line integral) from vector calculus
I discuss and solve an example involving a path integral (also known as a scalar line integral) from vector calculus. In particular, I integrate a given function over a helix in 3D-space, where the integration is with respect to arc length. Such concepts are seen in 2nd-year university mathematics and enjoy applications to engineering.
Line integral example in 3D-space
I discuss and solve an example involving a line integral of a vector field over a given curve. For this example, the parametrization of the curve is given. The method involves reducing the line integral to a simple ordinary integral. Such an example is seen in 2nd year university mathematics.
Line integral from vector calculus over a closed curve I present an example where I calculate the line integral of a given vector function over a closed curve. In particular, I the vector function is a $${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$ and the closed curve is the unit circle, oriented in the anticlockwise direction. I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics.
Line integral from vector calculus over a closed curve
I present an example where I calculate the line integral of a given vector function over a closed curve.. In particular, I the vector function is a $${\bf F}(x,y) := (-y/(x^2 + y^2), x/(x^2 + y^2)$$ and the closed curve is the unit circle, oriented in the anticlockwise direction.
I solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics.
Line integral example from Vector Calculus
I discuss and solve a simple problem that involves the evaluation of a line integral. This particular line integral is in the differential form. The method used to solve this problem is one that involves a simple substitution. Such an example is seen in 2nd-year university mathematics.

 



 

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