Functions: Definition of modulus function, solving basic equations and inequalities involving modulus functions, interval notation, function notation, domain and range, one-to-one and inverse functions, composite functions, odd and even functions.
Limits: Basic introduction to limits of a function, without epsilon-delta proofs; calculation of limits in simple cases involving indeterminate forms, including factoring, simple algebraic manipulation, and limits of rational functions; continuity of a function and asymptotes.
Differential Calculus: 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, differentiation of elementary functions, elementary properties of the derivative, including the product rule, quotient rule and the chain rule, using differentiation to find and classify stationary points, parametric and implicit differentiation of simple functions.
Applications of Differentiation: examples including finding tangents and normals to curves and optimisation problems.
Contact hours: 44
Private study: 156
Total: 200
Assessment 1 Exercises, requiring on average between 10 and 15 hours to complete 20%
Assessment 2 Exercises, requiring on average between 10 and 15 hours to complete 20%
Examination 2 hours 60%
The University is committed to ensuring that core reading materials are in accessible electronic format in line with the Kent Inclusive Practices.
The most up to date reading list for each module can be found on the university's reading list pages.
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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