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 CALCULUS II
Code MATH102
Coordinator Dr O Selsil
Mathematical Sciences
Oselsil@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 4 FHEQ Second Semester 15

Aims

·      To discuss local behaviour of functions using Taylor’s theorem.

·      To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.


Learning Outcomes

  use Taylor series to obtain local approximations to functions; 

obtain partial derivaties and use them in several applications such as, error analysis, stationary points change of variables

evaluate double integrals using Cartesian and Polar Co-ordinates


Syllabus

Power series and radius of convergence. Local behaviour of functions.  Taylor’s theorem.

Function of several variables (usually two), graphical depictions.  Gradient and directional derivatives.  Chain rule and change of variable.  Error analysis.  Stationary points, including constrained extrema.

Multiple Integrals. Evaluation of double integrals as repeated integrals for both Cartesian and plane polar co-ordinates.


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):

MATH101; MATH103  

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

MATH201; MATH224; MATH225; MATH227; MATH228; MATH241; MATH243; MATH244; MATH247; MATH248; MATH261; MATH263; MATH266; MATH267; MATH268; MATH270; MATH271; MATH272; MATH323; MATH324; MATH325; MATH326; MATH331; MATH332; MATH344; MATH349; MATH351; MATH421; MATH424; MATH426; MATH440; MATH446; MATH455; MATH456; MATH262; MATH265; MATH291; MATH302; MATH334; MATH340; MATH361; MATH363; MATH371; MATH374; MATH375; MATH376; MATH423; MATH425; MATH442; MATH443; MATH444; MATH448; MATH449; MATH273; MATH373; MATH410; MATH364 

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

Programme:G100 Year:1 Programme:G101 Year:1 Programme:G110 Year:1 Programme:G1N3 Year:1 Programme:NG31 Year:1 Programme:G1R9 Year:1 Programme:GG13 Year:1 Programme:GL11 Year:1 Programme:GN11 Year:1 Programme:GR11 Year:1 Programme:F344 Year:1 Programme:FG31 Year:1 Programme:FGH1 Year:1 Programme:GG14 Year:1 Programme:GV15 Year:1 Programme:G1F7 Year:1

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

Programme:BCG0 Year:1 Programme:L000 Year:1 Programme:Y001 Year:1

Assessment

EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Unseen Written Exam  2.5 hours  Second semester  80  Yes    Assessment 2 Notes (applying to all assessments) 10% key skills, 10% group coursework, 80% final exam with rubric: All answers to Section A and the best THREE answers to Section B will be taken into account.  
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework    Second semester  20  No reassessment opportunity  Standard UoL penalty applies  Assessment 1 There is no reassessment opportunity,