This module contains the first half of MA4102 and of MA4103. Purpose: To introduce mathematical concepts and techniques, with applications in economics, finance and in business in general. To develop an appropriate foundation in mathematics for students from diverse mathematical backgrounds.

Review of algebra: fractions and rational expressions, linear equations and inequalities. Economic models: cost and revenue, supply and demand curves. Simultaneous linear and quadratic equations (solved algebraically and graphically); applications to market equilibrium and break-even analysis. Linear programming: plotting linear inequalities in two variables, feasible region, constrained optimisation; solving linear optimisation problems using the graphical method; applications to maximising profit/revenue, minimising cost etc. Mathematics of finance: geometric sequences and series; applications to compound interest, present value, valuation of annuities and mortgages. Matrices: definitions, matrix algebra: addition, subtraction, scalar multiplication, matrix product; determinants (2X2); matrix inversion; representing and solving linear systems using matrices. Functions and their graphs: definition of a function (including function of several variables), combining functions, inverse functions; graphs of linear, quadratic, cubic polynomials; roots and factors; negative powers and rational powers. Exponents and logarithmic functions: laws of exponents (indices) and logarithms; the number e; the exponential function and natural log function; graphs of exponential and natural log; applications to population growth and depreciation of capital. Differential calculus: concept of continuity; small change, secant line, slope, tangent line, definition of derivative; differentiation from first principles (quadratics only); derivative as instantaneous rate of change: application to marginal cost and marginal revenue; power rule, derivative of negative powers, fractional powers, exponentials and logs; higher derivatives; the Product, Quotient and Chain Rules. Curve sketching using calculus and business applications: increasing and decreasing functions, turning points: local maxima and minima, the Second Derivative Test, concavity, points of inflection.

On successful completion of this module a student should be able to: 1. Solve simple equations and inequalities involving linear, quadratic, log and exponential functions and sketch the graphs of such functions. 2. Find equilibrium price and quantity in a supply and demand problem. 3. Plot the feasible region for a system of linear inequalities; determine the optimal point in a linear constrained optimisation. 4. Calculate any unknown variable in a compound interest formula; calculate the monthly/yearly (re)payments in an annuity or mortgage. 5. Add, subtract, multiply and invert 2X2 matrices and use matrices to solve 2X2 linear systems of equations. 6. Combine and invert simple functions; graph linear and quadratic functions; factorise simple polynomial expressions. 7. Simplify expressions using the laws of exponents and logarithms; recognise the graphs of exponential and natural log functions; solve simple problems in Malthusian population growth modelling and depreciation. 8. Differentiate a quadratic function from first principles; find the tangent line to a simple polynomial curve; calculate marginal cost and revenue and other rates of change; differentiate polynomials, negative powers, fractional powers, exponentials and logs; find higher derivatives; use the Product, Quotient and Chain Rules to differentiate a variety of functions. 9. Determine intervals where function is increasing/decreasing (cubics and quartics); find and classify turning points of a function of one variable; plot a graph using properties derived from first and second derivatives. 10. Apply differential calculus to: (i) cost/revenue optimisation problems, (ii) to finding the point of diminishing returns and (iii) to problems of labour and productivity, including marginal product of labour, average product of labour, point of diminishing return to labour and maximum productivity.

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Normal lecture and tutorial mode of delivery. Examples used should be appropriate and relevant to the field of business, as far as practicable. A mid-term should be used, along with an end-of-term written examination. Graduate attributes: After successful completion of this module students should have demonstrable and applicable mathematical skills that they can directly apply in economic analysis, finance and other business areas. They should be able to fully engage in discussions and debates with business professionals and media personnel on topics that require basic mathematical knowledge.