• 1.

  Ready to use
  Find $\displaystyle \int_{\Gamma} \left(x+y \right)\;dx+\left(y-x\right)\;dy,\;\Gamma$ is the line from $(0,0)$ to $(a,b)$.
• 2.

  Ready to use
  Determine if various combinations of vectors are defined or not.
• 3.

  Ready to use
  Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 
• 4.

  Ready to use
  Double integrals (2) with numerical limits
• 5.

  Ready to use
  (Green’s theorem). $\Gamma$ a rectangle, find: $\displaystyle \oint_{\Gamma} \left(ax^2-by \right)\;dx+\left(cy^2+px\right)\;dy$.
• 6.

  Ready to use
  Given a pair of 3D position vectors, find the vector equation of the line through both.  Find two such lines and their point of intersection.
• 7.

  Has some problems
  Find the cosine of the angle between two pairs of 3D and 4D vectors. The calculations and answers are correct, however the Advice should display the interim calculations of the lengths of vectors and their products to say 6dps. At present the student may be mislead into using 2dps at each stage - the instruction at the start of Advice is somewhat confusing.
• 8.

  Has some problems
  Determine the correct parametric representation of a given curve.  Curve is randomly chosen from a set of 20. The graph of the curve was not displayed on my machine.
• 9.

  Ready to use
  Calculations of the lengths of two 3D vectors, the distance between their terminal points, their sum, difference, and dot and cross products.
• 10.

  Ready to use
  Parametric form of a curve, cartesian points, tangent vector, and speed.
• 11.

  Ready to use
  Parametric form of a curve, cartesian points, tangent vector, and speed.
• 12.

  Ready to use
  Intersection points, tangent vectors, angles between pairs of curves, given in parametric form.
• 13.

  Has some problems
  Find a unit vector orthogonal to two others. Uses $\wedge$ for the cross product. The interim calculations should all be displayed to enough dps, not 3,  to ensure accuracy to 3 dps. If the cross product has a negative x component then it is not explained that the negative of the cross product is taken for the unit vector.
• 14.

  Has some problems
  Find the unit vector parallel to a given vector. Interim calculations in Advice should be presented in enough accuracy to ensure that the final calculations are to 3dps.
• 15.

  draft
  Calculation of the length and alternative form of the parameteric representation of a curve.
• 16.

  draft
  Calculation of the length and alternative form of the parameteric representation of a curve, involving trigonometric functions.
• 17.

  Has some problems
  Cartesian form of the parametric representation of a surface, normal vector, and magnitude. Accuracy for part c) should be made more stringent as can be marked correct for an incorrect answer. Use a different sample range rather than 0 to 1 would help as would setting accuracy to something less than 0.001.
• 18.

  draft
  Unit normal vector to a surface, given in Cartesian form.
• 19.

  draft
  Cartesian form of the parametric representation of a surface, normal vector, and magnitude.
• 20.

  Has some problems
  Gradient of $f(x,y,z)$. Should warn that multiplied terms need * to denote multiplication.
• 21.

  Has some problems
  Find all points for which the gradient of a scalar field is orthogonal to the $z$-axis. Should warn that multiplied terms need * to denote multiplication.
• 22.

  draft
  Divergence of vector fields.
• 23.

  Has some problems
  Curl and divergence of a vector field.  Determine whether the vector field is irrotational or solenoidal.
• 24.

  Ready to use
  Directional derivative of a scalar field.
• 25.

  Has some problems
  Curl of a vector field. Should warn that multiplied terms need * to denote multiplication.
• 26.

  draft
  Outward normals to the surfaces enclosing a region; volume of that enclosed region.
• 27.

  draft
  Outward normals to the surfaces enclosing a region; volume of that enclosed region.

There are no questions in this group.