# MATH07039 2019 Mathematics 302H

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**Description**

A geometric approach to vectors, matrices and vector fields in three dimensions.

This module will be approximately 8 weeks in duration due to work placement.

### 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 functions of vectors including linear transformations and isometries as matrix operations including rotation and reflection. Find eigenvalues and eigenvectors

### 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

Vector functions including linear transformations and isometries as matrix operations, including rotations, reflections and dilations.

Eigenvalues and eigenvectors.

### 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 | Continuous Assessment | Assessment | 20 % | OnGoing | 1,2,3,4 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Final Exam | Final Exam | Closed Book Exam | 80 % | End of Term | 1,2,3,4 |

### Full Time Mode Workload

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

Lecture | Flat Classroom | Lecture | 5 | Weekly | 5.00 |

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

Independent Learning | Not Specified | Independent Learning | 5 | Weekly | 5.00 |

### Part Time Mode Workload

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

Lecture | Flat Classroom | Lecture | 5 | Weekly | 5.00 |

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

Independent Learning | Not Specified | Independent learning | 5 | Weekly | 5.00 |

### 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