ADVANCED MATHEMATICS (CCE)
SHE Level  3 
SCQF Credit Points  20.00 
ECTS Credit Points  10.00 
Module Code  M3G124710 
Module Leader  Martin MacDonald 
School  School of Computing, Engineering and Built Environment 
Subject  SCEBE  School Office 
Trimesters 

PreRequisite Knowledge
Technical Mathematics 2
Summary of Content
The aim of the module is to impart student with the ability to apply mathematics through vector calculus, important transforms, numerical solutions, and probability and statistics as applied to engineering problems applications. Learning is emphasized on the development of students' ability to apply mathematics and statistics as a tool with understanding to solve engineering problems.Tutorials also serve as a platform of technical discussions to clarify any queries that arise from directed studies.
Syllabus
The teaching syllabus will cover the following areas: Probability and Statistics: Mean and standard deviation, correlation coefficient and equation of regression lines, Normal curve, Confidence interval, Testing of significance. Discrete, Continuous & mixed Random variables, Probability density function, cumulative distribution function, mathematical expectation, moments, moment generating function, Special distributions. Vector Calculus: Scalar & Vector fields, gradient, curl, divergence, change of variables, line integrals, surface integrals, volume integrals, Green's theorem in a plane, Gauss divergence theorem and Stoke's theorem. Fourier and Z Transforms: Fourier transforms & Z transforms: Definition, Properties, Transforms of elementary functions and derivatives, Convolution theorem, some useful Ztransforms and applications. Numerical Solution of equations : Bisection method, Fixed point iteration method, NewtonRaphson's method, Solution of linear system by Gauss elimination method, Inverse of a matrix by GaussJordan method; GaussJacobi and GaussSeidel methods. Numerical solution of Ordinary and Partial Differential Equations: Solution of ordinary differential equationsEuler's method, RungeKutta method of order 4. Finitedifference techniques to reduce PDEs to matrix problems, implicit/explicit time stepping.
Learning Outcomes
On completion of this module the student should be able to:1. Determine measures of central tendency, coefficient of correlation and regression lines(AM1, AM5)2. Apply the knowledge of normal distribution in fixing the confidence limits and testing the significance(AM1, AM5)3. Apply basic concepts of probability & analyse probability distributions(AM1, AM5)4. Distinguish scalar & vector fields and compute gradient, curl, divergence(AM1, AM5)5. Apply the knowledge of line integrals, surface integrals and volume integrals on vector fileds(AM5)6. Compute Fourier Transform and its applications(AM1, AM5)7. Compute Z Transform and its applications(AM1, AM5)8. Solve transcendental equations by numerical techniques(AM1)9. Solve the system of linear equations by numerical techniques(AM1)10. Apply gained knowledge of numerical methods to solve ordinary differential equations(AM1)11. Apply gained knowledge of Numerical methods to solve partial differential equations(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.
Indicative Reading
360 1. Kreyszig, E. (2011) Advanced Engineering Mathematics. John Wiley & Sons. 2. James, G. (2007) Advanced Modern Engineering Mathematics. Pearson Education. Grewal, B.S. (2007) Higher Engineering Mathematics. Delhi: Khanna Publishers.
Transferrable Skills
The module will enhance the student's ability in applying mathematical tools for solving problems occurring in engineering and technology. Through the study of mathematical techniques, the student will develop his/her analytical, numerical and problemsolving skills in engineering applications.
Module Structure
Activity  Total Hours 

Independent Learning (FT)  100.00 
Lectures (FT)  56.00 
Assessment (FT)  16.00 
Tutorials (FT)  28.00 
Assessment Methods
Component  Duration  Weighting  Threshold  Description 

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