## 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 A (September start) B (January start)

### Pre-Requisite 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 Z-transforms and applications. Numerical Solution of equations : Bisection method, Fixed point iteration method, Newton-Raphson's method, Solution of linear system by Gauss elimination method, Inverse of a matrix by Gauss-Jordan method; Gauss-Jacobi and Gauss-Seidel methods. Numerical solution of Ordinary and Partial Differential Equations: Solution of ordinary differential equations-Euler's method, Runge-Kutta method of order 4. Finite-difference 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 problem-solving skills in engineering applications.

### Module Structure

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

### Assessment Methods

Component Duration Weighting Threshold Description
Coursework 1 n/a 30.00 n/a Quizzes - FormativeWritten Assignment with questions Summative
Exam (School) 1.50 20.00 n/a 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