# 2007/08 Undergraduate Module Catalogue

## CIVE1619 Preparatory Mathematics For Engineers

### 10 creditsClass Size: 180

**Module manager:** Dr P A Sleigh**Email:** P.A.Sleigh@leeds.ac.uk

**Taught:** Semester 1 View Timetable

**Year running** 2007/08

**This module is not approved as an Elective**

### Objectives

To prepare students without A Level Mathematics for the Modules Engineering Mathematics 1.1 & 1.2.### Syllabus

Algebra and Functions:

- Simplification of rational algebraic expressions including factorising and cancelling, and dividing one polynomial by another,

- Rational functions and partial fractions,

- The Remainder Theorem.Co-ordinate geometry in the (x,y)-plane,

- Co-ordinate geometry of the circle, standard equation of the circle,

- Cartesian and parametric representations of curves and the conversion between them. Sequences and Series Expansions;

- The expansion of (1+x)^n, the notations n! and ,

- Binomial expansion of (1+x)^q where q is a rational number. Trigonometry;

- The secant, cosecant and cotangent functions,

- Inverse trigonometric functions, their graphs and their restricted domains and their relationship with the sine cosine and tangent functions,

- Knowledge and use of double angle formulas, the formulas for sin(A +/- B), cos(A +/- B and tan(A +/- B),

- Expression of a.cosq + b.sinq in the forms r.cos(q+a) and r.sin(q+a). Exponentials and logarithms;

- Exponential growth and decay,

- The solution of equations of the form a^x=b. Differentiation;

- The derivatives of the trigonometric functions,

- Application of differentiation to tangents and normals,

- Differentiation using the product, quotient and chain rules, and the formula dx/dy=1/(dy/dx),

- Differentiation of functions defined implicitly or parametrically,

- Formation of simple differential equations. Integration;

- Integration of sinx and cosx,

- Simple cases of integration by parts and using substitutions,

- Simple cases of integration using partial fractions,

- Analytical solution of first order differential equations with separable variables.

### Teaching methods

Delivery type | Number | Length hours | Student hours |

Lecture | 22 | 1.00 | 22.00 |

Practical | 11 | 1.00 | 11.00 |

Seminar | 11 | 1.00 | 11.00 |

Private study hours | 56.00 | ||

Total Contact hours | 44.00 | ||

Total hours (100hr per 10 credits) | 100.00 |

### Private study

33 hours - 1 hour reading per lecture, 2 hours per example sheet23 hours - exam preparation

### Opportunities for Formative Feedback

- 4 marked problem sheets during semester### Methods of assessment

**Coursework**

Assessment type | Notes | % of formal assessment |

Problem Sheet | Problem sheet 1 | 5.00 |

Problem Sheet | Problem sheet 2 | 5.00 |

Problem Sheet | Problem sheet 3 | 5.00 |

Problem Sheet | Problem sheet 4 | 5.00 |

Total percentage (Assessment Coursework) | 20.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

**Exams**

Exam type | Exam duration | % of formal assessment |

Standard exam (closed essays, MCQs etc) | 2 hr 00 mins | 80.00 |

Total percentage (Assessment Exams) | 80.00 |

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

### Reading list

The reading list is available from the Library websiteLast updated: 08/11/2007

## Browse Other Catalogues

- Undergraduate module catalogue
- Taught Postgraduate module catalogue
- Undergraduate programme catalogue
- Taught Postgraduate programme catalogue

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