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 electromagnetism( Maxwell equations, Gauss law on
electromagnetism, calculation of electric field, work, scalar potential of electric field etc. )
Course Content (Syllabus)
Multivariable functions. Limits, continuity, directional derivative, partial derivative and applications. Total derivative/Tangent plane. Chain rule. Implicit functions. Taylor series. Local extrema. Lagrange multiplies. Double and triple integrals and applications. Change of variables. Curves. Vector valued functions. Vector fields. The gradient, divergence, rotation, Laplace operators. Line integrals and applications. Conservative fields. Scalar and vector potential. Surfaces. Surface integrals and applications. Green, Gauss, Stokes theorems. Αpplications in electromagnetism.