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Module MAU22S02: Vector calculus for science
- Credit weighting (ECTS)
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5 credits
- Semester/term taught
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Hilary term 2018-19
- Contact Hours
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11 weeks, 3 lectures including tutorials per week
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- Lecturer
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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
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- 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.