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 Professor JA Gracey
Mathematical Sciences
Gracey@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2022-23 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

(LO1) A good knowledge of matrices and their use to solve systems of linear equations.

(LO2)  An understanding of how to find eigenvalues and eigenvectors.

(LO3) A good knowledge of multi-variable calculus.

(S1) Problem solving skills

(S2) Numeracy

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.

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

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

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

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
             
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Homework 2 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    15       
Homework 1 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    15       
Homework 3 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    20       
Homework 4 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    15       
Homework 5 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    15       
Homework 6 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.  0    20