Undergraduate Course: Calculus and its Applications (MATH08058)
|School||School of Mathematics
||College||College of Science and Engineering
||Availability||Available to all students
|Credit level (Normal year taken)||SCQF Level 8 (Year 1 Undergraduate)
|Home subject area||Mathematics
||Other subject area||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
|Displayed in Visiting Students Prospectus?||Yes
Course Delivery Information
|Delivery period: 2013/14 Semester 2, Available to all students (SV1)
||Learn enabled: Yes
|Course Start Date
|Breakdown of 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
Students must pass exam and course overall.
|Breakdown of Assessment Methods (Further Info)
|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.
|See 'Breakdown of Assessment Methods' and 'Additional Notes' above.|
||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.
||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.)
|Course organiser||Dr Arend Bayer
Tel: (0131 6)50 8572
|Course secretary||Ms Louise Durie
Tel: (0131 6)50 5050
© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am