MAU22S02 Vector calculus for science
| Module Code | MAU22S02 |
|---|---|
| Module Title | Vector calculus for science |
| Semester taught | Semester 2 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Joe Ó hÓgáin |
| Module Prerequisites | MAU22S01 Multivariable 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.
- Re-assessment, if needed, consists of 100% exam.
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.