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Vector calculus
This document covers key concepts in vector calculus including vector representations in Cartesian, cylindrical and spherical coordinate systems. It discusses techniques for calculating differential lengths, areas and volumes. The document also explains line, surface and volume integrals and provides examples of determining total surface areas. Additionally, it outlines ordinary derivatives of vectors, differentiation formulas, and applications involving streamlines and sketching vector fields. Drills with answers are included for practice problems.
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Vector calculus
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- 5. Differential Length, Area,and Volume
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- 11. Line, Surface, andVolume Integrals
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- 14. Drill ● Determine thetotal surface area enclosing a cylinder. ● Determine the total surface area enclosing a sphere.
- 15. Ordinary Derivative ofVectors Let R(u) be a vector depending on a scalar variable u.
- 16. Ordinary Derivative ofVectors Let R(u) be a vector depending on a scalar variable u.
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- 20. Streamlines and Sketchesof Fields Streamlines (flux lines or direction lines) are short line segments drawn with arrows pointing in the direction of E and the spacing of lines is inversely proportional to the strength of the field.
- 21. Streamlines and Sketchesof Fields
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- 25. Example Consider the vectorfield Find the equation of one particular streamline passing through P(-2,7,10).
- 26. Example Ans. y =-3.5x
- 27. Drill 2.7 Find theequation of the streamline that passes through the point P(1,4,-2) in the field E=: (a) -8x/y ax + 4x2/y2 ay;
- 28. Drill 2.7 Find theequation of the streamline that passes through the point P(1,4,-2) in the field E=: (a) -8x/y ax + 4x2/y2 ay; Ans. x2 + 2y2 = 33 ;
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