Undergraduate Course: Calculus and its Applications (MATH08058)
Course Outline
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 
SCQF Credits  20 
ECTS Credits  10 
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. 
Course description 
This syllabus is for guidance purposes only :
1. Functions, limits, continuity.
2. Derivatives  differentiation rules, implicit differentiation.
3. Inverse functions, exponential and logarithm, inverse trigonometric functions.
4. Applications of differentiation  extreme values, mean value theorem, curve sketching, optimization, antiderivatives.
5. Integrals  definite integral, fundamental theorem of calculus, substitution rule.
6. Techniques of integration : integration by parts, trigonomic substitution, partial factions, improper integrals.
7. Applications of integration : areas and volumes, arc length, applications to physics and engineering, differential equations.
8. Series: sequences, series, convergence tests, power series, Taylor and Maclaurin series, applications of Taylor polynomials.
9. Additional topics, including parametric curves and polar coordinates, will be discussed during workshops.

Information for Visiting Students
Prerequisites  None 
High Demand Course? 
Yes 
Course Delivery Information

Academic year 2015/16, Available to all students (SV1)

Quota: 483 
Course Start 
Semester 2 
Timetable 
Timetable 
Learning and Teaching activities (Further Info) 
Total Hours:
200
(
Lecture Hours 33,
Seminar/Tutorial Hours 17,
Supervised Practical/Workshop/Studio Hours 5,
Online Activities 5,
Summative Assessment Hours 3,
Revision Session Hours 4,
Programme Level Learning and Teaching Hours 4,
Directed Learning and Independent Learning Hours
129 )

Additional Information (Learning and Teaching) 
Students must pass exam and course overall.

Assessment (Further Info) 
Written Exam
80 %,
Coursework
20 %,
Practical Exam
0 %

Additional Information (Assessment) 
Coursework 20%, Examination 80% 
Feedback 
Not entered 
Exam Information 
Exam Diet 
Paper Name 
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  
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.

Reading List
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.)
ISBN 9781473707504
Blackwells only : book and web access £58.99 
Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  CAP 
Contacts
Course organiser  Dr Johan Martens
Tel: (0131 6)51 7759
Email: Johan.Martens@ed.ac.uk 
Course secretary  Ms Louise Durie
Tel: (0131 6)50 5050
Email: L.Durie@ed.ac.uk 

