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 I
2. Module Code MATH101
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 4 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Dr M Gorbahn Mathematical Sciences Martin.Gorbahn@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Mr AP Smithson School of Electrical Engineering, Electronics and Computer Science Alan.Smithson@liverpool.ac.uk
Dr JM Woolf Mathematical Sciences Jonathan.Woolf@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 36

   12

       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
 

1. To introduce the basic ideas of differential and integral calculus, to develop the basic skills required to work with them and to apply these skills to a range of problems.

2. To introduce some of the fundamental concepts and techniques of real analysis, including limits and continuity.

3. To introduce the notions of sequences and series and of their convergence.
 
28. Learning Outcomes
 

(LO1) Understand the key definitions that underpin real analysis and interpret these in terms of straightforward examples.
 

(LO2) Apply the methods of calculus and real analysis to solve previously unseen problems (of a similar style to those covered in the course).
 

(LO3) Understand in interpret proofs in the context of real analysis and apply the theorems developed in the course to straightforward examples.
 

(LO4) Independently construct proofs of previously unseen mathematical results in real analysis (of a similar style to those demonstrated in the course).
 

(LO5) Differentiate and integrate a wide range of functions;
 

(LO6) Sketch graphs and solve problems involving optimisation and mensuration
 

(LO7) Understand the notions of sequence and series and apply a range of tests to determine if a series is convergent
 

(S1) Numeracy
 
29. Teaching and Learning Strategies
 

Material is presented during lectures (3 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions.
 
30. Syllabus
   

Properties of subsets of the real numbers including their boundedness, supremum and infimum.

Algebraic and trigonometric functions.  
Absolute values and inequalities.  
Inverse functions. 
Sequences.
Limit of a sequence.
Continuity of functions (via sequences).
Derivative.
Differentiation of sums, products and quotients.  
Implicit differentiation.  
Critical points and extrema.
Optimisation.
L'Hôpital's Theorem.
Indefinite integrals, definite integrals and the Fundamental Theorem of Calculus.
The exponential and logarithm functions, hyperbolic functions.
Techniques of integration.
Series.
Convergence of a series.  
Tests for convergence.  
Alternating series and absolute convergence.

 
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
  Final Assessment on campus There is a resit opportunity. This is an anonymous assessment. One hour time on task 60 50
33. CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
  class test on campus This is an anonymous assessment. 40 25
  Homework Standard UoL penalty applies for late submission. This is not an anonymous assessment. 0 25