School of Mathematics and Statistics (SoMaS)

MAS252 Further Civil Engineering Mathematics and Computing

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

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