*GENG0002 *Mathematics B

## Module Overview

This module offers an introduction to the differential and integral calculus that underpins engineering mathematics.

### Aims and Objectives

#### Module Aims

â€¢ To present the mathematical methods of differential and integral calculus and to provide and introduction to differential equations and to vectors â€¢ To enable you to build a working toolbox of mathematical techniques for differentiating and integrating functions, for solving differential equations and for working with vector quantities. â€¢ To emphasise the meaning and purpose of these techniques and their use in solving Engineering and Physics problems

#### Learning Outcomes

##### Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

- The mathematical methods of differential and integral calculus and of some simple solution methods for various types of differential equations
- Vector operations

##### Subject Specific Intellectual and Research Skills

Having successfully completed this module you will be able to:

- Select and apply appropriate mathematical methods to solve abstract and real-world problems
- Show confidence in manipulating mathematical expressions, setting up and solving equations and constructing simple proofs

##### Transferable and Generic Skills

Having successfully completed this module you will be able to:

- Manage your own learning
- Apply problem solving techniques to familiar and unfamiliar problems

### Syllabus

Differentiation â€¢ understand the gradient of a curve at a point as the limit of the gradients of a sequence of chords â€¢ use the derivative of xn, lnx, ex, sinx, cosx, tanx and constant multiples, sums/differences of these â€¢ find gradient of a curve at a point â€¢ find equation of tangent/normal to a curve at a point â€¢ use the product and quotient rules â€¢ use the chain rule to differentiate functions of the form f(g(x)) â€¢ understand that a derivative gives a rate of change â€¢ find the second derivative of a function â€¢ understand and be able to use the relationship dydxdxdy1= â€¢ find the first derivative of a function which is defined parametrically â€¢ find the first derivative of a function which is defined implicitly â€¢ use logarithmic differentiation â€¢ locate stationary points and distinguish between maxima and minima (by any method) Integration â€¢ understand integration as the reverse of differentiation; integrate xn (including n =âˆ’1) ex sinx cosx sec2x together with sums/differences and constant multiples of these â€¢ recognise integrands of the form kf â€˜(x)/f(x) and kf(x)f â€˜(x) and integrate â€¢ integrate expressions requiring linear substitution e.g. sin(ax+b) and double angle formulae e.g. cos2x â€¢ use integration to find a region bounded by a curve and two ordinates or by two curves â€¢ recognise where an integrand may be regarded as a product and use integration by parts to integrate â€¢ integrate rational functions using partial fractions â€¢ integrate simple functions in parametric form â€¢ use the mid-ordinate rule, the trapezium rule and Simpsonâ€™s rule to obtain approximate values for definite integrals â€¢ apply integration to find volumes of revolution about the x-axis, centroids of uniform laminae, mean and rms values of functions Differential Equations â€¢ formulate a simple statement involving a rate of change as a differential equation â€¢ find by integration a general form of a solution for a differential equation in which the variable are separable â€¢ use initial condition(s) to find a particular integral Vectors â€¢ know difference between a scalar and a vector â€¢ use vector notation to locate points in 3 dimensions â€¢ add, subtract and multiply by a scalar â€¢ use unit vectors, position vectors and displacement vectors â€¢ find modulus of a vector â€¢ calculate scalar product and use to find angle between two vectors and to show that vectors are parallel or perpendicular â€¢ calculate vector product, interpret as area of a parallelogram and as a vector perpendicular to two others

### Learning and Teaching

#### Teaching and learning methods

Learning activities include â€¢ Individual work on examples, supported by tutorial/workshop sessions/extra support sessions. â€¢ Elements of the coursework module GENG0015 may support your learning in this module. Teaching methods include â€¢ Lectures, supported by example sheets. â€¢ Tutorials/Workshops/support sessions. â€¢ Printed notes will be available through Blackboard and/or through your module lecturer

Type | Hours |
---|---|

Preparation for scheduled sessions | 35 |

Follow-up work | 35 |

Completion of assessment task | 2 |

Tutorial | 36 |

Lecture | 36 |

Revision | 6 |

Total study time | 150 |

#### Resources & Reading list

Understanding Pure Mathematics Sadler & Thorning.

Thompson, Macmillan (1999). Calculus made easy.

Croft & Davison (1998). Mathematics for Engineers.

Stroud, Palgrave (2001). Engineering Mathematics.

### Assessment

#### Assessment Strategy

External repeat students will have marks carried forward from the previous year for tests (5%), and therefore exam will contribute 95% of total assessment.

#### Summative

Method | Percentage contribution |
---|---|

Examination (2 hours) | 100% |

#### Referral

Method | Percentage contribution |
---|---|

Examination | 100% |

#### Repeat Information

**Repeat type: Internal & External**