MATH314 - Differential Equations and Mechanics

Year

Credit points

Campus offering

Prerequisites

MATH104 Differential and Integral Calculus

Incompatible

MATH310 and MATH218 

Teaching organisation

Unit rationale, description and aim

This unit uses the knowledge and understanding of calculus developed in earlier units to provide a strong introduction to differential equations and mechanics, two important area in classical Applied Mathematics. Differential equations provide a common way for modeling problems in calculus. In particular problems in Mechanics are often framed and solved using DEs. Mechanics represents one of the early successes in mathematical modeling using differential equations.

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

On successful completion of this unit, students should be able to:

LO1 - Use differential equations to model simple situations (GA4, GA5, GA8, GA9) 

LO2 - Apply basic techniques to solve DEs, including Laplace transforms and numerical methods (GA4, GA5, GA8, GA10) 

LO3 - Use power series to set up DE solutions in standard cases (GA4, GA5, GA8) 

LO4 - Solve problems in basic kinematics including vector variables (GA4, GA5, GA8) 

LO5 - Solve problems in simple dynamics, circular motion and simple harmonic motion (GA4, GA5, GA8, GA10) 

LO6 - Solve problems in statics, balancing force and torque (GA4, GA5, GA8, GA10). 

Graduate attributes

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA9 - demonstrate effective communication in oral and written English language and visual media 

GA10 - utilise information and communication and other relevant technologies effectively.

Content

Topics may include: 

1. Review of First and Second order differential equations 
2. Orthogonal curves 
3. Numerical solutions. 
4. Systems of differential equations and higher order DEs 
5. Laplace transforms in DE solution. 
6. Power Series Solutions 
7. Kinematics 
8. Projectile Motion 
9. Force and Momentum 
10. Work, Energy and Power 
11. Rotational Motion 
12. Simple Harmonic Motion 
13. Statics 

Learning and teaching strategy and rationale

There will be 4 hours of class time each week with a two-hour lecture and two hour tutorial. 

Assessment strategy and rationale

A range of assessment procedures will be used to meet the unit learning outcomes and develop graduate attributes consistent with University assessment requirements. Such procedures may include, but are not limited to: essays, reports, examinations, student presentations or case studies. 

Overview of assessments

Representative texts and references

Anton, H., Bivens I., & Davis, S. (2009). Calculus: Early transcendentals, 9th ed.).New York: John Wiley & Sons. 

Ayres, F. (1981). Schaum's outline of theory and problems of differential equations in SI metric units SI Edition, adapted by J.C. Ault. Singapore: McGraw-Hill. 

Brannan, J.R., & Boyce, W.E. (2011). Differential equations: An introduction to modern methods and applications 2nd ed.). Hoboken, NJ: John Wiley & Sons. 

Edwards, C.H., & Penney, D.E. (2007). Calculus and early trancendentals. Prentice-Hall Inc. 

Nelson, E.W., Best, C.L., & McLean, W.G. (1998). Engineering Mechanics Statics and Dynamics (Schaum Outline Series) New York: McGraw-Hill. 

Reif, F. (1995). Understanding basic mechanics. New York: Wiley. 

Taylor, J. (2005). Classical mechanics. Hemdon, VA: University Science Books. 

Zill, D. G. (2013). A first course in differential equations with modeling applications (10th ed.). Boston, MA: Brooks/Cole, Cengage Learning.