## TECHNICAL MATHEMATICS 2 (CCE)

 SHE Level 2 SCQF Credit Points 20.00 ECTS Credit Points 10.00 Module Code M2G124708 Module Leader Calum MacDonald School School of Computing, Engineering and Built Environment Subject SCEBE - School Office Trimesters A (September start) B (January start) C (May start)

### Pre-Requisite Knowledge

Technical Mathematics 1

### 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: 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. Complex Variables: Analytic functions, Cauchy-Riemann equations Harmonic functions, Orthogonal System. Complex functions and mappings, Taylor and Laurent series, singularities. Fourier Series: Periodic function, Definition, Determination of Fourier series, Half range Fourier cosine series and sine series, Root Mean Square value. 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. Laplace Transforms: Laplace Transforms, Inverse Laplace transforms, Solution of Initial Value problems, Step functions, Impulse functions, Convolution integrals. Partial Differential Equations and Applications: Solution to Linear partial differential equations (PDEs) of first and second order, Practical applications in engineering including heat/diffusion and wave equations.

### Learning Outcomes

On completion of this module the student should be able to:1. Evaluate Double integrals in Cartesian coordinates and by Change of order of integration(AM1, AM5)2. Evaluate Triple integrals in Cartesian coordinates and apply the knowledge(AM1, AM5)3. Manipulate complex numbers, computations and conversion of Cartesian to polar forms(AM5)4. Outline concepts of analytic functions, mappings, Taylor and Laurent series, singularities(AM1, AM5)5. Determine Fourier series, half range sine and cosine series, R.M.S. value(AM1, AM5)6. Solve first and second order ordinary differential equations using appropriate methods(AM1, AM5)7. Compute Laplace Transforms and its applications(AM1, AM5)8. Solve first order and second order homogenous partial differential equations and applications(AM1, AM5)9. Apply the knowledge of partial differential equations(AM5)Complex Variables: Polar form of complex numbers, Analytic functions, Cauchy-Riemann equations Harmonic functions, Orthogonal System. Complex functions and mappings, Taylor and Laurent series, singularities.

### 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 Croft, A. (2001) Engineering Mathematics. Pearson Education. James, G. (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
Assessment (FT) 16.00
Lectures (FT) 56.00
Independent Learning (FT) 100.00
Tutorials (FT) 28.00

### 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) 2.00 50.00 45% Final Examination - Unseen written examination for 2 hours duration
Coursework 1 n/a 30.00 35% Quizzes - FormativeWritten Assignment with questions Summative