## MAS252 Further Civil Engineering Mathematics and Computing

 Semester 1, 2019/20 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.

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) Hicks Seminar Room F38 Thu 12:00 - 12:50 lecture Alfred Denny Building Lecture Theatre 1 Fri 12:00 - 12:50 tutorial (group CV2) 38 Mappin Street, Workroom 3 Fri 12:00 - 12:50 tutorial (group CV3) 38 Mappin Street, Workroom 4