## MECH1520 Engineering Mathematics

### 20 creditsClass Size: 350

Module manager: Dr Daya Pandey
Email: D.Pandey@leeds.ac.uk

Taught: Semesters 1 & 2 (Sep to Jun) View Timetable

Year running 2023/24

This module is not approved as a discovery module

### Objectives

- To equip students with the knowledge and understanding of mathematical concepts, notation and techniques relevant to mechanical engineering.
- To develop skills and confidence in mathematical modelling and problem solving.
- To support students in understanding mathematical aspects of other modules.

Learning outcomes
On successful completion of this module, students should be able to:

1. Use vectors to represent three-dimensional space, including points, lines and planes and find intersections among these.
2. Differentiate and integrate vectors in the context of dynamics problems, and understand scalar and vector products and their use in mechanics and dynamics.
3. Integrate and differentiate functions using a range of techniques and relate derivatives and integrals to engineering applications such as rates of change, maxima and minima, areas, volumes, averages, flow rates, work, centres of mass, etc.
4. Sketch (freehand) basic and composite functions, recognising limiting behaviours and discontinuities.
5. Create mathematical models of engineering systems described by first order ordinary differential equations, and solve the equations analytically and via Eulerâ€™s method.
6. Differentiate and integrate functions of more than one variable.
7. Understand the formation of matrices, their associated algebra, their use in the solution of simultaneous equations and in graphical transformations, and the concepts of eigenvalues and eigenvectors.
8. Understand, manipulate and plot complex numbers and functions in various forms, find complex solutions of equations, and appreciate the links between exponential, trigonometric and hyperbolic functions.
9. Present data effectively using a variety of techniques.
10. Calculate important statistical measures of central tendency and dispersion.
11. Understand the concept of correlation and regression, calculate the regression coefficient and determine regression lines via the least squares technique.
12. Understand the basic concepts of probability, including conditional probability and independence.

Upon successful completion of this module the following UK-SPEC learning outcome descriptors are satisfied:

A comprehensive knowledge and understanding of the scientific principles and methodology necessary to underpin their education in their engineering discipline, and an understanding and know-how of the scientific principles of related disciplines, to enable appreciation of the scientific and engineering context, and to support their understanding of relevant historical, current and future developments and technologies (SM1m)
Knowledge and understanding of mathematical and statistical methods necessary to underpin their education in their engineering discipline and to enable them to apply a range of mathematical and statistical methods, tools and notations proficiently and critically in the analysis and solution of engineering problems (SM2m)
A comprehensive knowledge and understanding of mathematical and computational models relevant to the engineering discipline, and an appreciation of their limitations (SM5m)
Ability to identify, classify and describe the performance of systems and components through the use of analytical methods and modelling techniques (EA2)
Apply their skills in problem solving, communication, information retrieval, working with others and the effective use of general IT facilities (G1)

Skills outcomes
- Mathematical modelling and problem solving skills
- Ability to apply mathematics to represent, analyse and design engineering systems.

### Syllabus

Definitions and use of vectors in 3D space; vector algebra; the scalar and vector products and their uses.
Functions and graphs; limits of functions.
Techniques for differentiation: product rule; quotient rule; chain rule; implicit differentiation; logarithmic differentiation; differentiating parametric equations; differentiating vectors in Cartesian and polar coordinate systems.
Techniques for integration: substitution; integration by parts; partial fractions; integration of vectors; numerical integration.
Engineering applications of integration and differentiation.
Functions of more than one variable: partial differentiation; multiple integrals.
First order differential equations; mathematical modelling and problem solving.
Vector equations of lines and planes.
Matrix algebra; transformation matrices; eigenvalues and eigenvectors.
Complex numbers; hyperbolic functions.
Statistics, regression and elementary probability.

### Teaching methods

 Delivery type Number Length hours Student hours Class tests, exams and assessment 1 2.00 2.00 Class tests, exams and assessment 2 1.00 2.00 Lecture 44 1.00 44.00 Practical 20 1.00 20.00 Tutorial 4 1.00 4.00 Private study hours 128.00 Total Contact hours 72.00 Total hours (100hr per 10 credits) 200.00

### Private study

Reviewing lecture notes, solving example sheets, preparing for tutorials and class tests. Revising for final exam. Students are to spend 1 hour preparation for each lecture; 2 hours preparation for each tutorial; 10 hours preparation for each class test; a further 56 hours for exam preparation.

### Opportunities for Formative Feedback

An online discussion board will be monitored during specified times each week.
Minerva/TopHat quiz eafter each topic.

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment Class test in semester 1 20.00 In-course Assessment Class test in semester 2 20.00 Total percentage (Assessment Coursework) 40.00

Coursework marks carried forward and 60% resit exam OR 100% resit exam

Exams
 Exam type Exam duration % of formal assessment Unseen exam 2 hr 60.00 Total percentage (Assessment Exams) 60.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated