## MAS252 Further Civil Engineering Mathematics and Computing

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 1, 2022/23 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.