# ENG06069 2019 Introduction to Engineering Mathematics

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**Description**

This module prepares the student for progression onto the degree level 7 mathematics. It reintroduces the ideas of differentiation from the basics up to partial differentiation and integration from the basics up to integration by parts. It also covers formula manipulation, the factor theorem, partial fractions and complex numbers. The course is designed so that real life situations are used to demonstrate where the techniques are used.

### Learning Outcomes

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

**1.**

Be able to manipulate mathematical equations

**2.**

Be able to graph linear, quadratic, exponential, log and trig functions

**3.**

Use the factor theorem and remainder theorem

**4.**

Find partial fractions

**5.**

Differentiate using the chain rule, product rule and quotient rule, find the maxima and minima of functions

**6.**

perform parametric, implicit differentiation and partial differentiation

**7.**

perform integration by substitution and by parts

**8.**

Calculate areas using integration

**9.**

Apply De Moivre's theorem to find the powers of complex numbers

### Teaching and Learning Strategies

Online lecture

### Indicative Syllabus

- Formula manipulation and solving equations
- Remainder and factor theorems
- Partial fractions
- Functions and graphs including trig functions
- differentiation by first principles
- differentiation rules, including chain rule, product rule and quotient rule
- Minimum and maximum calculations
- Parametric, implicit and partial differentiation
- Integration by substitution and by parts
- Applications of integration including finding areas
- Complex numbers, polar form, performing mathematical operations on complex numbers including De Moivre's theorem

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

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

1 | Continual Assessment | Continuous Assessment | Assessment | 20 % | OnGoing | 1,2,3,4,5,6,7,8,9 |

### End of Semester / Year Assessment

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

1 | Final Exam | Final Exam | Closed Book Exam | 80 % | End of Year | 1,2,3,4,5,6,7,8,9 |

### Online Learning Mode Workload

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

Lecture | Online | Lecture | 1 | Weekly | 1.00 |

Directed Learning | Not Specified | Directed Learning | 1 | Weekly | 1.00 |

### Required & Recommended Book List

**Recommended Reading**

2007

*Engineering Mathematics*Routledge

### Module Resources

**Non ISBN Literary Resources**

No books are essential for this course. Reference material provided in:

- Engineering mathematics by John Bird published by Routledge
- Engineering mathematics by KA Stroud published by Palmgrave
- Foundation Mathematics for Engineers by John Berry and Patrick Wainwright published by Macmillan
- Mathematical log tables

**Other Resources**

www.mathcentre.ac.uk

www.khanacademy.org

IT Sligo Maths Support Centre