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Module MA22S2: Vector Calculus for Science

Credit weighting (ECTS)
5 credits
Semester/term taught
Hilary term 2012-13
Contact Hours
11 weeks, 3 lectures including tutorials per week
Lecturer
Dr. Joe Ó hÓgáin
Learning Outcomes
On successful completion of this module, students will be able to:
  • Manipulate vectors in R^3 to evaluate dot products and cross products and investigate if vectors are linearly independent;
  • Understand the concepts of vector fields, conservative vector fields, curves and surfaces in R^3;
  • Find the equation of normal lines and tangent planes to surfaces in R^3;
  • Evaluate line integrals and surface integrals from the definitions;
  • Use Green's Theorem to evaluate line integrals in the plane and use the Divergence Theorem (Gauss's Theorem) to evaluate surface integrals;
  • Apply Stokes's 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 R^3. Vector fields, curves and surfaces in R^3.
  • Theorems of Green, Stokes and Gauss.
  • PDEs of first and second order.
Module Prerequisite
MA22S1, MA22S3
Assessment Detail
This module will be examined in a 2 hour examination in Trinity term.Continuous assessment will contribute 20% to the final grade for the module at the annual examination session and at supplementals where applicable.