Line and Surface Integrals Report two key concepts in vector calculus
- 1. Line and Surface Integrals Ayrton John V. Bantay EgyE 612 Tensor Analysis for Engineers
- 3. 3 Introduction A line integral is an integral where the function to be integrated is evaluated along a curve and a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. Given a surface, one may integrate over its scalar fields (that is, functions which return scalars as values), and vector fields (that is, functions which return vectors as values). Surface integrals have applications in physics, particularly with the theories of classical electromagnetism.
- 10. 10 Definition: Line Integral of a scalar Field
- 21. 21 Line Integral of a Vector Field
- 22. 22 Line Integral of a Vector Field
- 23. 23 Line Integral of a Vector Field
- 24. 24 Line Integral of a Vector Field
- 25. 25 Line Integral of a Vector Field
- 41. 41 Definition: Surface Integral of f over Σ surface integral of f over Σ
- 42. 42 Surface Integral of f over Σ
- 43. 43 Surface Integral of f over Σ
- 44. 44 Surface Integral of f over Σ
- 45. 45 Surface Integral of f over Σ
- 46. 46 Surface Integral of f over Σ
- 47. 47 Surface Integral of f over Σ
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- 50. 50 Example
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