MATH20320 Quantitative Methods in Business

Academic Year 2020/2021

This module covers a range of mathematical techniques that are used in business and economic theory. It builds on and uses techniques from MATH10030 (Maths for Business). Topics may include: (1) integration, with applications such as consumer and producer surplus, and continuous revenue streams; (2) first-order difference equations and their use in certain 'lagged' micro and macroeconomic models; (3) first and second-order differential equations; (4) Time permitting, other topics such as Power series, Taylor series and Series Solutions for Second Order Linear Equations.

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Curricular information is subject to change

Learning Outcomes:

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.

Indicative Module Content:

• 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.

Student Effort Hours: 
Student Effort Type Hours
Lectures

36

Tutorial

12

Specified Learning Activities

30

Autonomous Student Learning

22

Total

100

Approaches to Teaching and Learning:
Lectures, tutorials, enquiry and problem-based 
Requirements, Exclusions and Recommendations
Learning Recommendations:

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.


Module Requisites and Incompatibles
Incompatibles:
ACM10100 - Differential & Diff Equations


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Continuous Assessment: Varies Varies over the Trimester n/a Standard conversion grade scale 40% No

30

Examination: Two hour online examination 2 hour End of Trimester Exam Yes Standard conversion grade scale 40% No

70


Carry forward of passed components
No
 
Resit In Terminal Exam
Autumn Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

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

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