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DRPS : Course Catalogue : School of Mathematics : Mathematics

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

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 1 Undergraduate) AvailabilityNot available to visiting students
SCQF Credits20 ECTS Credits10
SummaryThe 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:

Sequences and series, 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.

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.
Entry Requirements (not applicable to Visiting Students)
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
Course Delivery Information
Academic year 2020/21, 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 50 %, Coursework 50 %, Practical Exam 0 %
Additional Information (Assessment) 50% of coursework: Students will complete interactive STACK workbooks and a STACK assessment each week. Students to gain mastery of fundamental skills.

50% of courses: Students will submit five pieces of written work. This will assess problem solving skills and presentation.
Feedback STACK questions (including practice) give feedback on submission. Written work will have written comments on return and solutions addressing common errors. Further feedback in workshop and peer discussions.
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May) 3:00
Resit Exam Diet (August)3:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Solve a variety of problems involving limits of sequences, series and functions.
  2. Compute derivatives, partial derivatives, higher derivatives and integrals of a variety of functions.
  3. Use calculus to compute extrema and arc length of functions, areas and volumes of surfaces of revolution, mean values and Taylor approximations of functions.
  4. Solve separable first and second order ordinary differential equations with boundary or initial conditions and simple inhomogeneous terms.
  5. Present clear written solutions to problems involving one of more area of the syllabus.
Reading List
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.
Additional Information
Graduate Attributes and Skills Students will gain key skills in calculus appropriate to degrees in the Natural Sciences.
KeywordsMNS1b,Sequences,series,power series,differentiation,integration,differential equations
Course organiserDr David Quinn
Course secretaryMrs Frances Reid
Tel: (0131 6)50 4883
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