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 I
Code MATH101
Coordinator Prof T Konstantopoulos
Mathematical Sciences
T.Konstantopoulos@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2019-20 Level 4 FHEQ First Semester 15

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.

Learning Outcomes

(LO1) Differentiate and integrate a wide range of functions;

(LO2) Sketch graphs and solve problems involving optimisation and mensuration

(LO3) Understand the notions of sequence and series and apply a range of tests to determine if a series is convergent

(S1) Numeracy

Syllabus
 

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.


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
Final exam There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment.  2.5 hours    70       
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Coursework component Standard UoL penalty applies for late submission. This is not an anonymous assessment.      30