## APPLICABLE MATHEMATICS II (CCE)

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2H124709 Module Leader Calum 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

### Summary of Content

This module aims to build on the work of Level 1 and extend those aspects of Mathematics required in this and later stages of the degree programme. The module also provides grounding in those aspects of Calculus required in this and later stages of the degree programme.

### Syllabus

The teaching syllabus will cover the following areas: Statistics: Determine mean and standard deviation, simple regression and correlation, Normal curve, Confidence interval, Testing of hypothesis. Multiple Integrals: Double integrals in Cartesian coordinates - Change of order of integration. Triple integration in Cartesian coordinates - Area as double integral and Volume as triple integral. 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. Ordinary Differential Equations: Analytical solutions of first order ordinary differential equations by variable separation method, first order linear differential equations, second order homogeneous and nonhomogeneous linear differential equations. Partial Differential Equations: Formations of Partial Differential Equations, Solution of first order PDEs -standard types, second order homogeneous linear PDEs and applications.

### Learning Outcomes

On completion of this module the student will be able to:1. Interpret data using basic statistics including correlation and regression analysis(AM1, AM5)2. Apply the knowledge of normal distribution and fix the confidence limits and testing hypothesis(AM1, AM5)3. Evaluate double integrals in Cartesian coordinates and by change of order of integration(AM1, AM5)4. Evaluate triple integrals in Cartesian coordinates and apply the knowledge(AM1, AM5)5. Distinguish scalar & vector fields and compute gradient, curl, divergence(AM1, AM5)6. Apply the knowledge of line integrals, surface integrals and volume integrals on vector fields(AM1)7. Solve first and second order ordinary differential equations using appropriate methods(AM1)8. Solve first and second order homogenous partial differential equations(AM1)9. Apply the knowledge of 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.

-360 1. Anthony Croft, , 2001. Engineering Mathematics , Pearson Education Glyn James, 2007. Advanced Modern Engineering Mathematics , Pearson Education.

### Transferrable Skills

Through the study of a variety of mathematical techniques, the student will develop his/her analytical and problem-solving skills. The module will enhance the student's ability in applying mathematical tools for solving problems occurring in engineering and technology.

### Module Structure

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

### Assessment Methods

Component Duration Weighting Threshold Description
Coursework 1 n/a 30.00 35% Quizzes - FormativeWritten Assignment with questions Summative
Exam (Exams Office) 2.00 50.00 45% Final Examination - Unseen written examination for 2 hours duration
Exam (School) 1.50 20.00 35% Midterm Test - Unseen written exam for 1½ hours duration