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MATH20320

Subject:
Mathematics
College:
Science
School:
Mathematics & Statistics
Level:
2 (Intermediate)
Credits:
5
Module Coordinator:
Dr Richard Smith
Trimester:
Spring
Mode of Delivery:
On Campus
Internship Module:
No

Curricular information is subject to change.

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.

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
Specified Learning Activities

30

Autonomous Student Learning

22

Lectures

36

Tutorial

12

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 Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): Two hour exam in exam centre End of trimester
Duration:
2 hr(s)
Standard conversion grade scale 40% No
70
No
Participation in Learning Activities: Solving home works and attending the tutorials Week 2, Week 3, Week 4, Week 5, Week 6, Week 7, Week 8, Week 9, Week 10, Week 11, Week 12 Standard conversion grade scale 40% No
30
No

Carry forward of passed components
No

Resit In Terminal Exam
Autumn Yes - 2 Hour
Feedback Strategy/Strategies

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

How will my Feedback be Delivered?

Not yet recorded.

Name Role
Mr Kevin Allen Tutor
Timetabling information is displayed only for guidance purposes, relates to the current Academic Year only and is subject to change.
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Thurs 13:00 - 13:50
Spring Lecture Offering 1 Week(s) - 20, 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Tues 09:00 - 10:50
Spring Tutorial Offering 1 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 13:00 - 13:50
Spring Tutorial Offering 2 Week(s) - 21, 22, 23, 24, 25, 26, 29, 30, 31, 32, 33 Wed 12:00 - 12:50