Vector analysis and field theory
Hey, I am taking a course in Vector analysis and field theory and I was wondering if anycone can recomend a text/work-book.
Scalar and vector fields. Scaling and dimensionless parameters. Equiscalar lines and surfaces, streamlines, field lines. Gradient vector, curl and divergence of vectors in Cartesian and polar coordinates with physical interpretation. Vector flux and circulation. Curve integrals, surface integrals, computation of pressure force. The divergence theorem (Gauss' theorem), Stokes' and Green's theorems. Mass conservation and equations of motion for fluids. Potential flows (source, sink, point vortex and dipole). Bernoulli's equation for stationary inviscid fluid flow. Convective and conductive heat flux, Fourier's law, equations for heat transport in fluids and solids. Use of Matlab for visualization of fields.
To give an introduction in field theory (vector calculus) with applications related mainly to fluid mechanics, geophysics, and physics. Through exercises using both analytical, numerical methods and computer graphics the students shall become familiar with the fundamental methods in field theory and its applications. The subject gives the students a good basis for further studies in mechanics and applied mathematics, physics, geosciences and astrophysics.