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 in calculus for students of Chemistry and related disciplines and follows on from MATH08072 Mathematics for the Natural Sciences 1a.
This course is restricted to students for whom it is a compulsory part of their Degree Programme.
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.
Fundamental Theorem of Calculus. Substitution. Area, arc-length, volume, mean values, rms values and other summation applications of integration. Integration by parts. Limits and 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, 1 tutorial hour and 1 workshop, each week. The workshop will be delivered by the School of Chemistry to showcase applications of the Mathematical topics covered.
Basic Mathematical skills will be developed using on-line quizzes and end of week e-assessments. Mathematical writing skills will be tested in three written assignments. Further more applied problems will be assessed in two Chemistry based assessments.
Course Delivery Information
|Academic year 2017/18, 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)
||On-line assessments: 5%, Written Mathematics Assignments: 5%, Written Chemistry based Mathematics assignments: 10%
||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.
||Hours & Minutes
|Main Exam Diet S2 (April/May)||Mathematics for the Natural Sciences 1b (MATH08073) ||3:00|
|Resit Exam Diet (August)||Mathematics for the Natural Sciences 1b (MATH08073)||3:00|
On completion of this course, the student will be able to:
- Students will be able to solve a variety of problems involving limits of sequences, series and functions.
- Students will be able to compute derivatives, partial derivatives, higher derivatives and integrals of a variety of functions.
- Students will be able to use calculus to compute extrema and arc length of functions, areas and volumes of surfaces of revolution, mean values and Taylor approximations of functions.
- Students will be able to 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 currently "Mathematics for Science and Engineering 1" by Glyn James. This special edition is available only from Blackwell's bookshop at South Bridge, Edinburgh. Students are advised not to commit to a purchase until this is confirmed by the Course Team and advice on Editions, etc is given.|
|Graduate Attributes and Skills
||Students will gain key skills in calculus appropriate to degrees in the Natural Sciences.
||Only available to students who are also taking CHEM08017 Chemistry 1B
|Keywords||MNS1b,Sequences,series,power series,differentiation,integration,differential equations,differ
|Course organiser||Dr Adri Olde-Daalhuis
Tel: (0131 6)50 5992
|Course secretary||Miss Corinna Bremer
Tel: (0131 6)50 5059