MATH20320 Quantitative Methods in Business

On completion of this module, the student will be able to: (1) apply various techniques of integration to integrate functions; (2) solve first-order linear difference equations; (3) solve first and second-order linear differential equations; (4) apply the above techniques to solve relevant business and economic applications.

• Integration

- Indefinite Integration, specifically of functions involving polynomial, exponential and
natural logarithm functions.
- Techniques of Integration: integration by substitution, integration by parts, partial fractions method.
- Definite Integral: definition, Fundamental Theorem of Calculus and properties.
- Applications to Business: total revenue & marginal revenue functions, total cost and marginal cost functions, production & marginal production functions. Consumer & Producer Surplus. Continuous revenue stream. Area.


• Geometric Series & Applications

- Definition and main properties.
- Applications to Business: Loan Payments, Annuity, Continuous Revenue Stream, Perpetual Revenue Stream.


• Difference Equations

- 1st Order Linear Difference Equations, homogenous and non-homogenous cases.
- Stability of solutions.
- Applications to Business: Harrod-Domar growth model.


• Differential Equations

- 1st order Ordinary Differential Equations: separation of variables, integrating factor.
- Applications to Business: continuously compounded interest and deposit/withdraw.
- 2nd Order Linear Differential Equations: homogenous and non-homogenous cases.

• Series and power series (Time Permitting)

- Definitions of infinite series, convergence, divergence, absolute convergence.
- Power Series.
- Taylor Series Expansion.
- Series solutions of 2nd order Differential Equations.

MATH10030 - Maths for Business is a pre-requisite to take this module.

Students taking this module should be able to:
- graph polynomial functions, the exponential and natural logarithm functions and analyse their graphs.
- use and manipulate polynomials.
- Explain the concept of the derivative and differentiate products, quotients and compositions of the functions listed above.
The knowledge of complex numbers is also recommended.

• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment

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