Different perspectives of Line integral of a vector field in parts

Linjing Guo published on 2022-02-24 included in category Calculus

the dimension of eigenspace and the multiplicity of corresponding eigenvlalue

Linjing Guo published on 2022-02-13 included in category Linear Algebra

Linjing Guo published on 2022-02-13 included in category Linear Algebra

Linjing Guo published on 2022-02-02 included in category Linear Algebra

Linjing Guo published on 2022-02-02 included in category Linear Algebra

Linjing Guo published on 2022-01-01 included in category Calculus

Evaluate $$ \int_C\frac{xdy-ydx}{\pi(x^2+y^2)}, $$

where $C_1$ is the circle $(x-1)^2+y^2=9$, traced in the anti-clockwise direction.

Linjing Guo published on 2022-01-01 included in category Calculus

Evaluate $$ \int_C\frac{xdy-ydx}{\pi(x^2+y^2)}, $$

where $C$ is a unit circle with centre $(0,0)$, traced in the anti-clockwise direction.