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 2020-21 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

(LO1) Use Taylor series to obtain local approximations to functions

(LO2) Obtain partial derivatives and use them in several applications such as, error analysis, stationary points change of variables.

(LO3) 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.

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
Class Test open book and remote  around 60-90 minutes    20       
Homework 3 Standard UoL penalty applies for late submission. Assessment Schedule (When) :Second semester  equivalent to 2-5 si    30       
Homework 2 Standard UoL penalty applies for late submission. Assessment Schedule (When) :Second semester  equivalent to 2-5 si    25       
Homework 1 Standard UoL penalty applies for late submission. Assessment Schedule (When) :Second semester  equivalent to 2-5 si    25