33190 Mathematical Modelling for Science
Warning: The information on this page is indicative. The subject outline for a
particular semester, location and mode of offering is the authoritative source
of all information about the subject for that offering. Required texts, recommended texts and references in particular are likely to change. Students will be provided with a subject outline once they enrol in the subject.
Subject handbook information prior to 2015 is available in the Archives.
Credit points: 6 cp
Result type: Grade and marks
Anti-requisite(s): 33130 Mathematical Modelling 1 AND 35101 Introduction to Linear Dynamical Systems AND 37131 Introduction to Linear Dynamical Systems
Recommended studies: two units of HSC Mathematics
Description
Mathematical modelling is essential in all branches of science. This subject develops the knowledge and skills necessary for problem-solving and mathematical modelling at an introductory level. Topics covered include: vectors and geometry; complex numbers; calculus and its relationship to science; differentiation and integration of functions; inverse, trigonometric and hyperbolic functions; the solution of differential equations with applications to exponential growth and decay and oscillating systems; Taylor series; and an introduction to linear algebra. The computer algebra system Mathematica is used for symbolic, graphical and numerical computations.
Subject objectives
Upon successful completion of this subject students should be able to:
| 1. | Understand the relevance of mathematics to science. |
|---|---|
| 2. | Understand the way in which mathematics can supply useful tools and resources to model real world problems. |
| 3. | Use mathematical terminology and concepts. |
| 4. | Use formal and informal language to demonstrate understanding of these concepts. |
| 5. | Demonstrate a high level of skill in the computational techniques of the subject. |
| 6. | Demonstrate understanding of the theoretical results that justify the use of these techniques. |
| 7. | Communicate the above knowledge clearly, logically and critically. |
| 8. | Be able to work independently to further their knowledge of mathematical modelling |
| 9. | Be able to apply the subject matter covered in lectures, tutorials and assignments to previously unseen problems. |
| 10. | Be aware of the historical context of mathematical development. |
| 11. | Use the computer algebra system Mathematica to perform calculations and explore mathematical ideas relevant to the subject content. |
This subject also contributes specifically to the development of following course intended learning outcomes:
- An understanding of the nature, practice and application of the chosen science discipline. (1.0)
- Encompasses problem solving, critical thinking and analysis attributes and an understanding of the scientific method knowledge acquisition. (2.0)
- The ability to acquire, develop, employ and integrate a range of technical, practical and professional skills, in appropriate and ethical ways within a professional context, autonomously and collaboratively and across a range of disciplinary and professional areas, e.g. time management skills, personal organisation skills, teamwork skills, computing skills, laboratory skills, data handling, quantitative and graphical literacy skills. (3.0)
- An understanding of the different forms of communication - writing, reading, speaking, listening -, including visual and graphical, within science and beyond and the ability to apply these appropriately and effectively for different audiences. (6.0)
Contribution to the development of graduate attributes
This subject contributes to the development of the following graduate attributes:
Graduate Attribute 1 - Disciplinary knowledge and its appropriate application
A broad introduction to the most important and widely used concepts in mathematics is given.
Graduate Attribute 2 - An Enquiry-oriented approach
Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems
Graduate Attribute 3 - Professional skills and their appropriate application
Throughout the subject mathematics is presented as a tool, which students are invited to use in the solution to real-world problems
Graduate Attribute 6 - Communication skills
Students will use formal and informal language to communicate knowledge clearly, logically and crtiically.
Teaching and learning strategies
Lectures: three hours/week
Tutorials: one hour per week
Content
Topics to be presented throughout semester will include:
- Vectors and scalars, and their relation to geometry.
- Complex numbers.
- Functions and derivatives, and their relationship to measurement and the interpretation of physical results.
- Differentiability.
- Differential equations arising from physical problems.
- Solution by series.
- Oscillatory motion.
- Trigonometric functions and inverse trigonometric functions. Integrals and logarithms, inverse functions.
- Methods of integration.
- Introduction to matrices and linear algebra.
The computer algebra system Mathematica will be used in the subject as an aid to computation, graph plotting and visualization.
Assessment
Assessment task 1: Final examination
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an enquiry-oriented approach 3. professional skills and their appropriate application 6. communication skills Final exam involves Problem posing and solving – ability to identify, assess and formulate problems relevant to one’s academic discipline and apply appropriate approaches and methods of problem solving. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 1, 10, 2, 3, 4, 5, 6, 7, 8 and 9 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0, 3.0 and 6.0 |
| Weight: | 37.5% |
| Criteria: | Students will be assessed on:
|
Assessment task 2: Mastery Tests
| Intent: | This assessment task contributes to the development of the following graduate attributes: 1. disciplinary knowledge and its appropriate application 2. an enquiry-oriented approach 3. professional skills and their appropriate application Mastery Tests targets Problem posing and solving – ability to identify, assess and formulate problems relevant to one’s academic discipline and apply appropriate approaches and methods of problem solving, as well as Graduate Attributes listed under “Personal Development” such as Awareness of the importance of self-motivation and taking responsibility of one’s own decisions. |
|---|---|
| Objective(s): | This assessment task addresses subject learning objective(s): 10, 11, 2, 3, 5, 8 and 9 This assessment task contributes to the development of course intended learning outcome(s): 1.0, 2.0 and 3.0 |
| Weight: | 62.5% |
| Length: | 45 minutes |
| Criteria: | Students will be assessed on:
See 'Further Information' for more detail on requirements. |
Minimum requirements
Students must receive a minimum of 50% of the overall mark to pass the subject.
Students should note that in order to sit the final exam they must achieve a minimum of 80% for each and every Mastery test.
Required texts
J. Stewart: Calculus - concepts and contexts, Metric International 4th Edition, Cengage
References
- G. H. Smith and G. J. McLelland (2003). On the shoulders of giants: A course in single variable calculus. Sydney, UNSW Press.
- C. H. Edwards and D. E. Penney, Calculus with Analytic Geometry, 3rd or 4th Editions. Prentice Hall.
- S.L. Salas and E. Hille, Calculus: one and several variables, 7th edition, John Wiley and Sons, 1995
- J. Callahan and K. Hoffman, Calculus in context, W. H. Freeman and Company, 1995
