# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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# 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 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.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1b (MATH08075) OR Mathematics for the Natural Sciences 1b (MATH08073) AND Accelerated Algebra and Calculus for Direct Entry (MATH08062) Other requirements Higher Mathematics or A-level at Grade A, or equivalent
 Pre-requisites None High Demand Course? Yes
 Academic year 2016/17, Available to all students (SV1) Quota:  None 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
 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.) ISBN 9781473707504 Blackwells only : book and web access £58.99
 Graduate Attributes and Skills Not entered Keywords CAP
 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
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