# MATH06069 2013 Mathematics 1

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**Description**

Mathematics for 1st year Mechanical, Mechatronic and Electronic Engineers

### Learning Outcomes

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

**1.**

Add, subtract, divide Natural Numbers, Integers, Rational Numbers and Real Numbers and demonstate knoweledge of the indice rules and riles of logs

**2.**

Solve linear, quadratic and simultaneous equations; expand (a+b)^{n }for n between 2 and 8; Solve equations with fractions; Manipulate formulae; State, prove and use the factor theorem.

**3.**

Use the ratio’s sine, cosine and tangent to calculate the side or an angle of a right angled triangle; Use pythagoras’ Theorem to calculate a side of a right angle d triangle; Become familiar with the sine, cosine and tangent of 30,45,60,90,180 etc. ; Use sine and cosine rule to calculate sides and angles of a triangle; Become familiar with standard trigonometric identities; Become familiar with compound and double angle formulae; Convert Degree’s to Radians and Radians to Degree’s.

**4.**

Add, subtract, divide complex numbers; calculate the complex conjugate, modulus and argument of a complex number; Be familiar with polar and exponential form; Multiply and divide complex numbers in polar form; Use De Moivre’s Theorem to calculate (a+bi)^n and find roots.

**5.**

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

**6.**

Become familiar with the basic rules of diferentations (x^{n}, e^{x},sin(x), cos(x), ln(x), etc.);Differentiate using 1^{st} principles; Be able to differentiate using the product, quotient and chain rule; Calculate the equation of a tangent to a curve; Use differentiation to find the Max/Min of a function.

**7.**

Add, subtract and scalar multiply vectors; Calculate the length and unit vector of a vector; Be familiar with their properties.

### Indicative Syllabus

- Revision of computation, algebraic operations, transposition of formulae, solution of algebraic equations, laws of indices and logs
- Elementary set theory, relations, functions and their graphs
- Solution of right-angled and other triangles, sin and cos rules, trigonometric identities, degrees and radians, area and circumference of circles
- Addition and subtraction of vectors and scalar multiples of vectors. Lengths and unit vectors of a vector.
- Addition, subtraction and multiplication of matrices. Scalar multiples of a matrix. The Zero and Identity matrix and their properties. Inversion of 2x2 matrices. Solution a system of linear equations with matrices.
- Add, subtract, divide complex numbers, and calculate the complex conjugate modulus and argument of a complex number. Be familiar with polar and exponential form. Multiply and divide complex numbers in polar form, DE Moivre’s Theorem
- 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.

### Coursework & Assessment Breakdown

**Coursework & Continuous Assessment**

**End of Semester / Year Formal Exam**

### Coursework Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Continuous Assessment | Continuous Assessment | UNKNOWN | 10 % | OnGoing | 4,5 |

2 | Continuous Assessment Christmas written | Continuous Assessment | UNKNOWN | 10 % | Week 12 | 1,2,3 |

3 | Continuous Assessment Easter written | Continuous Assessment | UNKNOWN | 10 % | Any | 5,6 |

4 | Continuous Assessment | Continuous Assessment | UNKNOWN | 10 % | OnGoing | 1,2,3 |

### End of Semester / Year Assessment

Title | Type | Form | Percent | Week | Learning Outcomes Assessed | |
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1 | Final Exam | Final Exam | UNKNOWN | 60 % | End of Year | 1,2,3,4,5,6,7 |

### Full Time Mode Workload

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

Tutorial | Not Specified | Tutorial | 1 | Weekly | 1.00 |

Lecture | Not Specified | Theory | 2 | Weekly | 2.00 |

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

### Part Time Mode Workload

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

Lecture | Distance Learning Suite | Lecture | 2 | Weekly | 2.00 |

Lecture | Not Specified | Independent Learning | 4 | Weekly | 4.00 |

### Module Resources

**Non ISBN Literary Resources**

Engineering Mathematics by K.A Stroud

**Other Resources**

None

**Additional Information**

None