After the succesful completion of the course, the students are able to:
1. Calculate first and higher order partial derivatives and differentials, apply chain rule and model problems
associated with the concept of rate of change.
2. Calculate local and global extrema of multivariable functions in optimization problems.
3. Linearize scalar/vector fields.
4. Compute double and triple integrals (in cartesian, polar, cylindrical and spherical coordinates).
5. Parametrize curves and surfaces and calculate surface area.
6. Identify linear and central vector fields and perform calculations using gradient, divergence, rotation and
Laplace operators in Cartesian, cylindrical, spherical coordinates. Also, to identify conservative,
irrotational, incompressible fields and compute scalar/vector potential.
7. Study qualitative characteristics of vector fields (circulation - flux) with the use of line or surface
8. Connect between the concepts of circulation and rotation and the between the concepts of flux and divergence
using Green’s, Gauss and Stokes theorems.
9. Apply the basic tools of vector calculus in fluid mechanics.
Course Content (Syllabus)
Many Variables Calculus:
Surrfaces, Partial Derivatices, Chain Rule, Taylor's Expansion,
Double and Triple Integrals
Vector Fields, Line and Surface Integrals,
Conservative Vector Fields
Frenet Frame, Greens, Gauss and Stokes Theorem