THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2012/2013
- ARCHIVE as at 1 September 2012 for reference only
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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Calculus and its Applications (MATH08058)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) Credits20
Home subject areaMathematics Other subject areaNone
Course website None Taught in Gaelic?No
Course descriptionCalculus is the most fundamental tool in mathematics and its applications. This course covers functions, limits, differentiation and applications, integration and applications, infinite and Taylor series, and a first introduction to differential equations.

The course also develops calculational facility that is essential for more advanced mathematical study.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Mathematics for Science and Engineering 1b (MATH08061) OR Practical Calculus (MATH08001) OR Mathematical Methods 1 (MATH08029) OR Mathematics for Informatics 1a (MATH08046) OR Mathematics for Informatics 1b (MINF08001)
Other requirements Higher Mathematics or A-level at Grade A, or equivalent
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Delivery period: 2012/13 Semester 2, Available to all students (SV1) Learn enabled:  Yes Quota:  None
Location Activity Description Weeks Monday Tuesday Wednesday Thursday Friday
CentralLectureAppleton Tower, Th 51-11 12:10 - 13:00
CentralLectureAppleton Tower, Th 51-11 12:10 - 13:00
CentralLectureAppleton Tower, Th 51-11 12:10 - 13:00
CentralLectureAppleton Tower, Th 41-11 12:10 - 13:00
First Class First class information not currently available
Additional information Tutorials: Tuesdays Appleton Tower Teaching Studio
9:00, 10:00, 11:10 or 12:10
Exam Information
Exam Diet Paper Name Hours:Minutes
Main Exam Diet S2 (April/May)Calculus and its Applications (MATH08058)3:00
Resit Exam Diet (August)Calculus and its Applications (MATH08058)3:00
Summary of Intended Learning Outcomes
1. Understanding of the ideas of limits and continuity and an ability to calculate with them and apply them.
2. Improved facility in algebraic manipulation.
3. Fluency in differentiation.
4. Fluency in integration using standard methods, including the ability to find an appropriate method for a given integral.
5. Facility in applying Calculus to problems including curve-sketching, areas and volumes.
6. Understanding the ideas of infinite series including Taylor approximations.
7. Understanding the ideas of differential equations and facility in solving simple standard examples.
Assessment Information
Up to 15% Continuous Assessment, the remainder examination.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus This syllabus is for guidance purposes only :

* Lectures 1-8: Functions (types/composition), limits (including precise definition) and continuity, chapters 1-2.
* Lectures 9-16: Differentiation (chain rule/implicit/differentials) and applications (max/min/mean value theorem/Newton's method), chapters 3-4.
* Lectures 17-22: Integration (fundamental theorem of calculus/substitution rule) and applications (Areas/volumes), chapters 5-6.
* Lectures 23-27: Inverse functions, definition of logarithm/exponential, and L'Hopital's rule, chapter 7.
* Lectures 28-31: Further integration (by parts/rational functions/approximate), and further applications (arc length/surface of revolution), chapters 8-9.
* Lectures 32-35: Differential equations (modelling/direction fields/separable/linear first order), chapter 10.
* Lectures 36-42: Curves, polar coordinates, Taylor series, some material of chapters 11-12.
Transferable skills Not entered
Reading list Students are expected to have a personal copy of 'Calculus', International Metric Edition 6e by James Stewart. (This book is also relevant for Y2 courses.)
Study Abroad Not entered
Study Pattern Not entered
KeywordsCAP
Contacts
Course organiserProf Michael Singer
Tel: (0131 6)50 5062
Email: M.A.Singer@ed.ac.uk
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk
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