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
Code MATH198
Coordinator Prof SM Rees
Mathematical Sciences
Maryrees@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 4 FHEQ Whole Session 22.5

Aims

To provide a basic level of mathematicsincluding calculus and extend the student''s knowledge to include an elementaryintroduction to complex variables and functions of two variables.


Learning Outcomes

• differentiate using the chain, product and quotient rules;

 

 sketch the graphs of elementary and rational functions;

integrate using list integrals, substitution and integration by parts with applications to simple geometrical problems;

 understand the basic properties of three dimensional vectors and apply them to elementary geometrical problems;

 understand the algebra of complex numbers in Cartesian and polar forms and their application to multiplication, division and roots.

 solve elementary first and second order differential equations with and without initial conditions and make simple mechanical applications;

 evaluate simple Laplace transforms and their inverses using tables with application to initial value problems;

 understand the graphical representation of functions of two variables;

find partial derivatives and use to locate and classify the stationary points of a function of two variables


Syllabus

Topic 1  Differential Calculus and Applications   
Preliminary revision (exponential number and function ex; natural logarithms and function ln x; hyperbolic functions). Definition of derivative, derivative as gradient; differentiation rules. Graph sketching (finding and classifying stationary points); revision of quadratics, cubics; sketching y = (xn – a)m; rational functions (vertical asymptotes; asymptotic behaviour at infinity, sketching functions involving  exponentials.

Topic 2  Vector Algebra
Revision of basic properties. Consolidation of scalar and vector products with further applications to calculation of angles between vectors and to simple areas. 3-dim. geometry of  lines  including line vectors, position vectors, parallel lines, angle of intersection of two lines, co-linearity, vector equat ion of the line through two given points. 

Topic 3  Integration and Applications
 Definition of the indefinite integral, relation to differentiation. Integration by parts and by change of variable; standard integrals; other simple methods. Definite integral and applications to simple averages, areas, centroids, centres of gravity and volumes of revolution.

Topic 4  Complex numbers and Differential Equations
Algebra of complex numbers in Cartesian form; transition to polar and exponential form; applications to multiplication, powers and roots. Simple first order differential equations (variable separable, and linear equations) with applications to exponential growth/decay. Second order linear differential equations with constant coefficients with simple forcing functions, applications to simple harmonic motion and, e.g ,. damped vibrations.

Topic 5  Laplace Transform and Applications
Definition and basic properties; tables of standard transforms and their use; transform of the Heaviside function. Applications of solving differential equations with constant coefficients (second-order and simultaneous first-order equations).

Topic 6  Functions of Two Variables
Representation by contour plots (level curves) and by surfaces; partial derivatives; finding and classifying stationary points.

Revision sessions


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):

*MATH199 is an alternative prerequisite for MATH299 

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

MATH299* 

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

Programme:HJ41 Year:1 Programme:J510 Year:1 Programme:J200 Year:1 Programme:HJ35 Year:1 Programme:BF92 Year:1 Programme:F2N2 Year:1 Programme:H652 Year:1 Programme:H650 Year:1 Programme:H200 Year:1 Programme:H220 Year:1 Programme:H221 Year:1 Programme:HK23 Year:1 Programme:HJ26 Year:1 Programme:H400 Year:1 Programme:H401 Year:1 Programme:H402 Year:1 Programme:H421 Year:1 Programme:H425 Year:1 Programme:H300 Year:1 Programme:H301 Year:1 Programme:H310 Year:1 Programme:H3N2 Year:1 Programme:H3NF Year:1 Programme:HH37 Year:1 Programme:HH73 Year:1 Programme:H100 Year:1 Programme:H101 Year:1 Programme:H102 Year:1 Programme:H1N2 Year:1 Programme:H1NF Year:1 Programme:H1NG Year:1 Programme:J500 Year:1 Programme:F200 Year:1

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
Written Exam  3 hours  Second semester  80  Yes  Standard UoL penalty applies  Written Exam Notes (applying to all assessments) Class tests 10% and homework 10% there will be 2 class tests (1 per semester) Written exam. Full marks will be awarded for correctly answering all questions.  
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework    First and Second semester  20  None: exemption approved November 2007  Standard UoL penalty applies  Coursework