Mathematics

ECM1705 - Advanced Calculus (2015)

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MODULE TITLEAdvanced Calculus CREDIT VALUE15
MODULE CODEECM1705 MODULE CONVENERProf Andrew Gilbert (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
Number of Students Taking Module (anticipated) 278
DESCRIPTION - summary of the module content


The advanced calculus topics in this module form the core knowledge base for much of applied mathematics.  Partial differentiation is vital for accurately modelling the real world, and you will use it for calculus problems in more than one dimension. Equally, you will find that most applied maths and engineering problems involve solving differential equations.
 

Calculus is also a fundamental tool for pure mathematicians; the topics covered in the course are fundamental to future studies in differential geometry.
 

Prerequisite module: ECM1702 or equivalent

 

AIMS - intentions of the module

This module aims to introduce you to advanced methods of calculus, building on the knowledge you acquired in the prerequisite module ECM1702 Calculus and Geometry. It develops further the key ideas and skills that will form necessary background for later study in all branches of the mathematical sciences. The main emphasis of the module will be on practical methods and problem solving; however, all results will be stated formally and each sub-topic will be reviewed from a mathematically rigorous standpoint.

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 apply advanced techniques for integration;
2 solve a number of classes of ordinary differential equations;
3 demonstrate an understanding of the fundamentals of calculus of several variables;
4 show knowledge of geometric applications of various calculus techniques;
5 appreciate that calculus techniques are underpinned by formal rigour.
Discipline Specific Skills and Knowledge:
6 exhibit a clear grasp of fundamental mathematical concepts, manipulations and results in calculus and of their importance within branches of the mathematical sciences;
7 reveal sufficient knowledge of those techniques to enable successful progression to further mathematical studies.
Personal and Key Transferable/ Employment Skills and  Knowledge:
8 reason using abstract ideas;
9 formulate and solve problems and communicate reasoning and solutions effectively in writing;
10 use learning resources appropriately;
11 display self management and time management skills.

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

- integration;

- integration techniques;

- ordinary differential equations;

- equations with constant coefficients;

- partial differentiation;

- calculus tools for optimisation;

- multiple integrals;

- curvilinear coordinate systems and area/volume elements.

 

 

 

 

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 Seminars
Scheduled learning and teaching activities 11 Tutorials
Guided independent study 101 Guided independent study

 

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 1 sheet of problems 1-11 Some questions marked by tutors.  Feedback given on all questions during tutorials
       
       
       
       

 

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 100 2 hours 1-11 Available on request
         
         
         
         

 

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

ELE – http://vle.exeter.ac.uk


 

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set McGregor C., Nimmo J. & Stothers W. Fundamentals of University Mathematics 2nd Horwood, Chichester 2000 000-1-898-56310-1 [Library]
Set Stewart J. Calculus 5th Brooks/Cole 2003 000-0-534-27408-0 [Library]
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]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM1702
CO-REQUISITE MODULES
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; integration; differential equations; Lagrange multipliers; partial differential equations.