MAU22S02 Vector calculus for science

Assessment Details

• This module is examined in a 2-hour examination at the end of Semester 2.
• Continuous assessment contributes 20% towards the overall mark.
• The module is passed if the overall mark for the module is 40% or more. If the overall mark for the module is less than 40% and there is no possibility of compensation, the module will be reassessed as follows: 
  1) A failed exam in combination with passed continuous assessment will be reassessed by an exam in the supplemental session; 
  2) The combination of a failed exam and failed continuous assessment is reassessed by the supplemental exam; 
  3) A failed continuous assessment in combination with a passed exam will be reassessed by one or more summer assignments in advance of the supplemental session.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

• Manipulate vectors in R³ to evaluate dot products and cross products and investigate if some given vectors are linearly independent.
• Derive basic properties of vector fields, conservative vector fields, curves and surfaces in R³.
• Find the equation of normal lines and tangent planes to surfaces in R³.
• Evaluate line integrals and surface integrals using their definitions.
• Use Green's theorem to evaluate line integrals in the plane and use Gauss' theorem to evaluate surface integrals.
• Apply Stokes' theorem to evaluate line integrals and surface integrals.
• Solve first-order PDEs using the method of characteristics and solve second-order PDEs using separation of variables.

Module Content

• Vector algebra in R³. Vector fields, curves and surfaces in R³.
• Theorems of Green, Stokes and Gauss.
• Partial differential equations of first and second order.