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Vector Differential And Integral Calculus: Solved Problem Sets - Differentiation of Vectors, Div, Curl, Grad; Green’s theorem; Divergence theorem of Gauss, etc.

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                                                              Vector Differential And Integral Calculus: Solved Problems


We take a look at a few problems based on Vector differential and Integral Calculus.


Here are a few of the problems

1. A projectile is moving with constant speed along a meridian of the rotating earth in Figure. Find its acceleration.

2. Show that work done equals the gain in kinetic energy.

3. Find the area of ellipse x2/a2 + y2/b2 = 1.

4. Evaluate , where C is the circle x2 +y2 = 4, z = -3, oriented counter clockwise as seen by a person standing at the origin, and, with respect to right-handed Cartesian coordinates, F = [y, xz3, -zy3]      = yi + xz3j - zy3k.

5. Find the work done by the force F = 2xy3sinz i + 3x2y2sin z j + x2y3cos z k in the displacement around the curve of intersection of the paraboloid z = and the cylinder (x-1)2 + y2 = 1.

You will apply concepts related to Vector Differential and Integral calculus, differentiation of Vectors, Div, Curl, Grad;  Green’s theorem in the plane; Divergence theorem of Gauss, etc.

Tutorial with Solved Problems :

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In case you're interested in learning more about Vectors, here's the full set of tutorials we have :

Vectors 1a ( Theory and Definitions: Introduction to Vectors; Vector, Scalar and Triple Products)
Introducing a vector, position vectors, direction cosines, different types of vectors, addition and subtraction of vectors. Vector and Scalar products. Scalar Triple product and Vector triple product and their properties. Components and projections of vectors.

Vectors 1b ( Solved Problem Sets: Introduction to Vectors; Vector, Scalar and Triple Products )
Solved examples and problem sets based on the above concepts. 



Vectors 2a ( Theory and Definitions: Vectors and Geometry ) Vectors and geometry. Parametric vectorial equations of lines and planes. Angles between lines and planes. Co-planar and collinear points. Cartesian equations for lines and planes in 3D. 

Vectors 2b ( Solved Problem Sets: Vectors and Geometry )

Solved examples and problem sets based on the above concepts.






Vectors 3a ( Theory and Definitions: Vector Differential and Integral Calculus ) Vector Differential Calculus. Derivative, curves, tangential vectors, vector functions, gradient, directional derivative, divergence and curl of a vector function; important formulas related to div, curl and grad. Vector Integral Calculus. Line integral, independence of path, Green's theorem, divergence theorem of Gauss, green's formulas, Stoke's theorems.


Vectors 3b ( Solved Problem Sets: Vector Differential and Integral Calculus ) - Solved examples and problem sets based on the above concepts.



 

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