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. |
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)
|
Other requirements |
Higher Mathematics or A-level at Grade A, or equivalent
|
| Additional Costs |
None |
Information for Visiting Students
| Pre-requisites |
None |
| Displayed in Visiting Students Prospectus? |
Yes |
Course Delivery Information
|
| Delivery period: 2011/12 Semester 2, Available to all students (SV1)
|
WebCT enabled: Yes |
Quota: None |
| Location |
Activity |
Description |
Weeks |
Monday |
Tuesday |
Wednesday |
Thursday |
Friday |
| No Classes have been defined for this Course |
| First Class |
First class information not currently available |
| Exam Information |
| Exam Diet |
Paper Name |
Hours:Minutes |
|
|
| Main Exam Diet S2 (April/May) | Calculus and its Applications (MATH08058) | 2:00 | | |
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&İs 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&İHopital&İs 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 |
| 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 |
|
copyright 2011 The University of Edinburgh -
1 September 2011 6:25 am
|
University Homepage