Mathematics 1 (half course)

Описание мероприятия

Описание программы

This half course develops basic mathematical methods and will emphasise their applications to problems in economics, management and related areas.

The objectives specifically include:

• To enable students to acquire skills in the methods of calculus (including multivariate calculus) and linear algebra, as required for their use in economics-based subjects.
• To prepare students for further units in mathematics and/or related disciplines.

Assessment

This half course is assessed by a two-hour unseen written examination.

Учебный план:

Basics: Basic algebra; Sets, functions and graphs; Factorisation (including cubics); Inverse and composite functions; Exponential and logarithm functions; Trigonometrical functions.

Differentiation: The meaning of the derivative; Standard derivatives; Product rule, quotient rule and chain rule; Optimisation; Curve sketching; Economic applications of the derivative: marginals and profit maximisation.

Integration: Indefinite integrals; Definite integrals; Standard integrals; Substitution method; Integration by parts; Partial fractions; Economic applications of integration: determination of total cost fr om marginal cost, and cumulative changes.

Functions of several variables: Partial differentiation; Implicit partial differentiation; Critical points and their natures; Optimisation; Economic applications of optimisation; Constrained optimisation and the Lagrange multiplier method; The meaning of the Lagrange multiplier; Economic applications of constrained optimisation.

Matrices and linear equations: Vectors and matrices, and their algebra; Systems of linear equations and their expression in matrix form; Solving systems of linear equations using row operations (in the case wh ere there is a unique solution); Some economic/managerial applications of linear equations.

Sequences and series: Arithmetic and Geometric Progressions; Some Financial application of sequences and series.

Результат обучения:

At the end of this half course and having completed the essential reading and activities students should have:

• used the concepts, terminology, methods and conventions covered in the half course to solve mathematical problems in this subject.
• the ability to solve unseen mathematical problems involving understanding of these concepts and application of these methods
• seen how mathematical techniques can be used to solve problems in economics and related subjects

Требования к поступающим:

This half course may not be taken with MT1174 Calculus