# MATH06096 2019 Mathematics 102

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**Description**

Introduction to linear algebra, calculus, statistics and probability

### Learning Outcomes

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

**1.**

Add and subtract vectors and find the scalar multiple of a vector. Calculate the length and unit vector of a vector.

**2.**

Add, subtract and multiply matrices. Find the scalar multiple of a matrix. Become familiar with the Zero and Identity matrix and their properties. Invert 2x2 matrices. Solve a system of linear equations with matrices.

**3.**

Differentiate polynomial, trigonometric, exponential and logarithmic functions. Differentiate using first principles. Differentiate using the product, quotient and chain rules. Calculate the equation of a tangent to a curve. Find the maxima and minima of a function. Calculate rates of change. Calculate velocities and accelerations.

**4.**

Calculate the mean, median, mode, standard deviation, range and variance of data. Plot a cumulative frequency polygon

**5.**

Use the normal distribution to calculate the probability of events

### Indicative Syllabus

1. Addition and subtraction of vectors and scalar multiples of vectors. Length and unit vector of a vector. The scalar product and its applications.

2. Addition, subtraction and multiplication of matrices. Scalar multiples of a matrix. The Zero and Identity matrix and their properties. Inversion of 2x2 matrices. Solution of a system of linear equations with matrices.

3. Differentiation of polynomial, trigonometric, exponential and logarithmic functions. Differentiation using first principles. Differentiation using the product, quotient and chain rules. Equation of a tangent to a curve. Maxima and minima of a function. Rates of change, velocity and acceleration as derivatives.

4. Mean, mode, median, range, interquartile range, standard deviation, and variance of data. Cumulative frequency.

### 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 |

### 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 | 1,2,3,4,5 |

### Full Time Mode Workload

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

Lecture | Flat Classroom | Lecture | 3 | Weekly | 3.00 |

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

Independent Learning | UNKNOWN | Study | 4 | Weekly | 4.00 |

### Module Resources

**Non ISBN Literary Resources**

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

Bird, J., (2007). Engineering Mathematics. Any Edition. Routledge.

**Other Resources**

www.mathcentre.ac.uk

www.khanacademy.org

IT Sligo Maths Support Centre