Course Outline

Week Topic Week 1 scalar & vector arithmetic vectors scalar & vector product vectors & points, curves, lines in 3D Week 2 vectors and planes in 3D calculation of distance in 3D differentiation of vectors integration of vectors Week 3 tangent vectors and arc length of curves in 3D curvature and centripetal acceleration Week 4 introduction to multivariable functions partial derivatives chain rule for partial derivatives Week 5 gradients directional derivatives tangent lines and tangent planes extrema of functions Week 6 mid term week Week 7 constrained max/min problems numerical integration method of least squares Week 8 review of single integrals double integrals surface areas from double integrals volumes from double integrals Week 9 triple integrals volume calculations in cylindrical & spherical coordinates moments of area, mass and volume Week 10 derivatives of definite integrals vector fields gradient, divergence and curl operations divergence, grad and curl identities Week 11 line integrals of scalar functions line integrals of vector functions conservative force fields surface integrals of scalar functions Week 12 surface integrals of vector functions integral theorems involving vector functions divergence theorem Green's theorem Week 13 Stoke's theorem Review