CURVES cvs1 Velocity vectors, velocity on parabola, movie of cycloid. cvs2a Compound motions, yoyo on helix. cvs2b Another example of compound motion. cvs3 Arc length, polygonal line approximation, numerical integration. 2D example and 3D example. cvs4 Acceleration, decomposition into tangential and normal components. cvs5 Curvature, 2D examples, parabola and another curve. cvs6 Curvature, 3D example. cvs7 Curvature, 3D example. FUNCTIONS OF TWO VARIABLES fun1 Graphs and level curves, two examples. fun2a Partial derivatives, slices of surface, smooth function fun2b Partial derivatives, surface with a ridge, f(x,y) = |x|y. fun3 Directional derivatives fun4 Gradient vector field, two examples in 2D fun5 Gradient vector field, example in 3D fun6 Tangent plane approximation with numerical calculation of error. crit1 graphs and level curves of f(x,y) = x^2 + 2bxy +y^2 for various values of b. crit2 graph and level curves of f(x,y) = 4xy +2x^2y - xy^2 crit3 Using contour maps to estimate and characterize critical pts. crit4 Max and min of f(x,y) = x^2 +y^2 + y^3 on a rectangle . crit5 Using contour maps to estimate solutions of constrained optimization problem. crit6 Using level curves to estimate solutions of constrained optimization problem, second example INTEGRATION int1 Approximation of integral by Riemann sums using the midpoint rule on each subrectangle int2 Transformation of a rectangle by a mapping. Approximation of area of image by linear approximations of the transformation on subrectangles VECTOR FIELDS vec1 Examples of vector fields in 2D: Rotational flow, a radial vector field, and the electric field produced by two line charges. vec2 Examples of vector fields in 3D: Rotational flow, gravitational field, electric field produced by two point charges. vec3 Curl of 2D vector fields: Shear flow. Two examples of counter clockwise rotational flow, one with positive curl, the other with negative curl. A more general vector field. vec4 Line integrals and a conservative vector field. An interactive way to plot polygonal paths and line integrals of a conservative vector field vec5 Line integrals and a nonconservative vector field. vec6 Divergence of 2D vector fields: Accelerated flow, a radial vector field, and a more general vector field. vec7 Flux through a boundary. A 2D vector field and an interactive to compute the flux through the boundary of a polygon. vec8 An interactive way of showing divergence by following an area carried by a flow. ( div(F) > 0). vec9 Same as vec8, but with vector field with div(F) < 0.