# MATH06091 2018 Mathematics 3

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**Description**

This subject adds further to the Mathematical skill set of computing students. The module begins with the student developing competence in the usage and application of various co-ordinate geometry formulae and then looks at the application of matrices to transformations of geometric objects. The middle section of the module spends time on differentiation and its applications. The final section develops competence in performing vector operations.

### Learning Outcomes

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

**1.**

Demonstrate competence in co-ordinate geometry calculations.

**2.**

Apply matrix algebra to linear transformations.

**3.**

Solve problems by determining and using derivatives.

**4.**

Show competence in the use of partial derivatives.

**5.**

Demonstrate competence in vector operations

### Teaching and Learning Strategies

The student will engage with the content of the module through lectures and tutorials.

The student will work on practical examples and exercise sheets to develop and apply their learning.

### Module Assessment Strategies

Written examination at end of semester and also a written examination around mid-semester.

### Repeat Assessments

The repeat assessment will involve a repeat examination.

### Indicative Syllabus

1. Co-ordinate geometry and linear transformations: Distance, midpoint, divisors, slope, angle between lines. Equation of a line and plane. Equation of a circle and sphere. Tangent and normal line and plane.

2. Matrix representation of transformations such as rotations and translations, Apply matrices to composite transformations on geometric objects.

3. Differentiation: Derivatives, higher derivatives of polynomial, trignometric, exponential and logarithmic functions. Product, quotient and chain rule. Applications such as finding equations of tangent and normal lines, rate of change problems, optimisation problems. Newton Raphson approximation method.

4.Partial Differentiation: Partial derivatives, higher partial derivatives. Applications such as finding equations of tangent planes and normal planes, rate of change problems, optimisation problems.

5. Vectors: components of a vector, unit vector, direction cosines, scaler product, vector product, angle between vectors, differentiation of vectors.

### 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 breakdown | Coursework Assessment | Closed Book Exam | 30 % | Week 7 | 1,2 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | End of term exam | Final Exam | Closed Book Exam | 70 % | Week 7 | 1,2,3,4,5 |

### Full Time Mode Workload

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

Lecture | Lecture Theatre | Lecture | 3 | Weekly | 3.00 |

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

Independent Learning | Not Specified | Independent Learning | 3 | Weekly | 3.00 |

### Required & Recommended Book List

**Recommended Reading**

2017

*Discrete Maths for Computing*Palgrave MacMillan

**Recommended Reading**

2017

*Maths for Computing and Information Technology*Prentice Hall