## Engineering Mathematics 2

 Unit code: CHEN10072 Credit Rating: 10 Unit level: Level 1 Teaching period(s): Semester 2 Offered by School of Mathematics Available as a free choice unit?: N

None

#### Aims

The unit aims to:   provide the background mathematics and IT skills required for subsequent chemical engineering courses in mathematically oriented topics.  Engineering applications are to be introduced where relevant.

#### Overview

Matrices and algebraic properties. Definition of determinant and properties. Identity, diagonal, transpose, upper/lower triangular and inverse matrices.

Solving systems of linear equations through Gaussian Elimination. Solving systems of nonlinear equations using the Newton-Raphson method.

First order ordinary differential equations (ODEs). Analytical solution by separation of variables and by the integrating factor.

Laplace transforms. Transforms and inverse transforms of functions. Transforms of derivatives. Application to solution of ordinary differential equations.

Numerical solution of ODEs and systems of ODEs using Euler and Runge-Kutta Methods.

#### Teaching and learning methods

This course will consist of lectures (2 hours) and enquiry-based learning sessions (1 hour). Resources with be available electronically on Blackboard and/or the course webpage.

#### Learning outcomes

 Category of outcome Students will be able to: Knowledge and understanding Recall definitions and facts relevant to syllabus topics.Carry our routine calculations using the syllabus topics. Intellectual skills Use the methods mentioned in the syllabus topics in order to carry out quantitative problem-solving. Practical skills Implement numerical methods computationally e.g. in MATLAB. Transferable skills and personal qualities Appreciate the use of techniques in a Chemical Engineering context and in relation to syllabus.Develop problem-solving skills.Develop independent critical thinking.

#### Knowledge and understanding

Recall definitions and facts relevant to syllabus topics.

Carry our routine calculations using the syllabus topics.

#### Intellectual skills

Use the methods mentioned in the syllabus topics in order to carry out quantitative problem-solving.

#### Practical skills

Implement numerical methods computationally e.g. in MATLAB.

#### Transferable skills and personal qualities

Appreciate the use of techniques in a Chemical Engineering context and in relation to syllabus.

Develop problem-solving skills.

Develop independent critical thinking.

#### Assessment Further Information

 Assessment task Length Weighting within unit CourseworkExamination N/A1.5 hours 10%90%

Stroud KA, and Booth DJ Engineering Mathematics, 5th Edition, Palgrave, 2001. ISBN: 0333919394. Joule Library 510.2462 STR.

Chapra SC, and Canale RP Numerical methods for engineering, 7th Edition, McGraw-Hill, 2006. ISBN: 0073101567. Main Library 518 C74.

Alfio Quarteroni, Fausto Saleri and Paola Gervasio, Scientific Computing with MATLAB and Octave, 4th Edition, Springer, 2010. ISBN: 9783642453663. Main Library 518.0285 Q3.

HELM : Helping Engineers Learn Mathematics : http://www.maths.manchester.ac.uk/study/undergraduate/information-for-current-students/service-teaching/resources/

#### Study hours

• Lectures - 20 hours
• Tutorials - 10 hours
• Independent study hours - 70 hours

#### Teaching staff

William Lionheart - Unit coordinator

Michael Crabb - Unit coordinator