||Curves in the plane and in three-dimensional space. Arc length. Change of parameter. Line or trajectory integrals with respect to the arc length of scalar fields. Line integral or circulation of vector fields. Properties. Fundamental theorem of line integrals. Green’s theorem on the plane.
Regular surfaces. Tangent plane. Normal vector. Area of a Surface. Surface integral of scalar fields. Flux or surface integral of vector fields. Divergence and curl operators. Characterization of conservative fields. Stokes’ theorem. Gauss’ theorem.
|Numerical methods for initial value problems.
||Introduction to numerical methods. Euler’s and improved Euler’s method. Runge-Kutta’s fourth order method.