Mathematics

ECM1702 - Calculus and Geometry (2015)

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MODULE TITLECalculus and Geometry CREDIT VALUE15
MODULE CODEECM1702 MODULE CONVENERMs Aileen MacGregor (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
Number of Students Taking Module (anticipated) 280
DESCRIPTION - summary of the module content

By taking this module, you will develop knowledge and skills in two and three dimensional analytic geometry and differential calculus. As a result, you will be able to quickly and accurately perform calculus on simple functions using a variety of standard techniques.
 

The module will introduce you to MAPLE, a symbolic manipulation and programming language used to investigate the properties of a function. You will also learn how to accurately sketch the graphs of functions. The module gives an informal treatment of theorems from analysis.


It will also teach you how to reason using abstract ideas, and how to formulate and solve problems and communicate reasoning and solutions effectively in writing. As with the other modules, it will develop your self management and time-management skills and broaden your use of learning resources, including the use of IT.

AIMS - intentions of the module

This module aims to develop your knowledge and skills in calculus and geometry. It is about developing methods and skills for calculus-related manipulation of the mathematical objects that form the basis of much of an undergraduate course in mathematics. Furthermore, it aims to introduce some formal definitions and statements of theorems from analysis, but with only limited formal proofs.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

 

Module Specific Skills and Knowledge:
1 demonstrate knowledge of basic two and three dimensional analytic geometry and differential calculus;
2 show understanding of basic concepts concerning functions, sequences, series and limits;
3 perform accurate calculus manipulations using a variety of standard techniques;
4 sketch the graphs of a variety of functions of one variable.
Discipline Specific Skills and Knowledge:
5 demonstrate a basic knowledge of functions, sequences, series, limits and differential calculus necessary for progression to successful further studies in the mathematical sciences;
Personal and Key Transferable/ Employment Skills and  Knowledge:
6 reason using abstract ideas, formulate and solve problems and communicate reasoning and solutions effectively in writing;
7 use learning resources approrpriately;
8 exhibit self management and time management skills.

SYLLABUS PLAN - summary of the structure and academic content of the module

- introduction to sets and inequalities, intervals; 
- introductory guidance for self-study of the MAPLE package;
- two and three dimensional analytic geometry as loci;
- coordinate forms of equations for lines, circles and planes
- normals and tangents;
- formulae for parabola, ellipse, hyperbola, planes, lines, spheres, cones;
- functions: dependent and independent variables;
- injections, surjections and bijections, image and preimage;
- graphs of real functions;
- even, odd functions, sums, differences, products, quotients, composition;
- inverse functions;
- trigonometric and hyperbolic functions;
- sequences and series: finite and infinite sequences;
- geometric and arithmetic progressions;
- definition of a limit of a sequence;
- partial sums and series;
- comparison and ratio tests;
- absolute convergence;
- continuity of functions: definition of a limit, limits from right and left, manipulation and calculation of limits;
- finite limits as the variable tends to infinity, infinite limits;
- continuity;
- statement of intermediate value theorem;
- differentiation: definitions, properties and applications of differentiation;
- first principles calculations;
- rules for differentiation;
- implicit differentiation;
- linearisation of functions;
- higher order derivatives;
- Leibniz's rule;
- logarithmic differentiation;
- introduction to integration;
- applications of differentiation: maxima and minima of functions;
- L'Hopital's rule;
- rolle and mean value theorems;
- Taylor and Maclaurin series with remainder;
- applications in geometry and curve sketching: tangents, normals, asymptotes, turning points. 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 49.00 Guided Independent Study 101.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning and teaching activities 33 Lectures
Scheduled learning and teaching activities 5 Problem class
Scheduled learning and teaching activities 11 Tutorials
Guided independent study 101 Lecture and assessment preparation, wider reading

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Fortnightly exercise 5 x 3 hours All Annotated scripts with oral feedback from tutor
Mid-term test 40 minutes All Peer-to-peer marked
       
       
       

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 0 Written Exams 100 Practical Exams
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam - Closed book 100 2 hours All Annotated scripts
         
         
         
         

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period
       
       

 

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.


If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading: Any A-level on mathematics and further mathematics

 

ELE: http://vle.exeter.ac.uk

 

 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Finney R.L., Maurice D., Weir M and Giordano F.R. Thomas' calculus based on the original work by George B. Thomas, Jr. 10th or later Addison-Wesley 2003 000-0-321-11636-4 [Library]
Set Tan, T Soo Calculus Early Transcendentals International edition Brooks Cole/Cengage learning 2010 978-1439045992 [Library]
Set Tan, Soo T Calculus International edition Brooks/Cole Cengage Learning 2010 978-0495832294 [Library]
Extended Stewart J. Calculus 5th Brooks/Cole 2003 000-0-534-27408-0 [Library]
Extended McGregor C., Nimmo J. & Stothers W. Fundamentals of University Mathematics 2nd Horwood, Chichester 2000 000-1-898-56310-1 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) 4 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Friday 09 January 2015
KEY WORDS SEARCH Calculus; series; limits; convergence; divergence.