Math. (II)
- Analytic Geometry in 3 dimensions: inner and cross product- matrices- lines-planes-basis in R^2 and R^3- polar coordinates
- Vector functions and curves: smooth curves-parametrizations of curves - arc length - the arc-length parametrizations - differentiation and integral of vector functions - planar curves - curvature and torsion - Frenet frame - the formulas of curvature and torsion in terms of arbitrary parameters - quadratic surfaces and the parametrization of their intersection
- Functions of several variables: surfaces - contour curves - limits and continuity - cylindrical and spherical coordinates
- Differentiation of functions with several variables: partial derivatives - higher order derivatives - the chain rule - differentiability and differentials - gradients and directional derivatives - implicit functions - critical points - Lagrange theorem
- Multiple integration: change of variables - Fubinis theorem
- Line and surface integrals - smooth surfaces
- Vector calculus and analysis: gradient - curl - divergence - Green, divergence and ُStokes theorems
- Linear algebra: Vector space and its well-known examples - linearly independence- linear subspaces