# MATH06099 2019 Mathematics 102H

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**Description**

Solution of first and second order differential equations using Laplace transforms and other techniques.

Linear algebra including eigenvalues and eigenvectors.

### Learning Outcomes

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

**1.**

Solve first order separable and linear differential equations

**2.**

Solve first and second order differential equations using Laplace transforms

**3.**

Solve second order differential equations using the auxiliary equation and the particular solution.

**4.**

Matrix addition, subtraction and multiplication, inverses, determinants, eigenvalues and eigenvectors.

**5.**

Solve linear systems of equations using Gaussian elimination

### Indicative Syllabus

Solution of first order separable and linear differential equations

Definition and calculation of Laplace transforms and inverse Laplace transforms

Solution of first and second order differential equations using Laplace transforms

Solution of second order differential equations using the auxiliary equation

Matrix addition, subtraction and multiplication

Solution of linear systems using row reduction of matrices, matrix inverses.

Determinants, 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 | 1,2,3,4,5 |

### 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 |

### 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

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

**Other Resources**

www.mathcentre.ac.uk

www.khanacademy.org

IT Sligo Maths Support Centre