# MATH06101 2019 Mathematics 202H

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**Description**

A geometric approach to vectors, matrices and vector fields and their applications to forces and velocities in three dimensions.

### Learning Outcomes

*On completion of this module the learner will/should be able to;*

**1.**

Find the scalar and cross product of vectors with applications including the projection of vectors, angles, areas, volumes and angular velocity

**2.**

Find the vector equations of lines and planes in three dimensions

**3.**

Determine the linear independence of vectors with geometric interpretation

**4.**

Find linear transformations and isometries as matrix operations including rotation and reflection. Find eigenvalues and eigenvectors

**5.**

Calculate the radial and tangential components of rotating systems

**6.**

Calculate the gradient of a scalar field and the divergence and curl of a vector field

### Indicative Syllabus

Vector algebra, addition and subtraction, scalar multiplication, triangle law for addition.

Scalar product and cross product of vectors with applications including the projection of vectors, angles, areas, volumes and angular velocity

Find the vector equations of lines and planes in three dimensions

Linear Independence of vectors, vector spaces, basis, dimension and rank

Linear transformations and isometries as matrix operations, including rotations, reflections and dilations. Eigenvalues and eigenvectors.

Calculus of vector functions and vector fields and applications (including coriolis force)

Calculate the gradient of a scalar field and the divergence and curl of a vector field

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Continuous Assessment | Coursework Assessment | Assessment | 20 % | OnGoing | 1,2,3,4,5,6 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
---|---|---|---|---|---|---|

1 | Final Exam | Final Exam | Closed Book Exam | 80 % | End of Term | 1,2,3,4,5,6 |

### Full Time Mode Workload

Type | Location | Description | Hours | Frequency | Avg Workload |
---|---|---|---|---|---|

Lecture | Flat Classroom | Lecture | 4 | Weekly | 4.00 |

Tutorial | Flat Classroom | Tutorial | 1 | Weekly | 1.00 |

Independent Learning | Not Specified | Independent Learning | 4 | Weekly | 4.00 |

### Module Resources

**Non ISBN Literary Resources**

K.A. Stroud: "Engineering Mathematics", any edition

K.A. Stroud: "Further Engineering Mathematics", any edition

**Other Resources**

www.mathcentre.ac.uk

www.khanacademy.org

IT Sligo Maths Support Centre