Syllabus
Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in Cartesian and cylindrical coordinates; higher order derivatives; Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities.
Course Curriculum
VECTOR ALGEBRA | |||
GRADIENT, DIVERGENCE AND CURL | |||
Gradient | 01:12:00 | ||
Tangent Plane and Normal | 00:18:00 | ||
Problems on Gradient | 00:07:00 | ||
Divergence and Curl | 00:41:00 | ||
LINE INTEGRAL | |||
Line Integral | 00:56:00 | ||
GREENS THEOREM | |||
Greens Theorem | 01:06:00 | ||
SURFACE INTEGRAL | |||
Surface Integral | 01:19:00 | ||
GAUSS DIVERGENCE THEOREM | |||
Gauss Divergence Theorem | 01:36:00 | ||
STOKES THEOREM | |||
Stokes Theorem | 00:56:00 | ||
CONSERVATIVE VECTOR FIELD | |||
Conservative Vector Field | 00:23:00 |
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