Calculus

Описание мероприятия

Описание программы

This unit develops a student’s proficiency in working with the mathematical methods of calculus, and it investigates some applications to problems in economics, management and related areas. The unit also develops the student’s understanding of the theoretical concepts behind these methods.

The objectives specifically include:

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

Assessment

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

Учебный план:

Basics: Revision of basic algebra; powers; sets; functions (including trigonometric functions); graphs; factorisation; inverse and composite functions; exponential and logarithm functions; conic sections; trigonometric identities.

Differentiation: The meaning of the derivative; standard derivatives; Product rule, quotient rule and chain rule; Tangent lines; Taylor series; using derivatives for approximations; marginals; elasticities.

One-variable optimisation: First-order conditions; first and second-order tests for nature of a critical point; convexity and concavity; profit maximisation; the effects of taxation; curve sketching.

Integration: Indefinite integrals; Definite integrals; Standard integrals; Substitution method (including trigonometric substitutions); Integration by parts; Partial fractions; consumer and producer surplus.

Functions of several variables: Contours, principal sections and partial derivatives; chain rule, homogeneous functions, gradient vectors, directional derivatives, tangent planes, Taylor series.

Multivariate optimisation: unconstrained optimisation; convex and concave functions; constrained optimisation; applications of unconstrained and constrained optimisation; the meaning of Lagrange multipliers.

Differential equations: Separable equations; first-order linear equations; homogeneous equations; exact equations; second-order equations with constant coefficients; systems of first-order equations; some applications.

Результат обучения:

At the end of the course and having completed the essential reading and activities students should be able to:

• use the concepts, terminology, methods and conventions covered in the unit to solve mathematical problems in this subject,
• solve unseen mathematical problems involving understanding of these concepts and application of these methods
• see how calculus can be used to solve problems in economics and related subjects
• demonstrate knowledge and understanding of the underlying principles of calculus.

Требования к поступающим:

This course may not be taken with:

1. MT105a Mathematics 1
2. MT105b Mathematics 2