This module is not currently running in 2024 to 2025.
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. Additional material may include L'Hopital’s Rule and 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.
Contact hours: 44
Private study: 106
Total: 150
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)
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.
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