Math 311 : Syllabus (outline)


Weeks 1-2 : Vector algebra (Chapter 1, 4 days)
                            Geometry
                             Equations of lines. Angles.
                             Dot Product. Equations of planes.
                             Cross Product.  Triple product. Vector algebraic identities.
Weeks 2-3 :  Space curves (Chapter 2, 4 days)
                              Space curves, differentiation rules. Tangents, velocity, arclength.
                              Acceleration and curvature.
                              Torsion. Frenet formulas.
                              Planar motion in polar coordinates

Weeks 4-5 :  Scalar and vector fields (Chapter 3, 8 days)
                             Scalar field. Gradient.
                             Vector fields.
                             Divergence.
                              Curl
                              Laplacian.
                              Vector identities.
                               Cylindrical and spherical coordinates.

                              EXAM 1

Weeks 6-9 :  Line, Surface and Volume integrals (Chapter 4, 11 days)
                             Line Integrals
                             Conservative Fields
                             Irrotational Fields
                             Oriented Surfaces
                             Surface integrals
                              Volume integrals

Weeks 10-13 :  Divergence and Stokes Theorem (Chapter 5, 8 days)
                             Divergence Theorem. Green's Theorem.

                             EXAM 2

                             Solutions to Laplace and Poisson Equation.
                              Helmholtz Decomposition Theorem
                             Stokes Theorem

Week 14    :   Applications
                    Possibilities: Fluid dynamics, electromagnetism, rotation matrices


University of New Mexico
Mathematics at UNM