# Foundation Mathematics 1 - MA361

Location Term Level Credits (ECTS) Current Convenor 2019-20
Canterbury Autumn
View Timetable
3 15 (7.5) DR N Sibilla

None

None

2019-20

## Overview

Functions: Functions, inverse functions and composite functions. Domain and range.

Elementary functions including the exponential function, the logarithm and natural logarithm functions and ax for positive real numbers a. Basic introduction to limits and continuity of a function, without epsilon-delta proofs.

The derivative: The derivative as the gradient of the tangent to the graph; interpretation of the derivative as a rate of change. The formal definition of the derivative and the calculation of simple examples from first principles. Elementary properties of the derivative, including the product rule, quotient rule and the chain rule; differentiation of inverse functions; calculating derivatives of familiar functions, including trigonometric, exponential and logarithmic functions. Applications of the derivative, including optimisation, gradients, tangents and normal. Parametric and implicit differentiation of simple functions. Taylor series.

Graphs: Curve sketching including maxima, minima, stationary points, points of inflection, vertical and horizontal asymptotes and simple transformations on graphs of functions. Additional material may include parametric curves and use of Maple to plot functions.

44 hours

## Method of assessment

80% examination, 20% coursework

Core Maths for Advanced Level, L Bostock and S Chandler, Nelson Thornes Ltd, 2013.
Calculus of One Variable, K.E.Hirst, Springer-Verlag (2006) (available through SpringerLink)

See the library reading list for this module (Canterbury)

## Learning outcomes

The intended subject specific learning outcomes.
On successfully completing the module students will be able to:
1 demonstrate understanding of the basic body of knowledge associated with functions of a single variable;
2 demonstrate the capability to solve problems in accordance with the basic theories and concepts in the following areas, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material: functions, differentiation of functions of a single variable and elementary curve sketching;
3 apply the basic techniques associated with single variable calculus in several well-defined contexts;
4 demonstrate a mathematical proficiency suitable for stage 1 entry.

The intended generic learning outcomes.
On successfully completing the module students will be able to:
Demonstrate an increased ability to:
1 manage their own learning and make use of appropriate resources;
2 understand logical arguments, identifying the assumptions made and the conclusions drawn;
3 communicate straightforward arguments and conclusions reasonably accurately and clearly;
4 manage their time and use their organisational skills to plan and implement efficient and effective modes of working;
5 solve problems relating to qualitative and quantitative information.
6 demonstrate an increased level of skill in numeracy and computation.

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