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
|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.
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.
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.
Course Delivery Information
|Academic year 2022/23, Not available to visiting students (SS1)
|Learning and Teaching activities (Further Info)
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
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 20%, Examination: 80%.
Students repeating the course will be assessed as 100% exam only.
Students must pass exam and course overall.
||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.
||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.
- Present clear written solutions to problems involving one of more area of the syllabus.
|Students will require a copy of the course textbook. This is "Mathematics for the Natural Sciences 1" compiled by Antony Maciocia ISBN:9781800063549. This special edition is available only from Blackwell's bookshop at South Bridge, Edinburgh, or electronically.|
|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
|Course secretary||Mrs Frances Reid
Tel: (0131 6)50 4883