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More Lessons Engineering Math

Math Worksheets

A series of free Engineering Mathematics video lessons.

**Path integral (scalar line integral) from vector calculus**

Example involving a path integral (also known as a scalar line integral) from vector calculus.

How to 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**

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**

How to 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.

How to 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.

More Lessons Engineering Math

Math Worksheets

A series of free Engineering Mathematics video lessons.

Example involving a path integral (also known as a scalar line integral) from vector calculus.

How to 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.

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.

How to 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.

How to solve the problem and discuss the significance of the line integral through the mention of specific applications to engineering and physics?

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.

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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