Undergraduate Course: Calculus and its Applications (MATH08058)
Course Outline
School  School of Mathematics 
College  College of Science and Engineering 
Course type  Standard 
Availability  Available to all students 
Credit level (Normal year taken)  SCQF Level 8 (Year 1 Undergraduate) 
Credits  20 
Home subject area  Mathematics 
Other subject area  None 
Course website 
None 
Taught in Gaelic?  No 
Course description  Calculus 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. 
Information for Visiting Students
Prerequisites  None 
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 
Central  Lecture  Appleton Tower, Th 5  111  12:10  13:00      Central  Lecture  Appleton Tower, Th 5  111    12:10  13:00    Central  Lecture  Appleton Tower, Th 5  111     12:10  13:00   Central  Lecture  Appleton Tower, Th 4  111      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 curvesketching, 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 18: Functions (types/composition), limits (including precise definition) and continuity, chapters 12.
* Lectures 916: Differentiation (chain rule/implicit/differentials) and applications (max/min/mean value theorem/Newton's method), chapters 34.
* Lectures 1722: Integration (fundamental theorem of calculus/substitution rule) and applications (Areas/volumes), chapters 56.
* Lectures 2327: Inverse functions, definition of logarithm/exponential, and L'Hopital's rule, chapter 7.
* Lectures 2831: Further integration (by parts/rational functions/approximate), and further applications (arc length/surface of revolution), chapters 89.
* Lectures 3235: Differential equations (modelling/direction fields/separable/linear first order), chapter 10.
* Lectures 3642: Curves, polar coordinates, Taylor series, some material of chapters 1112. 
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 
Keywords  CAP 
Contacts
Course organiser  Prof Michael Singer
Tel: (0131 6)50 5062
Email: M.A.Singer@ed.ac.uk 
Course secretary  Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk 

