### 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.

### 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.    15
Homework 1 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.    15
Homework 3 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.    20
Homework 4 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.    15
Homework 5 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.    15
Homework 6 online in Moebius There is a resit opportunity. Standard UoL penalty applies for late submission.    20