This module introduces widely-used mathematical methods for functions of a single variable. The emphasis is on the practical use of these methods; key theorems are stated but not proved at this stage.
Basic notation for sets and number systems including complex numbers (a+ib representation only). Standard functions: trig functions, polynomials, rational functions, exponentials and logarithms.
Single variable calculus: Differentiation, including product and chain rules; Fundamental Theorem of Calculus (statement only), elementary integrals, change of variables, integration by parts, differentiation of integrals with variable limits.
Curve sketching: graphs of elementary functions, maxima, minima and points of inflection, asymptotes.
Algebra of matrices and vectors; addition, multiplication, transposes, inner-products.
Row reduced echelon form, solving linear systems (homogeneous and inhomogeneous).
Inverse of a matrix.
Contact hours: 44
Private study: 106
70% examination and 30% coursework.
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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 basic mathematical methods for functions of a single variable, and algebraic operations with matrices and vectors.
2 demonstrate the capability to make sound judgements in accordance with the basic theories and concepts for single-variable calculus, vectors, and matrices, whilst demonstrating a reasonable level of skill in calculation and manipulation of the material;
3 apply the underlying concepts and principles associated with basic single-variable calculus techniques and matrix operations 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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