## MAS252 Further Civil Engineering Mathematics and Computing

Semester 1, 2018/19 | 10 Credits | ||||

Lecturer: | Dr Istvan Ballai | Timetable | Reading List | ||

Aims | Outcomes | Teaching Methods | Assessment |

**Prerequisites:** MAS151 (Civil Engineering Mathematics)

No other modules have this module as a prerequisite.

## Outline syllabus

- Non-linear equations Netwon-Raphson method, bisection method.
- Ordinary differential equations Taylor series solution, Runge-Kutta methods for initial value problems, numerical solution of boundary value problems.
- Partial differentiation First and second derivatives, use of chain rule.
- Fourier Series Full range series, sine series, cosine series.
- Partial differential equations Classification, parabolic equations, Fourier series solution, numerical solution, Elliptical equations, Fourier series solutions, numerical solution.
- Analytical solutions (by separation of variables) of the ideal and non-ideal wave equation

## Aims

- To consolidate and extend the understanding and use of various analytical and numerical techniques in the area of non-linear algebraic equations, Fourier series and partial differential equations.

## Learning outcomes

- Solve non-linear algebraic equations by Newton-Raphson and bisection;
- Use Runge-Kutta methods to solve first and second order differential equations;
- Obtain partial derivatives of a function of two variables and use the chain rule;
- Expand functions in Fourier series;
- Solve the heat-conduction equation in one space-variable using explicit schemes;
- Solve simple parabolic partial differential equations using explicit schemes;
- Solve the Laplace equation in (x,y) by Fourier series;
- Solve linear elliptic partial differential equations in (x,y) by numerical methods.
- Solve linear hyperbolic differential equations (the wave equation) using analytical methods

## Teaching methods

Lectures, tutorials, problem solving

24 lectures, 12 tutorials

## Assessment

One formal 2 hour exam. [80%]

Matlab computer assessment exercise (taught by Civil Engineering Department) counts as 20% of the final mark.

## Reading list

Type | Author(s) | Title | Library | Blackwells | Amazon |
---|---|---|---|---|---|

A |
Stephenson | Mathematical Methods for Science Students | 510 (S) | Blackwells | Amazon |

A |
Stroud | Engineering Mathematics | 510.2462 (S) | Blackwells | Amazon |

A |
Stroud | Further Engineering Mathematics | 510.2462 (S) | Blackwells | Amazon |

C |
Pivato | Linear Partial Differential Equations and Fourier Theory | Blackwells | Amazon |

(

**A**= essential,

**B**= recommended,

**C**= background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.

## Timetable

Mon | 10:00 - 10:50 | tutorial | (group CV1) | Mappin Building Lecture Room 15 | |||

Thu | 12:00 - 12:50 | lecture | Dainton Building Lecture Theatre 1 | ||||

Fri | 14:00 - 14:50 | tutorial | (group CV2) | 38 Mappin Street Room 106 | |||

Fri | 14:00 - 14:50 | tutorial | (group CV3) | 38 Mappin Street Room 107 |