Undergraduate Course: Calculus and its Applications (MATH08058)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
||Availability||Available to all students
|Summary||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.
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.
Information for Visiting Students
Course Delivery Information
|Academic year 2014/15, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 40,
Seminar/Tutorial Hours 10,
Supervised Practical/Workshop/Studio Hours 10,
Summative Assessment Hours 3,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
|Additional Information (Learning and Teaching)
Students must pass exam and course overall.
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination 80%
||Hours & Minutes
|Main Exam Diet S2 (April/May)||(MATH08058) Calculus and its Applications||3:00|
|Resit Exam Diet (August)||(MATH08058) Calculus and its Applications||3:00|
| 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.
|Students are expected to have a personal copy of |
'Essential Calculus: Early Transcendentals', International Metric Edition, 2nd Edition, by James Stewart. (This book is also relevant for Y2 courses.)
Blackwells only : book and web access £58.99
|Graduate Attributes and Skills
|Course organiser||Dr Johan Martens
Tel: (0131 6)51 7759
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050
© Copyright 2014 The University of Edinburgh - 12 January 2015 4:21 am