Module manager: Dr P A Sleigh
Email: P.A.Sleigh@leeds.ac.uk
Taught: Semesters 1 & 2 (Sep to Jun) View Timetable
Year running 2014/15
| CIVE1620 | Engineering Mathematics I |
This module is not approved as an Elective
To enable students to:
(i) understand the principles of general basic mathematical techniques of relevance to Civil Engineers;
(ii) appreciate the physical situations where these mathematical techniques are useful;
(iii) develop confidence in their mathematical abilities so that when this mathematics arises in the solution of an engineering problem they are able to understand (rather than merely accept) the results;
(iv) develop sufficient mathematical competence to cope with the compulsory content of a Civil Engineering degree;
(v) understand, calculate and interpret common statistical techniques likely to arise in a Civil Engineering context;
(vi) understand what is meant by numerically defined functions and apply numerical difference formulae;
(vii) numerically solve both nonlinear functions and first order differential equations that often arise in Civil engineering analysis;
(viii) recognise the limitations and accuracies of numerical solution techniques.
Vector Algebra: General introduction; scalars and vectors; direction cosines; modulus of a vector; unit vectors; Addition of vectors; parallelogram and polygon rule; basic rules; Scalar products; definition in component and geometrical form; basic rules; angle between two vectors; perpendicularity of vectors; work done by a force; force components; Vector products; definition in component and geometrical form; basic rules; moment of forces; areas of triangles and parallelograms; parallel vectors; Vector treatment of lines; representations in vector and Cartesian form; intersection of lines.
Series: Taylor polynomials; Taylor's theorem; expansion of functions; Maclaurin's expansion of functions; use of known series to give expansion of more complex functions; Approximations.
Limits: Sequences; Series: the limit of a series; convergence/divergence; the ratio test for convergence; power series; The limit of a function.
Partial Differentiation: Functions of more than one independent variables; First partial derivatives; The chain rule for first partial derivatives; Second partial derivatives; Small errors.
Summary statistics: these form an essential building block to the module and the module covers measures of central tendency spread etc that are likely to occur in an engineering context (mean, mode, standard deviation, quartiles etc)
Probability distributions: the basic rules of probability, the use and characteristics of the main probability distributions with illustrations (normal distribution, Poisson, binomial, t and f).
Hypothesis testing: for examination of significant differences between samples of data and also between the samples and an apriority belief of its population characteristics (null and alternative hypothesis, 1-tailed and 2-tailed tests, test statistics, significance levels.)
Basic regression modelling: basic principles of simple regression modelling including interpretation of diagnostic statistics.
Numerically defined functions: solution techniques, difference formulae, interpolation functions.
Taylor's series and truncation error.
Numerical differentiation: Euler's method, Higher order and Runge-Kutter methods.
Partial differential equations: Laplace equation and its solution.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Example Class | 20 | 1 | 20 |
| Consultation | 10 | 1 | 10 |
| Lecture | 44 | 1 | 44 |
| Private study hours | 126 | ||
| Total Contact hours | 74 | ||
| Total hours (100hr per 10 credits) | 200 | ||
Coursework and related reading 25hours, Problem sheets and related study 25hours, Computer based questions/study 20 hours, Other directed reading/study 30 hours, Revision 36 hours
The four problem are spread evenly throughout the module will serve as a close monitor of student learning - both for teachers and for learners.
| Assessment type | Notes | % of formal assessment |
|---|---|---|
| In-course Assessment | Problem Activities | 6 |
| In-course Assessment | Numerical Methods Coursework | 10 |
| In-course Assessment | Statistics Coursework | 24 |
| Total percentage (Assessment Coursework) | 40 | |
Internal resit as above. External resit 20% statistics coursework
| Exam type | Exam duration | % of formal assessment |
|---|---|---|
| Standard exam (closed essays, MCQs etc) | 3.0 Hrs 0 Mins | 60 |
| Total percentage (Assessment Exams) | 60 | |
External Resit 76% University exam 24% statistics coursework
The reading list is available from the Library website
Last updated: 06/01/2015
Errors, omissions, failed links etc should be notified to the Catalogue Team