Mathematics 10  Functions with One Variable.
20092010

REA1042F
 5 ECTS
Expected learning outcomes
The students shall
 be able to show skill in algebraic manipulations, transforming of function expressions, differentiation and integration.
 be able to show a good understanding of central concepts in the subjects of the course. The students shall be able to apply functions, differentiation, integration and differential equations on simple pravtical problems (modelling).
 have knowlede on plotting of function graphs, numerical solving of equations and numerical integration with calculator and computer programmes (Maple)
Topic(s)
Functions:
Explicitly and implicitly defined functions, inverse functions, limits, continuity. Parametrised curves, vector valued functions, position, velocity and acceleration. Trigonometric and inverse trigonometric functions, exponential and logaritmic functions.
Differentiation:
Definition and differentiation rules, differential and linear approximation, implicit differentiation. Modelling.
The integral:
Riemann sums, integration by substitution and by parts, partial fraction, arc length, area, volumes, mass centre, momentum.
Differential equations:
Linear and separable ordinary first order differential equations.
Basic use of the Computer Algebra Programme Maple.
Teaching Methods
Other
Teaching Methods (additional text)
Maple
Form(s) of Assessment
Written exam, 4 hours
Grading Scale
Alphabetical Scale, A(best) – F (fail)
External/internal examiner
Internal examiner
Resit examination
Ordinary resit examination.
Coursework Requirements
5 coursework requirements
Teaching Materials
Edwards & Penney: Calculus (7e) (Pearson), ISBN 9780136158400