# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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DRPS : Course Catalogue : School of Mathematics : Mathematics

# Undergraduate Course: Mathematics for the Natural Sciences 1b (MATH08073)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 1 Undergraduate) Availability Not available to visiting students SCQF Credits 20 ECTS Credits 10 Summary The course is a first university level course for students interested in the natural sciences and is compulsory for some degree programmes in the School of Chemistry. The course follows on naturally from MATH08072 Mathematics for the Natural Sciences 1a. Course description This course will cover topics in a first course on calculus for students in the Natural Sciences and includes the following syllabus: AP's, GP's, limits, power series, radius of convergence. Basic differentiation: rate of change, simple derivatives, rules of differentiation, maxima/minima. Derivatives of powers, polynomials, rational functions, circular functions. Chain rule. Differentiation of exponential and related functions, differentiation of inverse functions. Parametric and implicit differentiation, higher derivatives. Partial differentiation, directional derivatives, chain rule, total derivative, exact differentials. L'Hopital's rule. Taylor's Theorem and related results. Maclaurin series. Basic integration: anti-derivatives, definite and indefinite integrals, methods of substitution and integration by parts. Fundamental Theorem of Calculus. Area, arc-length, volume, mean values, rms values and other applications of integration. Improper integrals. Differential equations. General and particular solutions, boundary values. Separable differential equations. First order linear differential equations with constant coefficients. The course will consist of 3 lectures and 1 workshop each week. Basic mathematical skills will be developed using on-line quizzes and end of week e-assessments. Mathematical writing skills will be developed in five written assessments.
 Pre-requisites Co-requisites Prohibited Combinations Students MUST NOT also be taking Engineering Mathematics 1b (MATH08075) OR Calculus and its Applications (MATH08058) Other requirements None
 Academic year 2019/20, Not available to visiting students (SS1) Quota:  200 Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 33, Seminar/Tutorial Hours 11, Supervised Practical/Workshop/Studio Hours 5, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 144 ) Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 % Additional Information (Assessment) On-line assessments: 10%, Written Mathematics Assignments: 10% Examination: 80%. Students must pass exam and course overall. Students repeating the course will be assessed as 100% exam only. Feedback There will be five opportunities for feedback on written skills. Each lecture is accompanied by an on-line quiz which will provide instant feedback on basic skills. Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) 3:00 Resit Exam Diet (August) 3:00
 On completion of this course, the student will be able to: Solve a variety of problems involving limits of sequences, series and functions.Compute derivatives, partial derivatives, higher derivatives and integrals of a variety of functions.Use calculus to compute extrema and arc length of functions, areas and volumes of surfaces of revolution, mean values and Taylor approximations of functions.Solve separable first and second order ordinary differential equations with boundary or initial conditions and simple inhomogeneous terms.
 Students will require a copy of the course textbook. This is "Mathematics for the Natural Sciences 1" compiled by Antony Maciocia ISBN:9781787267725. This special edition is available only from Blackwell's bookshop at South Bridge, Edinburgh.
 Graduate Attributes and Skills Students will gain key skills in calculus appropriate to degrees in the Natural Sciences. Keywords MNS1b,Sequences,series,power series,differentiation,integration,differential equations
 Course organiser Dr David Quinn Tel: Email: D.Quinn@ed.ac.uk Course secretary Mrs Frances Reid Tel: (0131 6)50 4883 Email: f.c.reid@ed.ac.uk
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