Stokes' theorem, named after Sir George Stokes and originally formulated by William Thomson, relates the surface integral of a vector field's curl over a closed surface to the line integral around that surface. The theorem has significant applications in physics and engineering, including cloud formation analysis and separating oil from wastewater. Its mathematical expression is represented as the equality of the line integral of a vector function and the surface integral of its curl.

1. Stokes Theorem
Presented By,

2. History Definition Expression Proof Significance Application
Who invent Stokes Theorem?
Actually invented by William Thomson
Named after Sir George Stokes

3. History Definition Expression Proof Significance Application
Statement of Stoke’s Theorem
Stokes' theorem states that
the surface integral of a
function's curl over a
closed surface is equal to
the line integral of the
vector function around
that surface.

4. History Definition Expression Proof Significance Application
Mathematical Expression
𝑪
𝑭. 𝒅𝒓 =
𝑺
𝛁 × 𝑭 . 𝒏 𝒅𝑺

5. History Definition Expression Proof Significance Application
Mathematical Proof
𝛁𝑺𝟏 = 𝒌. 𝛁𝑺𝟏
Z
Y
X
∇𝑆1

6. History Definition Expression Proof Significance Application
Mathematical Proof 𝛁𝑺𝟏 = 𝒌. 𝛁𝑺𝟏
Z
Y
X
∇𝑆1

7. History Definition Expression Proof Significance Application
Mathematical Proof
Z
Y
X
∇𝑆1
𝑪
𝑭. 𝒅𝒓 =
𝑺
𝛁 × 𝑭 . 𝒏 𝒅𝑺

8. History Definition Expression Proof Significance Application
Physical Significance
𝑪
𝑭. 𝒅𝒓 = 𝟎 → irrotational or conservative vector
𝑪
𝑭. 𝒅𝒓 = Work done

9. History Definition Expression Proof Significance Application
Practical Application
𝑪𝒍𝒐𝒖𝒅 𝒇𝒐𝒓𝒎𝒂𝒕𝒊𝒐𝒏
𝑺𝒆𝒅𝒊𝒎𝒆𝒏𝒕𝒂𝒕𝒊𝒐𝒏 𝒂𝒏𝒂𝒍𝒚𝒔𝒊𝒔
𝑻𝒆𝒔𝒕𝒊𝒏𝒈 𝒇𝒍𝒖𝒊𝒅 𝒗𝒊𝒔𝒄𝒐𝒔𝒊𝒕𝒊𝒆𝒔
𝑺𝒆𝒑𝒂𝒓𝒂𝒕𝒊𝒏𝒈 𝒐𝒊𝒍 𝒇𝒓𝒐𝒎
𝒘𝒂𝒔𝒕𝒆𝒘𝒂𝒕𝒆𝒓

10. THANK YOU