Module Specification

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.
1. Module Title CALCULUS II
2. Module Code MATH102
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester Second Semester
7. CATS Level Level 4 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr O Selsil Mathematical Sciences Oselsil@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Professor A Movchan Mathematical Sciences Abm@liverpool.ac.uk
Dr SA Fairfax Mathematical Sciences Simon.Fairfax@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours     12

    36

48
17.

Private Study

102
18.

TOTAL HOURS

150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

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

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

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

27. Aims
 

To discuss local behaviour of functions using Taylor’s theorem.
To introduce multivariable calculus including partial differentiation, gradient, extremum values and double integrals.

 
28. 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.

 
29. Teaching and Learning Strategies
 

Material is provided in advance of classes for students to study asynchronously. The contact hours consist of one 2-hour active learning session and one 2-hour supported study/drop-in session.

 
30. 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.

 
31. Recommended Texts
  Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
 

Assessment

32. EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  on campus closed book 90 40
33. CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Class Test 1 on campus 60 30
  Class Test 2 on campus 60 30