Business Mathematics - I

Straight lines, Linear functions, Applications: demand, supply, cost, revenue, Elasticity of demand, Supply and income, Budget and cost constraints, Least square method and line of best fit (two variables only), Least square method for time series analysis.Lab. Work: Introducing Excel, Excel for linear functions.

Simultaneous linear equations, Equilibrium and break-even points, Consumer surplus, Producer surplus and Total surplus, National income and the IS- LM model Lab. Work: Excel for simultaneous linear equations

Graphs of Quadratic functions, Quadratic equations, Applications to economics and business;

Cubic and other polynomial functions, Exponential functions, Logarithmic functions, Hyperbolic functions of the form a/(bx + c); Bisection method, Newton-Raphson method for solving nonlinear equations.

Arithmetic and geometric sequences and series; Simple interest, compound interest and annual percentage rates, Depreciation, Net present value and internal rate of return, Annuities, debt repayments, sinking funds; Relationship between interest rates and the price of bonds. Lab. Work: Excel for financial mathematics.

Idea of limit, Limit of algebraic functions at a point and at infinity (basic concept only),Slope of a curve and differentiation, Rules of differentiation ( power rule, sum rule, product rule, quotient rule, and chain rule), Differentiation by first principle ( algebraic, logarithmic and exponential functions), Differentiation and marginal analysis (marginal cost, marginal revenue and marginal profit), Increasing and decreasing function, Stationary point, Point of inflection, Differentiation of implicit and parametric functions, Economic applications ofderivatives for maximum and minimum points, Higher order derivatives ( up to 3rd order),Curvature, Elasticity of demand and the derivatives. Lab. Work: Excel for applications of derivatives.