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Module MAU22S02: Vector calculus for science
 Credit weighting (ECTS)

5 credits
 Semester/term taught

Hilary term 2021.22
 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
 MAU22S01
 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. Reassessments if required will consist of 100% exam.