May not be taken with MT105A Mathematics 1.
May not be taken with MT105B Mathematics 2.
This course develops basic mathematical methods and concepts of calculus and will include their applications to problems in economics, management and related areas.
Revision of basic algebra; powers; sets; functions (including trigonometric functions); graphs; factorisation; inverse and composite functions; exponential and logarithm functions; conic sections; trigonometric identities.
The meaning of the derivative; standard derivatives; Product rule, quotient rule and chain rule; Tangent lines; Taylor series; using derivatives for approximations; marginals; elasticities.
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.
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.
Unconstrained optimisation; convex and concave functions; constrained optimisation; applications of unconstrained and constrained optimisation; the meaning of Lagrange multipliers.
Separable equations; first-order linear equations; homogeneous equations; exact equations; second-order equations with constant coefficients; systems of first-order equations; some applications.