Module Details

The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title ENGINEERING MATHEMATICS II
Code MATH299
Coordinator Dr M Domijan
Mathematical Sciences
Mirela.Domijan@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2017-18 Level 5 FHEQ First Semester 7.5

Aims

To introduce some advanced Mathematics required by Engineers, Aerospace Engineers, Civil Engineers and Mechanical Engineers.

To develop the students ability to use the mathematics presented in the module in solving problems.


Learning Outcomes

A good knowledge of matrices and their use to solve systems of linear equations.

 An understanding of how to find eigenvalues and eigenvectors.

A good knowledge of multi-variable calculus.

Syllabus

Part 1: Matrices

Basic concepts (definition, shapes and sizes), addition, multiplication by scalars and transpose of a matrix

Matrix multiplication, systems of linear equations, Gauss elimination, elementary row operations, echelon form

Rank of a matrix, general properties of solutions of systems of linear equations, inverse of a matrix

Determinants, Cramer''s rule

Eigenvalues and eigenvectors

Part 2: Calculus of functions of several variables

Partial differentiation, differentials

Change of variables, chain rule, implicit differentiation

Taylor''s expansion, error estimates.

Constrained maxima and minima (Lagrange multipliers) and applications to optimal design

Scalar and vector fields; gradient, divergence and curl; tangent planes and directional derivative


Recommended Texts

Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

MATH198*; MATH199* *Either MATH198 or MATH199 is a prerequisite. 

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

MATH492 

Programme(s) (including Year of Study) to which this module is available on a required basis:

Programme:H100 Year:2 Programme:H101 Year:2 Programme:H200 Year:2 Programme:H202 Year:2 Programme:H220 Year:2 Programme:H300 Year:2 Programme:H301 Year:2 Programme:H3N2 Year:2 Programme:H3NF Year:2 Programme:H401 Year:2 Programme:H402 Year:2 Programme:H421 Year:2 Programme:H425 Year:2 Programme:HJ35 Year:2 Programme:HJ3M Year:2

Programme(s) (including Year of Study) to which this module is available on an optional basis:

 

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Unseen Written Exam  2 hours  First  90  Yes  Standard UoL penalty applies  Assessment 2 Notes (applying to all assessments) Assessment 1: Five problem sets, distributed on a fortnightly basis throughout semester. This work is not marked anonymously. Assessment 2: Full marks will be awarded for complete answers to all questions.  
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework  5 problem sheets, ap  First  10  No reassessment opportunity  Standard UoL penalty applies  Fortnightly problem sheets There is no reassessment opportunity, Exemption granted