ADVANCED MATHEMATICS FOR CIVIL ENGINEERS (CCE)

 SHE Level 3 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M3G124711 Module Leader Martin MacDonald School School of Computing, Engineering and Built Environment Subject SCEBE - School Office Trimesters A (September start) B (January start)

Pre-Requisite Knowledge

Applicable Mathematics I and II

Summary of Content

The aim of the module is to impart the student with the knowledge of applications of mathematics to engineering.

Syllabus

The teaching syllabus will cover the following areas: Numerical Solution of equations : Bisection method, Fixed point iteration method, Newton-Raphson's method, Solution of linear system by direct methods: Gauss elimination method, Inverse of a matrix by Gauss-Jordan method; Iterative methods: Gauss-Jacobi and Gauss-Seidel methods. Interpolation and approximation: Finite differences, Interpolation for equal intervals by Newton's forward and backward interpolation formulae, Lagrange's interpolation formula for unequal intervals. Numerical Differentiation and Integration : Derivatives from difference table, Numerical differentiation using Newton's formulae, Numerical integration using Trapezoidal rule and Simpson's rule. Numerical solution of Ordinary Differential Equations: Numerical Solution of ordinary differential equations-Initial value problems -Simple Euler's method, Improved Euler's method, Runge-Kutta method of order 4. Numerical solution of Partial Differential Equations: Numerical Solution of PDEs-Boundary value problems. Finite difference approximations, One dimensional wave equation and two dimensional Laplace and Poisson's equations.

Learning Outcomes

On completion of this module the student should be able to:1. Solve transcendental equations by numerical techniques(AM1, AM5)2. Solve the system of linear equations using numerical techniques(AM1, AM5)3. Interpret finite difference methods(AM1, AM5) 4. Apply the knowledge for interpolation techniques(AM1, AM5)5. Approximate numerical differentiation and its applications (AM1, AM5)6. Approximate numerical integration and its applications(AM1, AM5)7. Solve ordinary differential equations using numerical techniques and its applications(AM1)8. Solve partial differential equations using numerical techniques and its applications (AM1).

Teaching / Learning Strategy

Combination of lectures and tutorials: Lectures: 4 hours/week and Tutorials: 2 hours/week Lectures will be used to convey basic concepts and principles with explanatory examples. Tutorials hours will be used to reinforce the module material taught during the lectures.

-360 1. Erwin Kreyszig, 2011. Advanced Engineering Mathematics , John Wiley & Sons. 2. Glyn James, 2007. Advanced Modern Engineering Mathematics , Pearson Education. B.S. Grewal, 2007. Higher Engineering Mathematics , Khanna Publishers, Delhi.

Transferrable Skills

Combination of lectures and tutorials: Lectures: 4 hours/week and Tutorials: 2 hours/week Lectures will be used to convey basic concepts and principles with explanatory examples. Tutorials hours will be used to reinforce the module material taught during the lectures.

Module Structure

Activity Total Hours
Independent Learning (FT) 100.00
Tutorials (FT) 28.00
Assessment (FT) 16.00
Lectures (FT) 56.00

Assessment Methods

Component Duration Weighting Threshold Description
Exam (School) 1.50 20.00 35% Midterm Test - Unseen written exam for 1½ hours duration
Exam (Exams Office) 3.00 50.00 45% Final Examination - Unseen written examination for 3 hours duration
Coursework 1 n/a 30.00 35% Quizzes - FormativeWritten Assignment with questions Summative