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 Dr JM Woolf
Mathematical Sciences
Jonathan.Woolf@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 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

 differentiate and integrate a wide range of functions;


sketch graphs and solve problems involving optimisation and mensuration

understand the notions of sequence and series and apply a range of tests to determine if a series is convergent


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.
< div xmlns="http://www.w3.org/1999/xhtml">
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.
Explanation of Reading List:

Calculus: a complete course (7th edition), Adams and Essex. Pearson, 2010.


Available in the library, or you can buy your own copy from Blackwells or from a well-known on-line book supplier. This text book also covers the material in MATH102 (second semester). If you purchase your own copy you will have access to MyMathLab, an online facility which complements the book, provides practice online tests with instant feedback and so on. It''s certainly worth having a lo ok at this if you do purchase the book; you may find it a helpful learning tool.


Thomas'' Calculus (12th edition),  Weir, Hass and Giordano. Pearson, 2010.


Similar to the first, but slightly less highly recommended as its treatment is less rigorous. Available in the library, in Blackwells or other booksellers. This also comes with access to MyMathLab if you purchase your own copy.


Yet another introduction to analysis, Bryant. Cambridge University Press, 1990.


A much smaller and more rigorous book than the above two. It does not cover all the material in the module, but what it covers it does so in more detail. If you wan t to become a mathematician rather than simply use mathematics, then it''s well worth looking at this. Available in the library, or from booksellers. 



Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

A Level Mathematics.  

Co-requisite modules:

 

Modules for which this module is a pre-requisite:

MATH102; MATH122; MATH201; MATH224; MATH225; MATH227; MATH228; MATH241; MATH243; MATH244; MATH247; MATH248; MATH261; MATH262; MATH263; MATH264; MATH265; MATH266; MATH267; MATH268; MATH270; MATH271; MATH272; MATH291; MATH302; MATH322; MATH323; MATH324; MATH325; MATH326; MATH331; MATH332; MATH334; MATH340; MATH342; MATH343; MATH344; MATH349; MATH350; MATH351; MATH360; MATH361; MATH362; MATH363; MATH366; MATH371; MATH374; MATH375; MATH376; MATH410; MATH421; MATH423; MATH424; MATH425; MATH426; MATH440; MATH442; MATH443; MATH444; MATH446; MATH448; MATH449; MATH455; MATH480; MATH481; MATH482; MATH483; MATH273; MATH373; MATH456; 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:GN11 Year:1 Programme:FGH1 Year:1 Programme:FG31 Year:1 Programme:GL11 Year:1 Programme:GR11 Year:1 Programme:GV15 Year:1 Programme:GG14 Year:1 Programme:F344 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  First semester  80  Yes  Standard UoL penalty applies  Final exam Notes (applying to all assessments) Coursework: comprises weekly written home-works, assessed both for their mathematical content and written quality, and submitted revision notes for the class test. Work will be done in small groups of 3-5 students. Participation in tutorials will also be assessed. Final exam rubric: Full marks can be obtained by fully answering all questions in Section A and THREE questions from Section B. Section A carries 55% of the total marks. Only the best THREE solutions to Section B will be counted. 
CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
Coursework    First semester  20  No reassessment opportunity  Standard UoL penalty applies  Coursework component There is no reassessment opportunity, Exemption granted.