Real Numbers: Rational and real numbers, absolute value and metric structure on the real numbers, induction, infimum and supremum.
Limits of Sequences: Sequences, definition of convergence, epsilon terminology, uniqueness, algebra of limits, comparison principles, standard limits, subsequences and non-existence of limits, convergence to infinity.
Completeness Properties: Cantor's Intersection Theorem, limit points, Bolzano-Weierstrass theorem, Cauchy sequences.
Continuity of Functions: Functions and basic definitions, limits of functions, continuity and epsilon terminology, sequential continuity, Intermediate Value Theorem.
Differentiation: Definition of the derivative, product rule, quotient rule and chain rule, derivatives and local properties, Mean Value Theorem, L'Hospital's Rule.
Taylor Approximation: Taylor's Theorem, remainder term, Taylor series, standard examples, limits using Taylor series.
Contact hours: 42
Private study: 108
Total: 150
Assessment: Best of 6 out of 8 short exercise-based assessments. Each individual assessment is equally weighted and requires on average 3 hours to complete. (40%)
Examination: 2 hours (60%)
Reassessment methods:
Like-for-like
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.
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 knowledge of the underlying concepts and principles associated with continuity and differentiability of real functions;
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts of limits of sequences and continuity and differentiability of real functions, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material;
3 apply the underlying concepts and principles associated with continuity and differentiability in several well-defined contexts, showing an ability to evaluate the appropriateness of different approaches to solving problems in this area.
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