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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Calculus and its Applications (MATH08058)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryCalculus 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.
Entry Requirements (not applicable to Visiting Students)
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
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2019/20, 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 Applications3:00
Resit Exam Diet (August)(MATH08058) Calculus and its Applications3:00
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 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.
Reading List
Students will require a copy of the course textbook. This is currently "Essential Calculus: Early Transcendentals, International Metric Edition" by James Stewart. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Nikola Popovic
Tel: (0131 6)51 5731
Course secretaryMs Louise Durie
Tel: (0131 6)50 5050
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